Method of passive determination of target data

0001The invention relates to a method for the passive determination of target data by directionally selective reception of sound waves of the type mentioned in the preamble of claim 1.

0002In order to determine the position, speed and course of a target, e.g. a surface ship, submarine or torpedo, as target data without a betrayal of a carrier vehicle, e.g. a surface ship or submarine, sound waves of the target noise are received with a sonar reception system and the bearing angle at Target measured. From these bearing angles, a position of the target is estimated together with the carrier vehicle's own positions and an associated estimated bearing angle is calculated. The difference between the measured and the estimated bearing angle is iteratively reduced until an error limit is undershot. The underlying estimated position is recognized as the target position.

0003Starting from a starting position of the target, which is, for example, selected arbitrarily as the starting position on a first direction finding beam or is known from other sensors on board, positions are calculated from estimated xy components for the target and estimated bearing angles are determined therefrom. The carrier vehicle travels for the bearing angle measurements at a constant course for a predetermined period of time and travels a distance called the self-lay. After a change of course, the target is further aimed by this self-lay. The respectively measured bearing angles are compared with the estimated bearing angles and a bearing angle difference is formed, at the minimum of which the estimated bearing angle delivers the true bearing angle except for a residual error. The remaining error depends on a predefinable threshold. Such a filter arrangement is for example in the<patcit id="pcit0001" dnum="DE3446658C2"><text>DE 34 46 658 C2</text></patcit> described. The iteration time of this filter arrangement is largely determined by additional inputs. For example, the starting position or base values, which are determined by observing or measuring values ​​of other sensors on board the carrier vehicle, for example periscope observations or radar measurements, are entered. Filter coefficients are determined from these base values, which lead to an improved first estimate of the target position.

0004From the <patcit id="pcit0002" dnum="US5877998A"><text>U.S. Patent 5,877,998</text></patcit> Another method is known in which, in contrast to the described iterative minimization of the bearing angle difference, the position and speed of a target are recursively estimated as target data. With a movement model for the carrier vehicle, movement data of the carrier vehicle are obtained from navigation sensor data. In a second model, target movement data are modeled for prediction. Bearing angles, the change in the bearing angle over time, that is to say the bearing angle speed, and the change in the bearing angle speed are obtained from received signals which are received while driving along a self-lay. This measurement data is smoothed and used to predict target data. The predicted target data are corrected with the smoothed measurement data from two previous Eigenlegs and fed to the target movement data model for the next prediction. For each new target data estimate, a maneuver of the carrier vehicle is necessary, since only then is there again smoothed measurement data for a correction and a new prediction.

0005In the <patcit id="pcit0003" dnum="US6009185A"><text>US 6 009 185</text></patcit> describes a method in which the starting position of the target and prior knowledge about the target, the target behavior and the target area are used for estimating the target data by means of a neural network. A priori knowledge includes, for example, the maximum possible speed of the target, depth and depth changes of the target, accelerations, typical maneuvering behavior and environmental data. In a three-dimensional coordinate system, hypotheses about travel paths of the target based on the known starting position and with the aid of the a-priori knowledge are made and compared with the travel paths of the target estimated from contacts with the target by correlation. Knowledge of the base values ​​of other sensors, in particular the starting position of the target, is necessary for the function of this method.

0006It is an object of the present invention to provide a method of the type mentioned in the preamble of claim 1, in which the iteration time when using the filter arrangement mentioned is comparable or even shorter without measurement values ​​of other sensors on board the carrier vehicle being required as support values.

0007The object is achieved by the features in the characterizing part of claim 1.

0008Received signals of at least one electroacoustic transducer arrangement, for example a horseshoe base or side antenna on board a submarine as the carrier vehicle and / or a trailing antenna towed by a surface ship or a submarine, are combined in the sonar receiving system in a directionally selective manner into group signals and the levels of the group signals are observed. An increase in the level indicates that a target lies on a bearing beam of a first bearing angle assigned to the group signal. The distance of the target is unknown, only its bearing is available. For example, the location specifies a limit value for a maximum possible distance from the target, which it derives from geographic and oceanographic knowledge and the specification of the sonar reception system, for example sixty kilometers. A minimal distance, e.g. one kilometer is derived from a possible threat situation for the carrier vehicle. Speed ​​limits range from slightly above zero knots to rule out static targets and maximum speed information from speedboats or torpedoes. Even rough specifications shorten the computing time and enable estimates of target positions to be excluded, which cannot be recorded with the sonar reception system. From these specified limit values, boundary conditions for position components and speed components are determined and used as a basis for estimating the position of the target, with which the estimated bearing angle is determined in order to minimize the bearing angle difference.

0009The advantage of the method according to the invention is that the limit values ​​are used to enter only physically and technically meaningful parameters about the position of the target, its speed and its course in the iterative estimation process. Completely illogical results, such as a speed of a hundred knots or a distance of a thousand kilometers are excluded from the outset, which up to now could have arisen in the context of the iteration in the case of heavily noisy reception signals.

0010The upper limit for the target distance is derived, for example, from on-board sound propagation programs for the sea area. Since the target can only be located in those zones that allow sound transmission from the target to the receiving location and correspond to the location range of the sonar receiving system, it is advantageous to use this knowledge, since targets that are further away could not be detected at all.

0011Alone the restriction of the course to target targets according to the advantageous development of the method according to the invention according to claim 2 drastically increases the convergence speed of the position estimate, even if the course of the target is almost at right angles to the bearing beam and a slightly different course in the position estimation is no longer taken into account. The first entry of the course's limitation to tariff targets ensures that erroneous position estimates are excluded.

0012The limit values ​​for the target speed are derived from the driving characteristics of different watercraft, e.g. surface ships, submarines and torpedoes.

0013By measuring the change in the bearing angle, it is possible, according to the advantageous development of the method according to the invention, to determine the direction of the course with respect to the first bearing beam and, with this side identifier, to further restrict the limits for the course with which the aim of the sonar receiving system is is approaching.

0014By specifying limit values, the estimate of the target data is adapted to reality. A non-recursive iterative calculation method for minimizing the bearing angle difference or the square of this difference is solved by a method for solving linear equations under constraints according to the method of least squares and in Chapter 23, pages 158 to 173, Linear Least Squares with linear inequality constraints, in the book "Solving least squares problems" by Charles R. Lawson, Richard J. Hansen, Classics, In Applied Mathematics, SIAM, ISBN-0-89871-356-0, 1995. There is also a program LSQLIN.M and LSI.M in MATLAB optimization tool box, which numerically solve the algorithm specified in the book. This mathematical tool is ideally suited to determine the target position from given limit values ​​with the advantage that the convergence times for determining the target data are almost halved even under the most difficult location conditions.

0015Bearing angles are continuously measured while the carrier vehicle is traveling on its own leg along its course. In the advantageous development of the method according to the invention according to claims 4 and 5, the bearing angle last measured after a predeterminable time interval is used to further limit the limit values ​​for possible speeds and distances of the target when the course is starting. So that the target of the maximum distance on the first sighting beam can just reach the last measured sighting beam in order to be sighted there, it must travel there at maximum speed. The upper limit of the speed is determined from the plumb length between the maximum distance and the bearing beam assigned to the last bearing divided by the time interval. The plumb length to the first bearing beam includes the minimum course angle for the starting course and forms the lower limit for the course. The lower limit of speed or the minimum distance is determined by the fact that the target travels a distance from the minimum distance of the target on the first beacon to the last beacon during the time interval along the middle limit for the course. This path divided by the time interval specifies the limit for the minimum speed.

0016The other upper limit value of the course is determined in accordance with the advantageous development according to claim 6, in that the target reaches the second bearing beam from the minimum distance on the first bearing beam at maximum speed during the time interval. A path section corresponding to the maximum speed, taking into account the time interval, cuts the last direction finding beam and includes the maximum heading angle.

0017The boundary conditions in an xy coordinate system for estimating a new target position are calculated from the limit values ​​for the speeds and the course according to the advantageous development of the method according to claims 7, 8 and 9. It is assumed that the target could move along the two limit values ​​for the course with minimum and maximum speed within the time interval and assume new positions on the next direction finding beam. The speed limit values ​​are broken down into orthogonal speed components, the extreme values ​​of which span a limit area. This border area limits all possible speed vectors for the target according to magnitude and direction and specifies the associated speed components. With these speed components and the position components in the xy direction for all distances within the predetermined limits on the first direction finding beam, a target position and a speed vector of the target pointing in the direction of the course are estimated. Target positions are estimated and estimated bearing angles are determined from the resulting target path, which crosses a bearing fan made of bearing beams of the bearing angles previously measured. All estimated bearing angles with the measured bearing angles are used to determine the smallest square of error and the minimum of the bearing angle differences is sought. The advantage is in particular a further restriction of the area of ​​uncertainty for possible target start positions and speed vectors and thus faster convergence of the filtering method due to fewer iteration steps.

0018The advantageous developments of the method according to the invention according to claims 10 to 12 take into account the difference between the limit values ​​for a starting course when determining the boundary conditions for the speed components, so that the convergence times can be further minimized. The Cartesian coordinate system for determining the boundary conditions is rotated in relation to the reference system for bearing and course by an optimization rotation angle, which is selected depending on the difference between the course angles determined by the limit values. As a result, the limit region is limited to one quadrant if the limit values ​​are either only pointing to the right or only pointing to the left and there is a difference of less than 90 °. If the course angle determined by the limit values ​​differs between 90 ° and 180 °, the optimization rotation angle is chosen such that the maximum and minimum speeds along the limit values ​​of the course are symmetrical to the y-axis in two quadrants.

0019With the advantageous development of the method according to the invention, the optimization rotation angle is selected equal to the negative measured bearing angle in the event of a difference between the predetermined course angles greater than 180 °, at which the course can even be estimated in progress.

0020In order to passively determine the target data, the carrier vehicle travels along a self-lay at constant speed and course and measures the bearing angle to the target. When using an antenna on board and a towed antenna further behind the carrier vehicle, the target data can already be determined without changing course. If the carrier vehicle has only a single receiving antenna for direction finding, the target data can only be determined after a first self-maneuver. The advantageous development of the method according to the invention according to claim 14 allows a target data measurement already when passing through the first self-laying when using only one receiving antenna. From the<patcit id="pcit0004" dnum="DE10129726A1"><text>DE 101 29 726 A1</text></patcit> it is known that the reception frequency depends on the own radial speed component of the carrier vehicle and the radial speed of the target pointing in the same direction. If you know your own speed, you can eliminate your own share of the Doppler shift and only consider the target share. Apart from the frequency change over time, the so-called Frequency deviation, there is a change in the bearing angle over time while driving along the Eigenleg. The time until target data can be stably estimated is called convergence time. The convergence time is shorter, the larger the frequency swing is when driving through a self-lay.

0021After a target detection, the group signals of the electroacoustic transducer arrangement are subjected to a Fourier transformation and the frequency of spectral lines in the frequency spectrum of the group signals is determined. The frequency of the spectral line with the greatest level or the frequency spacing of adjacent spectral lines is used as the receiving frequency together with the measured bearing angle of the target data estimate. Target positions are estimated and the bearing direction estimated. A bearing angle difference is determined between the measured and estimated bearing angle. In addition, a Doppler shift and a transmission frequency emitted or emitted by the target are estimated from the same estimated target positions and their changes over time. The estimated transmission frequency is frequency-shifted in accordance with the estimated Doppler shift and forms the estimated Doppler frequency from which the received frequency is subtracted. The difference between the received frequency and the estimated Doppler frequency is used as the frequency difference together with the bearing angle difference for the determination of the target data according to the least mean square algorithm.

0022For the predetermined limit values ​​of the speed, limits of the Doppler shift are determined according to the advantageous development of the method according to claim 14 and linked to the measured reception frequency. This gives limit values ​​for the estimated transmission frequency. Doppler shifts are determined from the estimated target positions and linked to the estimated transmission frequency and its limits. The frequency difference to the measured reception frequency is iteratively minimized together with the bearing angle difference for the target data determination. The advantage of the method according to the invention is, in particular, that when the frequency difference is minimized, the estimated Doppler frequencies are used, which are determined from possible speed components of the estimated target position and its limits. Taking the bearing to the target into account, these speed components correspond to the limits of a radial speed component, which in turn causes the Doppler shift in the transmission frequency of the target. By determining and using the reception frequency for estimating the target data, there is the advantage of determining a first target position or the starting position without self-maneuvers, separating and determining several targets and their target data under the same bearing, and further reducing the convergence times for the target position estimates.

0023The invention is described in more detail with reference to the drawing in an exemplary embodiment for a method for the passive determination of target data with a sonar receiving system. Show it:<dl id="dl0001"><dt>Fig. 1</dt><dd>a scenario for the determination of target data with limit values,</dd><dt>Fig. 2,3</dt><dd>xy coordinate systems for determining the boundary conditions for orthogonal speed components,</dd><dt>Fig. 4</dt><dd>Diagrams illustrating the convergence of target data</dd><dt>Fig. 5</dt><dd>a modified scenario,</dd><dt>Fig. 6</dt><dd>an xy coordinate system with true and estimated target positions,</dd><dt>Fig. 7</dt><dd>a block diagram,</dd><dt>Fig. 8.9</dt><dd>Error plots for different target distances.</dd></dl>

00241 shows a scenario in an xy coordinate system for the passive determination of target data. With an electroacoustic transducer arrangement of a sonar receiving system, for example a linear antenna on board a carrier vehicle or a towing antenna, a noise radiated from a target from an incident direction along a first direction finding beam P_first at a first bearing angle B_first detected. The finish line is on course B_first + 90 &lt;K_min≤ K ≤ K_Max&lt;B_first - 90. At the time to, the carrier vehicle is at origin 0/0. The y-axis gives the north direction N₀ as the reference direction. At time t₁ the carrier vehicle has location II with constant airspeed V_Own reached while the target on its course K at a speed V takes a next target position. On the first DF P_first are predetermined limit values ​​R_min and R_Max for the distance of the target with Z_0min and Z_0max designated and predetermined limit values ​​K_min and K_Max registered for a starting course of the target. If the target is directly on the beacon P_first approaches the carrier vehicle on a collision course, the maximum limit for the course is <maths id="math0001" num="(1)."><math display="block"><msub><mi mathvariant="normal">K</mi><mi>Max</mi></msub><mo mathvariant="normal">=</mo><msub><mi mathvariant="normal">B</mi><mi>first</mi></msub><mo mathvariant="normal">+</mo><mn mathvariant="normal">180</mn><mo>⁢</mo><mi mathvariant="normal">°</mi></math><img file="EP1531339B1_D0001.tif" /></maths>

0025If the target moves further down the course angle is <maths id="math0002" num="(2)."><math display="block"><msub><mi mathvariant="normal">K</mi><mi>min</mi></msub><mo mathvariant="normal">=</mo><msub><mi mathvariant="normal">B</mi><mi>first</mi></msub><mo mathvariant="normal">+</mo><mn mathvariant="normal">90</mn><mo>⁢</mo><mi mathvariant="normal">°</mi></math><img file="EP1531339B1_D0002.tif" /></maths>

0026An emigration of the bearing from the bearing angle B_first to the bearing angle B_load shows that the target is not on a collision course. The change in the bearing over time limits the course by a side identifier to the right or left of the bearing beam P._first and thus limits the course: <maths id="math0003" num="(3)."><math display="block"><msub><mi mathvariant="normal">B</mi><mi>first</mi></msub><mo mathvariant="normal">+</mo><mn mathvariant="normal">90</mn><mo>⁢</mo><mi mathvariant="normal">°</mi><mo mathvariant="normal">≤</mo><mi mathvariant="normal">K</mi><mo mathvariant="normal">&lt;</mo><msub><mi mathvariant="normal">B</mi><mi>first</mi></msub><mo mathvariant="normal">+</mo><mn mathvariant="normal">180</mn><mo>⁢</mo><mi mathvariant="normal">°</mi></math><img file="EP1531339B1_D0003.tif" /></maths>

0027There is a limit for the maximum speed V_Max predefined and provided that the target Z moves so that the lower limit of the speed V_min > 0 is: <maths id="math0004" num="(4)."><math display="block"><mn mathvariant="normal">0</mn><mo mathvariant="normal"><</mo><mi mathvariant="normal">V</mi><mo mathvariant="normal">≤</mo><msub><mi mathvariant="normal">V</mi><mi>Max</mi></msub></math><img file="EP1531339B1_D0004.tif" /></maths>

0028The target of Z_0max at R_Max or from Z_0min at R_min to the way V_Max dt at a course angle B_first + 90 ° ≤ K &lt;B_first + 180 ° to a location on circular arcs 10 and 11. If the speed V is lower, the target is within the specified circle segments. The boundary conditions for the coordinates for the estimated target position are taken into account the limit values ​​R_min, R_Max, K_min, K_Max and V_Max calculated.

0029Since the distance R to the destination between R_min and R_Max the possible target area is outlined and limited by the hatched area in FIG. 1.

0030In FIG. 2a, a starting course of the target of, for example, 100 <K <260 is specified as limit values ​​for the course as a further example. The bearing angle is B_first = 0 °. From observations, for example, limit values ​​of the speed V_min <V <V_Max determined with 5Kn <V <20Kn. The difference between the maximum course angle K_Max <260 ° and minimum course angle K_min Is> 100 ° <maths id="math0005" num=""><math display="block"><msub><mi mathvariant="normal">K</mi><mi>Max</mi></msub><mo mathvariant="normal">-</mo><msub><mi mathvariant="normal">k</mi><mi>min</mi></msub><mo mathvariant="normal">=</mo><mn mathvariant="normal">160</mn><mo>⁢</mo><mi mathvariant="normal">° and is smaller than</mi><mspace width="1em" /><mn mathvariant="normal">180</mn><mo>⁢</mo><mi mathvariant="normal">°</mi><mn mathvariant="normal">.</mn></math><img file="EP1531339B1_D0005.tif" /></maths>

0031For this example, FIG. 2a shows the decomposition of the limit values ​​of the speed along the maximum and minimum course angle K in a Cartesian coordinate system_Max, K_min in orthogonal xy velocity components at any distance between the limits of R. The origin of the coordinate system marks this distance. In addition to the xy position components for the limit values ​​of the distance, the xy-speed components are the boundary conditions for the input into the iteration calculation to determine the minimum of the bearing angle difference or the squared bearing angle difference from the measured and estimated bearing angle. The limit values ​​V pointing in minimum and maximum course directions_Max and V_min The speed is expressed in speed components ± V_xmax/ ± V_ymax and ± V_{xmin /}+ V_ymin disassembled. A hatched rectangle enclosed by the maximum and minimum speed components in the x and y directions encloses a border area within which the target can move at a respective speed, which is due to the boundary conditions<maths id="math0006" num=""><math display="block"><mo mathvariant="normal">-</mo><msub><mi mathvariant="normal">V</mi><mi>xmax</mi></msub><mo mathvariant="normal">&lt;</mo><msub><mi mathvariant="normal">V</mi><mi mathvariant="normal">x</mi></msub><mo mathvariant="normal">&lt;</mo><mo mathvariant="normal">+</mo><msub><mi mathvariant="normal">V</mi><mi>xmax</mi></msub></math><img file="EP1531339B1_D0006.tif" /></maths><maths id="math0007" num=""><math display="block"><mo mathvariant="normal">-</mo><msub><mi mathvariant="normal">V</mi><mi>Max</mi></msub><mo mathvariant="normal">&lt;</mo><msub><mi mathvariant="normal">V</mi><mi mathvariant="normal">y</mi></msub><mo mathvariant="normal">&lt;</mo><mo>-</mo><msub><mi mathvariant="normal">V</mi><mi>ymin</mi></msub></math><img file="EP1531339B1_D0007.tif" /></maths>are limited. Eight boundary conditions are determined from the six limit values ​​and are processed in the calculation algorithm. With these speed boundary conditions from the limit values ​​of course and speed and the position boundary conditions from the limit values ​​for the distance, target positions are determined and an associated bearing angle is estimated. These associated estimated bearing angles are compared with the measured bearing angle. The smallest bearing angle difference then characterizes the estimated position on the measured bearing beam with the associated speed vector in the course direction. At the beginning of the determination of the target data, the position and speed vector differ very greatly for each determined minimum bearing angle difference, until they converge and, when calculated, come back to a starting position on the first bearing beam with the same values. The convergence times are shorter, the better the limit values ​​effective for the calculation match the specified limit values ​​for speed V and course K.

0032The effective limit values ​​V *_min, V *_Max for the speed that the specified limit values ​​V_min and V_Max according to FIG. 2 include: <maths id="math0008" num=""><math display="block"><msubsup><mi>V</mi><mi>min</mi><mo>*</mo></msubsup><mo><</mo><mi>V</mi><mo><</mo><msubsup><mi>V</mi><mi>Max</mi><mo>*</mo></msubsup></math><img file="EP1531339B1_D0008.tif" /></maths><maths id="math0009" num=""><math display="block"><mo>-</mo><msub><mi>V</mi><mrow><mi>y</mi><mspace width="1em" /><mi>min</mi></mrow></msub><mo><</mo><mi>V</mi><mo><</mo><msqrt><msup><msub><msub><mi>V</mi><mrow><mi>x</mi><mspace width="1em" /><mi>min</mi></mrow></msub><mi /></msub><mn>2</mn></msup><mo>+</mo><msup><msub><mi>V</mi><mi>Max</mi></msub><mn>2</mn></msup></msqrt></math><img file="EP1531339B1_D0009.tif" /></maths>With <maths id="math0010" num=""><math display="block"><msub><mi mathvariant="normal">V</mi><mi>ymin</mi></msub><mo mathvariant="normal">=</mo><msub><mi mathvariant="normal">V</mi><mi>min</mi></msub><mspace width="1em" /><mi>sin</mi><mspace width="1em" /><mfenced separators=""><msub><mi mathvariant="normal">K</mi><mi>min</mi></msub><mo mathvariant="normal">-</mo><mn mathvariant="normal">90</mn><mo>⁢</mo><mi mathvariant="normal">°</mi></mfenced></math><img file="EP1531339B1_D0010.tif" /></maths>and <maths id="math0011" num=""><math display="block"><msub><mi mathvariant="normal">V</mi><mi>xmax</mi></msub><mo mathvariant="normal">=</mo><msub><mi mathvariant="normal">V</mi><mi>Max</mi></msub><mo>•</mo><mi>cos</mi><mspace width="1em" /><mfenced separators=""><msub><mi mathvariant="normal">K</mi><mi>min</mi></msub><mo mathvariant="normal">-</mo><mn mathvariant="normal">90</mn><mo>⁢</mo><mi mathvariant="normal">°</mi></mfenced><mn>.</mn></math><img file="EP1531339B1_D0011.tif" /></maths>

0033The effective limit values ​​K *_min, K *_Max, which include the specified limit values ​​for K, are: <maths id="math0012" num=""><math display="block"><msubsup><mi>K</mi><mi>min</mi><mo>*</mo></msubsup><mo>&lt;</mo><mi>K</mi><mo>&lt;</mo><msubsup><mi>K</mi><mi>Max</mi><mo>*</mo></msubsup></math><img file="EP1531339B1_D0012.tif" /></maths><maths id="math0013" num=""><math display="block"><mn>90</mn><mo>+</mo><mi>tan</mi><mfrac><msub><mi>V</mi><mrow><mi>y</mi><mspace width="1em" /><mi>min</mi></mrow></msub><msub><mi>V</mi><mrow><mi>x</mi><mspace width="1em" /><mi>Max</mi></mrow></msub></mfrac><mo>&lt;</mo><mi>K</mi><mo>&lt;</mo><mn>270</mn><mo>-</mo><mi>tan</mi><mfrac><msub><mi>V</mi><mrow><mi>y</mi><mspace width="1em" /><mi>min</mi></mrow></msub><msub><mi>V</mi><mrow><mi>x</mi><mspace width="1em" /><mi>Max</mi></mrow></msub></mfrac></math><img file="EP1531339B1_D0013.tif" /></maths>

0034In order to achieve the symmetrical relationships shown in FIG. 2a for the determination of the boundary conditions from the limit values ​​for speed and course, so that the deviation of the limits effective by the decomposition into components from the predetermined limit values ​​is the smallest, the coordinate system is rotated by an optimization angle α rotated according to FIG. 2b against the north direction N for the bearing and the course. The optimization rotation angle α depends on the limit values ​​for the course K <maths id="math0014" num=""><math display="block"><mn mathvariant="normal">180</mn><mo mathvariant="normal">-</mo><mfenced separators=""><msub><mi mathvariant="normal">K</mi><mi>Max</mi></msub><mo mathvariant="normal">+</mo><msub><mi mathvariant="normal">k</mi><mi>min</mi></msub></mfenced><mo mathvariant="normal">/</mo><mn mathvariant="normal">2</mn><mo mathvariant="normal">=</mo><mi mathvariant="normal">α</mi></math><img file="EP1531339B1_D0014.tif" /></maths>

0035In the case according to FIG. 2a, α = 0, since the y-axis is also the reference direction N for the bearing and the limit values ​​K with K_Max and K_min lie symmetrically to the y-axis in two quadrants.

00363 shows a determination of the boundary conditions from the limit values ​​of the speed when the limit values ​​for the course K lie in the same quadrant. The limits for course K are specified:<maths id="math0015" num=""><math display="block"><mn mathvariant="normal">90</mn><mo mathvariant="normal">&lt;</mo><mi mathvariant="normal">K</mi><mo mathvariant="normal">&lt;</mo><msub><mi mathvariant="normal">K</mi><mi>Max</mi></msub><mo mathvariant="normal">,</mo></math><img file="EP1531339B1_D0015.tif" /></maths>With <maths id="math0016" num=""><math display="block"><msub><mi mathvariant="normal">K</mi><mi>Max</mi></msub><mo mathvariant="normal">-</mo><msub><mi mathvariant="normal">K</mi><mi>min</mi></msub><mo mathvariant="normal">&lt;</mo><mn mathvariant="normal">90</mn><mo>⁢</mo><mi mathvariant="normal">°</mi></math><img file="EP1531339B1_D0016.tif" /></maths>

0037The limit values ​​for the speed V are specified: <maths id="math0017" num=""><math display="block"><msub><mi mathvariant="normal">V</mi><mi>min</mi></msub><mo mathvariant="normal">&lt;</mo><mi mathvariant="normal">V</mi><mo mathvariant="normal">&lt;</mo><msub><mi mathvariant="normal">V</mi><mi>Max</mi></msub><mn mathvariant="normal">.</mn></math><img file="EP1531339B1_D0017.tif" /></maths>The boundary conditions result from this <maths id="math0018" num=""><math display="block"><msub><mi mathvariant="normal">V</mi><mi>xmin</mi></msub><mo mathvariant="normal">&lt;</mo><msub><mi mathvariant="normal">V</mi><mi mathvariant="normal">x</mi></msub><mo mathvariant="normal">&lt;</mo><msub><mi mathvariant="normal">V</mi><mi>Max</mi></msub><mn mathvariant="normal">.</mn></math><img file="EP1531339B1_D0018.tif" /></maths><maths id="math0019" num=""><math display="block"><mo>-</mo><msub><mi mathvariant="normal">V</mi><mi>ymax</mi></msub><mo mathvariant="normal">&lt;</mo><msub><mi mathvariant="normal">V</mi><mi mathvariant="normal">y</mi></msub><mo mathvariant="normal">&lt;</mo><mn>0</mn></math><img file="EP1531339B1_D0019.tif" /></maths>in which <maths id="math0020" num=""><math display="block"><msub><mi mathvariant="normal">V</mi><mi>xmin</mi></msub><mo mathvariant="normal">=</mo><msub><mi mathvariant="normal">V</mi><mi>min</mi></msub><mspace width="1em" /><mi>cos</mi><mspace width="1em" /><mfenced separators=""><msub><mi mathvariant="normal">K</mi><mi>Max</mi></msub><mo mathvariant="normal">-</mo><msub><mi mathvariant="normal">K</mi><mi>min</mi></msub></mfenced></math><img file="EP1531339B1_D0020.tif" /></maths>and <maths id="math0021" num=""><math display="block"><msub><mi mathvariant="normal">V</mi><mi>ymax</mi></msub><mo mathvariant="normal">=</mo><msub><mi mathvariant="normal">V</mi><mi>Max</mi></msub><mspace width="1em" /><mi>sin</mi><mspace width="1em" /><mfenced separators=""><msub><mi mathvariant="normal">K</mi><mi>Max</mi></msub><mo mathvariant="normal">-</mo><msub><mi mathvariant="normal">K</mi><mi>min</mi></msub></mfenced></math><img file="EP1531339B1_D0021.tif" /></maths>

0038The hatched rectangle indicates the border area within which the target can reach the next position under the respective course at the respective speed.

0039The effective limit values ​​V *_min,V *_Max for the speed V. <maths id="math0022" num=""><math display="block"><mi mathvariant="normal">V</mi><mo>⁢</mo><msub><mo mathvariant="normal">*</mo><mi>min</mi></msub><mo mathvariant="normal">&lt;</mo><mi mathvariant="normal">V</mi><mo mathvariant="normal">&lt;</mo><mi mathvariant="normal">V</mi><mo>⁢</mo><msub><mo mathvariant="normal">*</mo><mi>Max</mi></msub></math><img file="EP1531339B1_D0022.tif" /></maths><maths id="math0023" num=""><math display="block"><msub><mi mathvariant="normal">V</mi><mi>xmin</mi></msub><mo>&lt;</mo><mi mathvariant="normal">V</mi><mo>&lt;</mo><msqrt><msup><msub><mi>V</mi><mi>Max</mi></msub><mn>2</mn></msup><mo>+</mo><msup><msub><mi>V</mi><mrow><mi>y</mi><mspace width="1em" /><mi>Max</mi></mrow></msub><mn>2</mn></msup></msqrt></math><img file="EP1531339B1_D0023.tif" /></maths>and for effective limit values ​​K *_min, K *_Max for course K result from: <maths id="math0024" num=""><math display="block"><msub><mi>K</mi><mi>min</mi></msub><mo>&lt;</mo><mi>K</mi><mo>&lt;</mo><mn>180</mn><mo>-</mo><mi>tan</mi><mfrac><msub><mi>V</mi><mrow><mi>x</mi><mspace width="1em" /><mi>min</mi></mrow></msub><msub><mi>V</mi><mrow><mi>y</mi><mspace width="1em" /><mi>Max</mi></mrow></msub></mfrac></math><img file="EP1531339B1_D0024.tif" /></maths>

0040The effective limits include the specified limits for V and K.

0041FIG. 4 shows the convergence process in the passive determination of the target data in diagrams in succession in FIGS. 4.1 to 4.4. Starting from a bearing B_first 4.1, the predetermined limit values ​​for the distance R with R_Max and R_min applied to the first directional beam. The specified limit values ​​for course K are K_Max and K_min as well as predetermined limit values ​​for the speed V with V_Max and V_min are at the maximum distance R_Max and the minimum distance R_min plotted as speed vectors. The target can be any starting distance between R_Max and R_min with the given limits for V and K. The target is assumed to move at a constant speed and a constant course while traveling. After several time intervals and measurements of the bearing angle, at time t₁ 4.2 the bearing angle B₁ measured. The boundary conditions for the distance and the speed are entered into the calculation algorithm as position components and speed components in accordance with the explanations in connection with FIGS. 2a and 2b. The minimum between all measured bearing angles up to the bearing angle B₁ and the estimated bearing angles and the resulting state vector of the target, namely the starting position, speed and course of the target, is estimated. The associated course K₁ and the speed V₁ are also entered in Fig. 4.2 and the starting position R₀₁ on the first beam. A finish line V₁ t of the target, starting with the first bearing beam at the measured bearing angle B_first , cuts a direction finder fan that spans all measured bearing angles and marks B on the direction finding beam at the last measured bearing angle₁ the target position Z₁.

0042After another time t₂ 4.3 a final bearing angle B₂ measured. To determine the target position Z₂ the same boundary conditions for speed and distance according to FIG. 4.1 are entered into the calculation algorithm. With the bearing angle differences between the measured and estimated bearing angles now determined, the position Z₂ and the associated speed vector of the target is determined. The associated course K₂ and the speed V₂ leave on a starting position R₀₂ conclude. This starting position is between R_Max and R_min on the first DF and is different from the start position R₀₁ according to Fig. 4.2.

0043The next measurements of the bearing angle including the last bearing angle B_load at the time t₃ confirm the starting position R₀₂who have favourited Speed ​​V₂ and the course angle K₂, because the last state estimate is at a minimum of the bearing angle difference that this course K₂ and this speed V₂ is to be assigned. This confirms the starting position with R₀₂ between R_min and R_Max·

00445 illustrates the geometric relationship of the position determination from the boundary conditions for the speed components and the distance components. 1, after the time interval dt, the carrier vehicle has taken up place II. The target is at a bearing angle B_load direction. With this bearing and the bearing angle B_load the boundary conditions for estimating the next target position can be further restricted. At the time t₀ the bearing angle B_first measured, a minimum target distance R_min ≤ R and an ongoing course <maths id="math0025" num=""><math display="block"><msub><mi mathvariant="italic">B</mi><mi mathvariant="italic">first</mi></msub><mo mathvariant="normal">+</mo><mn mathvariant="normal">90</mn><mo>&lt;</mo><mi>K</mi><mo>&lt;</mo><msub><mi mathvariant="italic">B</mi><mi mathvariant="italic">first</mi></msub><mo>-</mo><mn>90</mn></math><img file="EP1531339B1_D0025.tif" /></maths>given.

0045At the time t₁ the bearing angle B_load measured and thus limited the market values: <maths id="math0026" num="(3)"><math display="block"><msub><mi mathvariant="normal">B</mi><mi>first</mi></msub><mo mathvariant="normal">+</mo><mn mathvariant="normal">90</mn><mo>⁢</mo><mi mathvariant="normal">°</mi><mo mathvariant="normal">≤</mo><mi mathvariant="normal">K</mi><mo mathvariant="normal">&lt;</mo><msub><mi mathvariant="normal">B</mi><mi>first</mi></msub><mo mathvariant="normal">+</mo><mn mathvariant="normal">180</mn><mo>⁢</mo><mi mathvariant="normal">°</mi></math><img file="EP1531339B1_D0026.tif" /></maths>

0046Limit values ​​are assumed for the speed <maths id="math0027" num="(4),"><math display="block"><mn mathvariant="normal">0</mn><mo mathvariant="normal">&lt;</mo><mi mathvariant="normal">V</mi><mo mathvariant="normal">≤</mo><msub><mi mathvariant="normal">V</mi><mi>Max</mi></msub><mo>,</mo></math><img file="EP1531339B1_D0027.tif" /></maths>with which the target has moved until it is at the bearing angle B_load is taken. To do this, it must be from an R_Max on the first DF P_first with the speed V_Max just the last Peilstrahl P_load reachable. This condition, the upper limit of the speed, leads to the limit R_Max on the first DF P_first and is as part V_Max dt marked. This section V_Max dt is in Z_0min plotted and cut with the Peilstrahl P_load brought. This route forms the limitation of the maximum course K_Max, with which the target hits the second beam P_load at maximum speed V_Max reached: <maths id="math0028" num="(7)."><math display="block"><msub><mi mathvariant="normal">B</mi><mi>first</mi></msub><mo mathvariant="normal">+</mo><mn mathvariant="normal">90</mn><mo>⁢</mo><mi mathvariant="normal">°</mi><mo mathvariant="normal">≤</mo><mi mathvariant="normal">K</mi><mo mathvariant="normal">&lt;</mo><msub><mi mathvariant="normal">K</mi><mi>Max</mi></msub></math><img file="EP1531339B1_D0028.tif" /></maths>

0047A movable limit value for the minimum speed results from the point of intersection of the perpendicular to the first direction finding beam P._first at Z_0min and the intersection with the last DF P_loadwhen the target is at minimum speed V_min along the minimum course angle to the bearing beam P_load moves. The limit values ​​for the speed are now specified with:<maths id="math0029" num="(8)."><math display="block"><msub><mi mathvariant="normal">V</mi><mi>min</mi></msub><mo>≤</mo><mi mathvariant="normal">> V</mi><mo>≤</mo><msub><mi mathvariant="normal">V</mi><mi>Max</mi></msub></math><img file="EP1531339B1_D0029.tif" /></maths>

0048The speed limit values ​​are expressed in speed component V_x, V_y converted and extreme values ​​per coordinate as boundary conditions for V_x and V_y certainly: <maths id="math0030" num="(9)"><math display="block"><msub><mi mathvariant="normal">V</mi><mi>Max</mi></msub><mo mathvariant="normal">⋅</mo><mi>sin</mi><mspace width="1em" /><msub><mi mathvariant="normal">K</mi><mi>Max</mi></msub><mo mathvariant="normal">≤</mo><msub><mi mathvariant="normal">V</mi><mi mathvariant="normal">x</mi></msub><mo mathvariant="normal">≤</mo><msub><mi mathvariant="normal">V</mi><mi>min</mi></msub><mo>⁢</mo><msub><mrow><mspace width="1em" /><mi>cos K</mi></mrow><mi>min</mi></msub></math><img file="EP1531339B1_D0030.tif" /></maths><maths id="math0031" num="(10)"><math display="block"><msub><mi mathvariant="normal">V</mi><mi>min</mi></msub><mo mathvariant="normal">⋅</mo><mi>sin</mi><mspace width="1em" /><msub><mi mathvariant="normal">K</mi><mi>min</mi></msub><mo mathvariant="normal">≤</mo><msub><mi mathvariant="normal">V</mi><mi mathvariant="normal">y</mi></msub><mo mathvariant="normal">≤</mo><msub><mi mathvariant="normal">V</mi><mi>Max</mi></msub><mo>⁢</mo><msub><mrow><mspace width="1em" /><mi>cos K</mi></mrow><mi>Max</mi></msub></math><img file="EP1531339B1_D0031.tif" /></maths>From the speed components V_x and V_y are calculated by multiplying by the time interval dt path components. With the path components and the coordinates of the destinations Z_0min (minX₀/ minY₀) and Z_0max (maxX₀/ maxY₀) sum components are calculated and from this boundary conditions for the estimation of the position of the target on the last direction finding beam are determined.

0049At the limit values ​​for the distance R, boundary conditions for the position Z₀ of the target determines: <maths id="math0032" num="(12)"><math display="block"><mtable><mtr><mtd><msub><mi mathvariant="normal">R</mi><mi>min</mi></msub><mo>⁢</mo><msub><mrow><mspace width="1em" /><mi>sin B</mi></mrow><mi>first</mi></msub><mo mathvariant="normal">≤</mo><msub><mi mathvariant="normal">X</mi><mn mathvariant="normal">0</mn></msub><mo mathvariant="normal">≤</mo><msub><mi mathvariant="normal">R</mi><mi>Max</mi></msub><mspace width="1em" /><mi>sin</mi><mspace width="1em" /><msub><mi mathvariant="normal">B</mi><mi>first</mi></msub><mo>⁢</mo><msub><mrow><mspace width="1em" /><mi>minX</mi></mrow><mn mathvariant="normal">0</mn></msub><mo mathvariant="normal">≤</mo><msub><mi mathvariant="normal">X</mi><mn mathvariant="normal">0</mn></msub><mo mathvariant="normal">≤</mo><msub><mi>maxX</mi><mn mathvariant="normal">0</mn></msub><mspace width="1em" /><mi>or</mi></mtd></mtr><mtr><mtd><msub><mi mathvariant="normal">R</mi><mi>min</mi></msub><mo>⁢</mo><msub><mrow><mspace width="1em" /><mi>cos B</mi></mrow><mi>first</mi></msub><mo mathvariant="normal">≤</mo><msub><mi mathvariant="normal">Y</mi><mn mathvariant="normal">0</mn></msub><mo mathvariant="normal">≤</mo><msub><mi mathvariant="normal">R</mi><mi>Max</mi></msub><mspace width="1em" /><mi>cos</mi><mspace width="1em" /><msub><mi mathvariant="normal">B</mi><mi>first</mi></msub><mo>⁢</mo><msub><mrow><mspace width="1em" /><mi>minY</mi></mrow><mn mathvariant="normal">0</mn></msub><mo mathvariant="normal">≤</mo><msub><mi mathvariant="normal">Y</mi><mn mathvariant="normal">0</mn></msub><mo mathvariant="normal">≤</mo><msub><mi>maxY</mi><mn mathvariant="normal">0</mn></msub><mspace width="1em" /><mi>or</mi></mtd></mtr></mtable></math><img file="EP1531339B1_D0032.tif" /></maths>

0050The speed components multiplied by the time interval dt according to inequalities (9) and (10) are converted into path components from which the target position between Z_1min (minX₁/ minY₁) and Z_1max (maxX₁/ maxY₁) is estimated: <maths id="math0033" num="(13)"><math display="block"><mtable><mtr><mtd><msub><mi mathvariant="normal">R</mi><mi>min</mi></msub><mo>⁢</mo><msub><mrow><mspace width="1em" /><mi>sin B</mi></mrow><mi>first</mi></msub><mo mathvariant="normal">-</mo><msub><mi mathvariant="normal">V</mi><mi>Max</mi></msub><mo>⁢</mo><msub><mrow><mspace width="1em" /><mi>sin K</mi></mrow><mi>Max</mi></msub><mspace width="1em" /><mi>German</mi><mspace width="1em" /><mo mathvariant="normal">≤</mo><msub><mi mathvariant="normal">X</mi><mn mathvariant="normal">1</mn></msub><mo mathvariant="normal">≤</mo><msub><mi mathvariant="normal">R</mi><mi>Max</mi></msub><mo>⁢</mo><msub><mrow><mspace width="1em" /><mi>sin B</mi></mrow><mi>first</mi></msub><mo mathvariant="normal">+</mo><msub><mi mathvariant="normal">V</mi><mi>min</mi></msub><mo>⁢</mo><msub><mrow><mspace width="1em" /><mi>cos K</mi></mrow><mi>min</mi></msub><mo>⁢</mo><msub><mrow><mspace width="1em" /><mi>dt minX</mi></mrow><mn mathvariant="normal">1</mn></msub><mo mathvariant="normal">≤</mo><msub><mi mathvariant="normal">X</mi><mn mathvariant="normal">1</mn></msub><mo mathvariant="normal">≤</mo><msub><mi>maxX</mi><mn mathvariant="normal">1</mn></msub></mtd></mtr></mtable></math><img file="EP1531339B1_D0033.tif" /></maths><maths id="math0034" num="(14)"><math display="block"><msub><mi mathvariant="normal">R</mi><mi>min</mi></msub><mo>⁢</mo><msub><mrow><mspace width="1em" /><mi>cos B</mi></mrow><mi>first</mi></msub><mo mathvariant="normal">-</mo><msub><mi mathvariant="normal">V</mi><mi>Max</mi></msub><mo>⁢</mo><msub><mrow><mspace width="1em" /><mi>cos K</mi></mrow><mi>Max</mi></msub><mspace width="1em" /><mi>German</mi><mspace width="1em" /><mo mathvariant="normal">≤</mo><msub><mi mathvariant="normal">Y</mi><mn mathvariant="normal">1</mn></msub><mo mathvariant="normal">≤</mo><msub><mi mathvariant="normal">R</mi><mi>Max</mi></msub><mo>⁢</mo><msub><mrow><mspace width="1em" /><mi>cos B</mi></mrow><mi>first</mi></msub><mo mathvariant="normal">-</mo><msub><mi mathvariant="normal">V</mi><mi>Max</mi></msub><mo>⁢</mo><msub><mrow><mspace width="1em" /><mi>cos K</mi></mrow><mi>Max</mi></msub><mo>⁢</mo><msub><mrow><mspace width="2em" /><mi>dt minY</mi></mrow><mn mathvariant="normal">1</mn></msub><mo mathvariant="normal">≤</mo><msub><mi mathvariant="normal">Y</mi><mn mathvariant="normal">1</mn></msub><mo mathvariant="normal">≤</mo><msub><mi>maxY</mi><mn mathvariant="normal">1</mn></msub><mo>,</mo></math><img file="EP1531339B1_D0034.tif" /></maths>the on the last Peilstrahl P_load at the last measured bearing angle B_load lies. With these boundary conditions, the target start position is determined again by means of an iterative process by minimizing the bearing differences.

0051The minimum gives the target start position Z₀ and the speed components v_x and V_y which determine a speed vector V in the direction of the course K. If this state estimate is confirmed with every next bearing angle measurement by the fact that the associated bearing angle differences are a minimum, then the target position estimated on the last bearing beam is also the true target position and the associated course and the associated speed in accordance with the true target data of the target.

00526 shows an example of the estimation of the associated bearing angle B_est and minimizing the bearing angle difference of the measured bearing angle B_load = B_mess and the estimated bearing angle B_estwhich for all measurements B_imess the bearing angle simultaneously with the same boundary conditions for the x and y speed components and x and y position components, starting from a starting position Z₀that are within the limits for R₀ lies, is carried out. <maths id="math0035" num="(15)"><math display="block"><mfenced separators=""><msub><mi mathvariant="normal">B</mi><mi>mess</mi></msub><mo mathvariant="normal">-</mo><msub><mi mathvariant="normal">B</mi><mi>est</mi></msub></mfenced><mo mathvariant="normal">=</mo><mi>min</mi></math><img file="EP1531339B1_D0035.tif" /></maths>

0053In the xy coordinate system from FIG. 1, t is at a point in time₁ the carrier vehicle with its own position x_E, y_E, shown in the origin of the xy coordinate system. At this point, the destination is at position Z_true. It has its starting or starting position Z₀ at the coordinates x_{0 true}, Y_{0 true}that are within the boundary conditions for the starting position min x₀/ miny₀ and max x₀/ max y₀ lie at the speed v_xtrue, v_ytruethat are within the boundary conditions for the velocity v_xmin and V_ymin lie, leave and the path components v_xtrue Δt and V_ytrue. Δt traveled. The new true position e.g._true of the target leads to the measurement of a bearing angle B_mess. The new position Z_true is determined by an estimated position Z_est and calculating the associated estimated bearing angle B_est iteratively by minimizing the bearing angle difference between B_mess and B_est determined for all specified effective limit values.

0054It is assumed that the target differs from the coordinate x_{0 true} with a path error Δx₀ to the coordinate R_xest in the x direction at a speed v_x and a speed component error Δv_x moved in a time interval Δt. In the y direction, the target has a distance from the coordinate y during the time interval Δt_otrue to the coordinate R_yest with a path error Δy₀ and a speed v_yest with a speed component error Δv_y emotional. The coordinates of the target are estimated to be:<maths id="math0036" num="(A)"><math display="block"><msub><mi mathvariant="normal">R</mi><mi>x est</mi></msub><mo mathvariant="normal">=</mo><msub><mi mathvariant="normal">x</mi><mrow><mn mathvariant="normal">0</mn><mspace width="1em" /><mi>true</mi></mrow></msub><mo mathvariant="normal">+</mo><msub><mi mathvariant="normal">v</mi><mi mathvariant="normal">x</mi></msub><mo mathvariant="normal">⋅</mo><mi mathvariant="normal">Δt</mi><mo mathvariant="normal">+</mo><mfenced separators=""><msub><mi mathvariant="normal">Δx</mi><mn mathvariant="normal">0</mn></msub><mo mathvariant="normal">+</mo><msub><mi mathvariant="normal">Δv</mi><mi mathvariant="normal">x</mi></msub><mo mathvariant="normal">⋅</mo><mi mathvariant="normal">Δt</mi></mfenced><mo mathvariant="normal">=</mo><msub><mi mathvariant="normal">R</mi><mi>x true</mi></msub><mo mathvariant="normal">+</mo><msub><mi mathvariant="normal">ΔR</mi><mi mathvariant="normal">x</mi></msub></math><img file="EP1531339B1_D0036.tif" /></maths><maths id="math0037" num="(B)"><math display="block"><msub><mi mathvariant="normal">R</mi><mi>y est</mi></msub><mo mathvariant="normal">=</mo><msub><mi mathvariant="normal">x</mi><mrow><mn mathvariant="normal">0</mn><mspace width="1em" /><mi>true</mi></mrow></msub><mo mathvariant="normal">+</mo><msub><mi mathvariant="normal">v</mi><mi mathvariant="normal">y</mi></msub><mo mathvariant="normal">⋅</mo><mi mathvariant="normal">Δt</mi><mo mathvariant="normal">+</mo><mfenced separators=""><msub><mi mathvariant="normal">Δy</mi><mn mathvariant="normal">0</mn></msub><mo mathvariant="normal">+</mo><msub><mi mathvariant="normal">Δv</mi><mi mathvariant="normal">y</mi></msub><mo mathvariant="normal">⋅</mo><mi mathvariant="normal">Δt</mi></mfenced><mo mathvariant="normal">=</mo><msub><mi mathvariant="normal">R</mi><mi>y true</mi></msub><mo mathvariant="normal">+</mo><msub><mi mathvariant="normal">ΔR</mi><mi mathvariant="normal">y</mi></msub></math><img file="EP1531339B1_D0037.tif" /></maths>with the errors ΔR_x, ΔR_y. After reshaping you get<maths id="math0038" num="(a)"><math display="block"><msub><mi mathvariant="normal">R</mi><mi>x true</mi></msub><mo mathvariant="normal">=</mo><msub><mi mathvariant="normal">R</mi><mi>x est</mi></msub><mo mathvariant="normal">-</mo><msub><mi mathvariant="normal">ΔR</mi><mi mathvariant="normal">x</mi></msub><mo mathvariant="normal">=</mo><msub><mi mathvariant="normal">R</mi><mi>xest</mi></msub><mo mathvariant="normal">-</mo><mfenced separators=""><msub><mi mathvariant="normal">Δx</mi><mn mathvariant="normal">0</mn></msub><mo mathvariant="normal">+</mo><msub><mi mathvariant="normal">Δv</mi><mi mathvariant="normal">x</mi></msub><mo mathvariant="normal">⋅</mo><mi mathvariant="normal">Δt</mi></mfenced></math><img file="EP1531339B1_D0038.tif" /></maths><maths id="math0039" num="(b)"><math display="block"><msub><mi mathvariant="normal">R</mi><mi>y true</mi></msub><mo mathvariant="normal">=</mo><msub><mi mathvariant="normal">R</mi><mi>y est</mi></msub><mo mathvariant="normal">-</mo><msub><mi mathvariant="normal">ΔR</mi><mi mathvariant="normal">y</mi></msub><mo mathvariant="normal">=</mo><msub><mi mathvariant="normal">R</mi><mi>yest</mi></msub><mo mathvariant="normal">-</mo><mfenced separators=""><msub><mi mathvariant="normal">Δy</mi><mn mathvariant="normal">0</mn></msub><mo mathvariant="normal">+</mo><msub><mi mathvariant="normal">Δv</mi><mi mathvariant="normal">y</mi></msub><mo mathvariant="normal">⋅</mo><mi mathvariant="normal">Δt</mi></mfenced></math><img file="EP1531339B1_D0039.tif" /></maths>

0055This makes the estimated bearing angle B_est calculated: <maths id="math0040" num="I"><math display="block"><msub><mi mathvariant="normal">B</mi><mi>est</mi></msub><mo mathvariant="normal">=</mo><mi>arctan</mi><mfrac><mrow><msub><mi mathvariant="normal">R</mi><mi>xest</mi></msub><mo mathvariant="normal">-</mo><msub><mi mathvariant="normal">ΔR</mi><mi mathvariant="normal">x</mi></msub></mrow><mrow><msub><mi mathvariant="normal">R</mi><mi>yest</mi></msub><mo mathvariant="normal">-</mo><msub><mi mathvariant="normal">ΔR</mi><mi mathvariant="normal">y</mi></msub></mrow></mfrac></math><img file="EP1531339B1_D0040.tif" /></maths>

0056The true position Z_true is determined when the errors ΔR_x = Δx₀ + Δv_x . Δt and ΔR_y = Δy₀ + Δv_y · Δt are zero. Then the velocity components v_x and V_y correctly estimated that to take the new true position Z_true of the goal. The associated estimated bearing angle B_est is equal to the true bearing angle B_true and is: <maths id="math0041" num=""><math display="block"><msub><mi mathvariant="normal">B</mi><mi>est</mi></msub><mo mathvariant="normal">=</mo><msub><mi mathvariant="normal">B</mi><mi>true</mi></msub><mo mathvariant="normal">=</mo><mi>arctan</mi><mfrac><mrow><msub><mi mathvariant="normal">x</mi><mrow><mn mathvariant="normal">0</mn><mo>⁢</mo><mi>true</mi></mrow></msub><mo mathvariant="normal">+</mo><msub><mi mathvariant="normal">v</mi><mi>xtrue</mi></msub><mo mathvariant="normal">⋅</mo><mi mathvariant="normal">Δt</mi><mo mathvariant="normal">-</mo><msub><mi mathvariant="normal">x</mi><mi mathvariant="normal">E</mi></msub></mrow><mrow><msub><mi mathvariant="normal">y</mi><mrow><mn mathvariant="normal">0</mn><mo>⁢</mo><mi>true</mi></mrow></msub><mo mathvariant="normal">+</mo><msub><mi mathvariant="normal">v</mi><mi>ytrue</mi></msub><mo mathvariant="normal">⋅</mo><mi mathvariant="normal">Δt</mi><mo mathvariant="normal">-</mo><msub><mi mathvariant="normal">y</mi><mi mathvariant="normal">E</mi></msub></mrow></mfrac><mo mathvariant="normal">=</mo><msub><mi mathvariant="normal">B</mi><mi>mess</mi></msub></math><img file="EP1531339B1_D0041.tif" /></maths>

0057The target data P = (x₀, y₀, v_x, v_y) are correctly estimated if the error vector is zero: <maths id="math0042" num=""><math display="block"><mi mathvariant="normal">ΔP</mi><mo>=</mo><mfenced><msub><mi mathvariant="normal">Δx</mi><mn>0</mn></msub><mo>⁢</mo><msub><mi mathvariant="normal">Δy</mi><mn>0</mn></msub><mo>⁢</mo><msub><mi mathvariant="normal">Δv</mi><mi>x</mi></msub><mo>⁢</mo><msub><mi mathvariant="normal">Δv</mi><mi>y</mi></msub></mfenced><mo>=</mo><mn>0</mn><mspace width="1em" /><mi>With</mi></math><img file="EP1531339B1_D0042.tif" /></maths><maths id="math0043" num=""><math display="block"><msub><mi mathvariant="normal">ΔP</mi><mn mathvariant="normal">1</mn></msub><mo mathvariant="normal">=</mo><msub><mi mathvariant="normal">Δx</mi><mn mathvariant="normal">0</mn></msub><mo mathvariant="normal">,</mo><msub><mi mathvariant="normal">Δp</mi><mn mathvariant="normal">2</mn></msub><mo mathvariant="normal">=</mo><msub><mi mathvariant="normal">Δy</mi><mn mathvariant="normal">0</mn></msub><mo mathvariant="normal">,</mo><msub><mi mathvariant="normal">Δp</mi><mn mathvariant="normal">3</mn></msub><mo mathvariant="normal">=</mo><msub><mi mathvariant="normal">Δvx and Δp</mi><mn mathvariant="normal">4</mn></msub><mo mathvariant="normal">=</mo><msub><mi mathvariant="normal">Δv</mi><mi mathvariant="normal">y</mi></msub><mn mathvariant="normal">.</mn></math><img file="EP1531339B1_D0043.tif" /></maths>

0058For the determination of the target data, the sum of the bearing angle differences between the estimated bearing angles, the speed and the course and the measured bearing angles is iteratively minimized for all measurements: <maths id="math0044" num=""><math display="block"><mstyle displaystyle="false"><mstyle displaystyle="true"><munder><mo>∑</mo><mi>i</mi></munder></mstyle><mfenced separators=""><msub><mi mathvariant="italic">B</mi><mi mathvariant="italic">iest</mi></msub><mo mathvariant="italic">-</mo><msub><mi mathvariant="italic">B</mi><mi mathvariant="italic">imess</mi></msub></mfenced><mo>=</mo><mi>min or</mi><mspace width="1em" /></mstyle><mstyle displaystyle="false"><mstyle displaystyle="true"><munder><mo>∑</mo><mi>i</mi></munder></mstyle><msup><mfenced separators=""><msub><mi>B</mi><mi mathvariant="italic">iest</mi></msub><mo>-</mo><msub><mi>B</mi><mi mathvariant="italic">imess</mi></msub></mfenced><mn>2</mn></msup><mo>=</mo><mi>min</mi></mstyle></math><img file="EP1531339B1_D0044.tif" /></maths>

0059The starting position Z₀ and target positions Z_itrue are then determined except for a residual error, which is determined by a threshold determining the minimum. Then<maths id="math0045" num=""><math display="block"><msub><mi mathvariant="normal">B</mi><mi>iest</mi></msub><mo mathvariant="normal">≈</mo><msub><mi mathvariant="normal">B</mi><mi>itrue</mi></msub></math><img file="EP1531339B1_D0045.tif" /></maths>

0060The inclusion of an estimated Doppler frequency makes it possible to estimate the position without self-maneuvers by simultaneously minimizing a frequency difference between the measured received frequency and the estimated Doppler frequency, taking into account the bearing angle estimate according to I.

0061The target has the starting position Z₀ leave at speed v as shown in FIG. 6. Knowing the true bearing angle B_true the velocity components v_x and V_y of the target into a radial speed component V_R converted into the direction between the own position x_E, y_E and the true target position P_true points. <maths id="math0046" num="(1c)"><math display="block"><msub><mi mathvariant="normal">V</mi><mi mathvariant="normal">R</mi></msub><mo mathvariant="normal">=</mo><msub><mi mathvariant="normal">V</mi><mi mathvariant="normal">R</mi></msub><mo mathvariant="normal">+</mo><msub><mi mathvariant="normal">V</mi><mi mathvariant="normal">R</mi></msub><mo mathvariant="normal">"</mo><mo mathvariant="normal">=</mo><msub><mi mathvariant="normal">v</mi><mi mathvariant="normal">y</mi></msub><mo mathvariant="normal">⋅</mo><mi>cos</mi><mspace width="1em" /><msub><mi mathvariant="normal">B</mi><mi>true</mi></msub><mo mathvariant="normal">+</mo><msub><mi mathvariant="normal">v</mi><mi mathvariant="normal">x</mi></msub><mo>⁢</mo><msub><mrow><mspace width="1em" /><mi>sin B</mi></mrow><mi>true</mi></msub></math><img file="EP1531339B1_D0046.tif" /></maths>

0062This radial speed component V_R takes into account the correct added radial velocity components of the target V_RZ and the carrier vehicle V_RE<maths id="math0047" num="(d)"><math display="block"><msub><mi mathvariant="normal">V</mi><mi mathvariant="normal">R</mi></msub><mo mathvariant="normal">=</mo><msub><mi mathvariant="normal">V</mi><mi>RE</mi></msub><mo mathvariant="normal">-</mo><msub><mi mathvariant="normal">V</mi><mi>RZ</mi></msub></math><img file="EP1531339B1_D0047.tif" /></maths>

0063Because of the radial speed component V_R is a transmission frequency F contained in the transmission signal or in the noise of the target and emitted_strue frequency shifted and a Doppler transmission frequency as the reception frequency F_true received, as in chapter 7.4 "The Doppler Effect", page 334, 335 in the textbook "Experimentalphysik I", part 2, Edgar Lüscher, University pocketbook, Bibliographisches Institut, Mannheim. Described in 1967, the following applies to the Doppler frequency:<maths id="math0048" num="(2c)"><math display="block"><msub><mi>F</mi><mi mathvariant="italic">true</mi></msub><mo>=</mo><msub><mi>F</mi><mi mathvariant="italic">strue</mi></msub><mo>⁢</mo><mfenced><mfrac><mrow><mi mathvariant="italic">c</mi><mo mathvariant="italic">+</mo><msub><mi mathvariant="italic">V</mi><mi mathvariant="italic">RE</mi></msub></mrow><mrow><mi mathvariant="italic">c</mi><mo mathvariant="italic">+</mo><msub><mi mathvariant="italic">V</mi><mi mathvariant="italic">RZ</mi></msub></mrow></mfrac></mfenced><mo>=</mo><msub><mi>F</mi><mi mathvariant="italic">strue</mi></msub><mo>⁢</mo><mfenced open="[" close="]" separators=""><mn>1</mn><mo>-</mo><mfrac><msub><mi>v</mi><mi>R</mi></msub><mi>c</mi></mfrac></mfenced></math><img file="EP1531339B1_D0048.tif" /></maths>

0064The radial speed component V_R is according to equations (1c, 2c) dependent on the speed of sound c, the speed components in the x and y directions v_x and V_y and the bearing angle B_true:

0065The speed components of_x and V_y are equal to the temporal change in the xy coordinates of the target: <maths id="math0049" num=""><math display="block"><msub><mi mathvariant="normal">v</mi><mi mathvariant="normal">x</mi></msub><mo mathvariant="normal">=</mo><mfrac><msub><mi>dR</mi><mi>xtrue</mi></msub><mi>German</mi></mfrac><mo mathvariant="normal">=</mo><msub><mover><mi mathvariant="normal">R</mi><mo mathvariant="normal">˙</mo></mover><mi>xtrue</mi></msub></math><img file="EP1531339B1_D0049.tif" /></maths><maths id="math0050" num=""><math display="block"><msub><mi mathvariant="normal">v</mi><mi mathvariant="normal">y</mi></msub><mo mathvariant="normal">=</mo><mfrac><msub><mi>dR</mi><mi>ytrue</mi></msub><mi>German</mi></mfrac><mo mathvariant="normal">=</mo><msub><mover><mi mathvariant="normal">R</mi><mo mathvariant="normal">˙</mo></mover><mi>ytrue</mi></msub></math><img file="EP1531339B1_D0050.tif" /></maths>

0066With equations (a) and (b) we get: <maths id="math0051" num="(e)"><math display="block"><msub><mi mathvariant="normal">v</mi><mi mathvariant="normal">x</mi></msub><mo mathvariant="normal">=</mo><msub><mover><mi mathvariant="normal">R</mi><mo>˙</mo></mover><mi>xtrue</mi></msub><mo mathvariant="normal">=</mo><msub><mover><mi mathvariant="normal">R</mi><mo>˙</mo></mover><mi>xest</mi></msub><mo mathvariant="normal">-</mo><msub><mrow><mi mathvariant="normal">Δ</mi><mo>⁢</mo><mover><mi mathvariant="normal">R</mi><mo>˙</mo></mover></mrow><mi mathvariant="normal">x</mi></msub></math><img file="EP1531339B1_D0051.tif" /></maths><maths id="math0052" num="(f)"><math display="block"><msub><mi mathvariant="normal">v</mi><mi mathvariant="normal">y</mi></msub><mo mathvariant="normal">=</mo><msub><mover><mi mathvariant="normal">R</mi><mo>˙</mo></mover><mi>ytrue</mi></msub><mo mathvariant="normal">=</mo><msub><mover><mi mathvariant="normal">R</mi><mo>˙</mo></mover><mi>yest</mi></msub><mo mathvariant="normal">-</mo><msub><mrow><mi mathvariant="normal">Δ</mi><mo>⁢</mo><mover><mi mathvariant="normal">R</mi><mo>˙</mo></mover></mrow><mi mathvariant="normal">y</mi></msub></math><img file="EP1531339B1_D0052.tif" /></maths>

0067Using the true bearing angle B_true between the reference direction N₀ and the direction to the true target position Ptrue <maths id="math0053" num="(g)"><math display="block"><msub><mi>sin B</mi><mi>true</mi></msub><mo mathvariant="normal">=</mo><mfrac><msub><mi mathvariant="normal">R</mi><mi>xtrue</mi></msub><msub><mi mathvariant="normal">R</mi><mi>true</mi></msub></mfrac></math><img file="EP1531339B1_D0053.tif" /></maths><maths id="math0054" num="(h)"><math display="block"><mi>cos</mi><mspace width="1em" /><msub><mi mathvariant="normal">B</mi><mi>true</mi></msub><mo mathvariant="normal">=</mo><mfrac><msub><mi mathvariant="normal">R</mi><mi>ytrue</mi></msub><msub><mi mathvariant="normal">R</mi><mi>true</mi></msub></mfrac></math><img file="EP1531339B1_D0054.tif" /></maths>is obtained with equations (a) and (b) for the true distance R_true to the goal <maths id="math0055" num=""><math display="block"><msub><mi mathvariant="normal">R</mi><mi>true</mi></msub><mo mathvariant="normal">=</mo><msqrt><msup><msub><mi mathvariant="normal">R</mi><mi mathvariant="normal">x</mi></msub><mn mathvariant="normal">2</mn></msup><mo>⁢</mo><mi>true</mi><mo mathvariant="normal">+</mo><msup><msub><mi mathvariant="normal">R</mi><mi mathvariant="normal">y</mi></msub><mn mathvariant="normal">2</mn></msup><mo>⁢</mo><mi>true</mi></msqrt></math><img file="EP1531339B1_D0055.tif" /></maths><maths id="math0056" num="(i)"><math display="block"><msub><mi mathvariant="normal">R</mi><mi>true</mi></msub><mo mathvariant="normal">=</mo><msqrt><msup><mfenced separators=""><msub><mi mathvariant="normal">R</mi><mi>xest</mi></msub><mo mathvariant="normal">-</mo><msub><mi mathvariant="normal">ΔR</mi><mi mathvariant="normal">x</mi></msub></mfenced><mn mathvariant="normal">2</mn></msup><mo>⁢</mo><msup><mfenced separators=""><msub><mi mathvariant="normal">R</mi><mi>yest</mi></msub><mo mathvariant="normal">-</mo><msub><mi mathvariant="normal">ΔR</mi><mi mathvariant="normal">y</mi></msub></mfenced><mn mathvariant="normal">2</mn></msup></msqrt></math><img file="EP1531339B1_D0056.tif" /></maths>is there <maths id="math0057" num=""><math display="block"><msub><mi mathvariant="normal">ΔR</mi><mi mathvariant="normal">x</mi></msub><mo mathvariant="normal">=</mo><msub><mi mathvariant="normal">Δx</mi><mn mathvariant="normal">0</mn></msub><mo mathvariant="normal">+</mo><msub><mi mathvariant="normal">Δv</mi><mi mathvariant="normal">x</mi></msub><mo mathvariant="normal">⋅</mo><mi mathvariant="normal">Δt</mi></math><img file="EP1531339B1_D0057.tif" /></maths><maths id="math0058" num=""><math display="block"><msub><mi mathvariant="normal">ΔR</mi><mi mathvariant="normal">y</mi></msub><mo mathvariant="normal">=</mo><msub><mi mathvariant="normal">Δy</mi><mn mathvariant="normal">0</mn></msub><mo mathvariant="normal">+</mo><msub><mi mathvariant="normal">Δv</mi><mi mathvariant="normal">x</mi></msub><mo mathvariant="normal">⋅</mo><mi mathvariant="normal">Δt</mi><mn>.</mn></math><img file="EP1531339B1_D0058.tif" /></maths>

0068In equation (c) for the radial velocity component V_R Equations (e), (f), (g), (h) and (i) are now used, and one obtains for the Doppler shift depending on the error vector ΔP = (Δx₀, ΔY₀, Δv_{x '} Δv_y): <maths id="math0059" num=""><math display="block"><mi>Q</mi><mfenced separators=""><mi mathvariant="normal">Δ</mi><mo>⁢</mo><mi>P</mi></mfenced><mo>=</mo><mfrac><msub><mi>v</mi><mi>R</mi></msub><mi>c</mi></mfrac><mo>=</mo><mfrac><mn>1</mn><mi>c</mi></mfrac><mo>⁢</mo><mfrac><mrow><mfenced separators=""><msub><mover><mi>R</mi><mo>˙</mo></mover><mi mathvariant="italic">xest</mi></msub><mo>-</mo><mi mathvariant="normal">Δ</mi><mo>⁢</mo><msub><mover><mi>R</mi><mo>˙</mo></mover><mi>x</mi></msub></mfenced><mo>⁢</mo><mfenced separators=""><msub><mi>R</mi><mi mathvariant="italic">xest</mi></msub><mo>-</mo><msub><mrow><mi mathvariant="normal">Δ</mi><mo>⁢</mo><mi>R</mi></mrow><mi>x</mi></msub></mfenced><mo>+</mo><mo>(</mo><msub><mover><mi>R</mi><mo>˙</mo></mover><mi mathvariant="italic">yest</mi></msub><mo>-</mo><mi mathvariant="normal">Δ</mi><mo>⁢</mo><msub><mover><mi>R</mi><mo>˙</mo></mover><mi>y</mi></msub><mo>)</mo><mfenced separators=""><msub><mi>R</mi><mi mathvariant="italic">yest</mi></msub><mo>+</mo><msub><mrow><mi mathvariant="normal">Δ</mi><mo>⁢</mo><mi>R</mi></mrow><mi>y</mi></msub></mfenced></mrow><msqrt><msup><mfenced separators=""><msub><mi>R</mi><mi>sest</mi></msub><mo>-</mo><msub><mrow><mi mathvariant="normal">Δ</mi><mo>⁢</mo><mi>R</mi></mrow><mi>x</mi></msub></mfenced><mn>2</mn></msup><mo>⁢</mo><mfenced><msup><mfenced separators=""><msub><mi>R</mi><mi>yest</mi></msub><mo>-</mo><msub><mrow><mi mathvariant="normal">Δ</mi><mo>⁢</mo><mi>R</mi></mrow><mi>y</mi></msub></mfenced><mn>2</mn></msup></mfenced></msqrt></mfrac></math><img file="EP1531339B1_D0059.tif" /></maths>

0069The transmission frequency F_sthat is emitted from the target will result in an error ΔF_s estimated <maths id="math0060" num=""><math display="block"><msub><mi mathvariant="normal">F</mi><mi>sest</mi></msub><mo mathvariant="normal">=</mo><msub><mi mathvariant="normal">F</mi><mi>strue</mi></msub><mo>+</mo><msub><mi mathvariant="normal">ΔF</mi><mi mathvariant="normal">s</mi></msub></math><img file="EP1531339B1_D0060.tif" /></maths><maths id="math0061" num=""><math display="block"><msub><mi mathvariant="normal">F</mi><mi>strue</mi></msub><mo mathvariant="normal">=</mo><msub><mi mathvariant="normal">F</mi><mi>sest</mi></msub><mo mathvariant="normal">-</mo><msub><mi mathvariant="normal">ΔF</mi><mi mathvariant="normal">s</mi></msub></math><img file="EP1531339B1_D0061.tif" /></maths>and together with the Doppler shift Q provides the reception frequency F_mess.

0070The Doppler frequency F_true is estimated as an error with an error difference ΔF. <maths id="math0062" num=""><math display="block"><msub><mi mathvariant="normal">F</mi><mi>true</mi></msub><mo mathvariant="normal">=</mo><msub><mi mathvariant="normal">F</mi><mi>est</mi></msub><mo mathvariant="normal">-</mo><mi mathvariant="normal">ΔF</mi></math><img file="EP1531339B1_D0062.tif" /></maths>

0071Since the transmission frequency F_s is unknown, the error vector is ΔP by a further error term ΔF_s for the estimation of the transmission frequency F_sest to expand: <maths id="math0063" num=""><math display="block"><msub><mi mathvariant="normal">ΔP</mi><mn mathvariant="normal">1</mn></msub><mo mathvariant="normal">=</mo><mfenced><msub><mi mathvariant="normal">Δx</mi><mn mathvariant="normal">0</mn></msub><mo>⁢</mo><msub><mi mathvariant="normal">Δy</mi><mn mathvariant="normal">0</mn></msub><mo>⁢</mo><msub><mi mathvariant="normal">Δv</mi><mi mathvariant="normal">x</mi></msub><mo>⁢</mo><msub><mi mathvariant="normal">Δv</mi><mi mathvariant="normal">y</mi></msub><mo>⁢</mo><msub><mi mathvariant="normal">ΔF</mi><mi mathvariant="normal">s</mi></msub></mfenced></math><img file="EP1531339B1_D0063.tif" /></maths>

0072The estimated Doppler frequency is F_iest equal to the measured reception frequency F_imess for ΔP = 0, namely if the transmission frequency has been correctly estimated.

0073One obtains for the estimated Doppler frequency F_iest a sum equal to the measured reception frequency F_imess plus the frequency difference ΔF_i is. <maths id="math0064" num=""><math display="block"><msub><mi mathvariant="normal">F</mi><mi>imess</mi></msub><mo mathvariant="normal">+</mo><msub><mi mathvariant="normal">ΔF</mi><mi mathvariant="normal">i</mi></msub><mo mathvariant="normal">=</mo><msub><mi mathvariant="normal">F</mi><mi>iest</mi></msub></math><img file="EP1531339B1_D0064.tif" /></maths><maths id="math0065" num=""><math display="block"><msub><mi mathvariant="normal">ΔF</mi><mi mathvariant="normal">i</mi></msub><mo mathvariant="normal">=</mo><msub><mi mathvariant="normal">F</mi><mi>imess</mi></msub><mo mathvariant="normal">-</mo><msub><mi mathvariant="normal">F</mi><mi>iest</mi></msub><mn mathvariant="normal">.</mn></math><img file="EP1531339B1_D0065.tif" /></maths>

0074To determine the Doppler frequency, the frequency difference ΔF_i be minimized.

0075The determination of the target data is improved for the transmission frequency F emitted by the target_S Limit values ​​are specified and added to the algorithm. The transmission frequency F emitted by the target_S experiences through the radial velocity component V_R to the carrier vehicle its Doppler shift and is used as the receiving frequency F_mess = F together with the first bearing angle B_first measured: <maths id="math0066" num="(16)"><math display="block"><mi>F</mi><mo>=</mo><msub><mi>F</mi><mi>s</mi></msub><mo>⁢</mo><mfrac><mrow><mi>c</mi><mo>+</mo><msub><mi>V</mi><mi mathvariant="italic">REigen</mi></msub></mrow><mrow><mi>c</mi><mo>-</mo><msub><mi>V</mi><mi mathvariant="italic">Target</mi></msub></mrow></mfrac></math><img file="EP1531339B1_D0066.tif" /></maths>Taking the Doppler shift into account, the transmission frequency is F_s: <maths id="math0067" num="(17)."><math display="block"><msub><mi>F</mi><mi>S</mi></msub><mo>=</mo><mi>F</mi><mo>⁢</mo><mfrac><mrow><mi>C.</mi><mo>-</mo><msub><mi>V</mi><mi mathvariant="italic">Target</mi></msub></mrow><mrow><mi>c</mi><mo>+</mo><msub><mi>V</mi><mi mathvariant="italic">REigen</mi></msub></mrow></mfrac></math><img file="EP1531339B1_D0067.tif" /></maths>From the limit values ​​for the speed V_min ≤ V ≤ V_Max limit values ​​for the transmission frequency F_S determined: <maths id="math0068" num="(18)"><math display="block"><mi>F</mi><mo>⁢</mo><mfrac><mrow><mi>c</mi><mo>-</mo><msub><mi>V</mi><mi>Max</mi></msub></mrow><mrow><mi>c</mi><mo>+</mo><msub><mi>V</mi><mi mathvariant="italic">REigen</mi></msub></mrow></mfrac><mo>≤</mo><msub><mi>F</mi><mi>s</mi></msub><mo>≤</mo><mi>F</mi><mo>⁢</mo><mfrac><mrow><mi>c</mi><mo>-</mo><msub><mi>V</mi><mi>min</mi></msub></mrow><mrow><mi>c</mi><mo>+</mo><msub><mi>V</mi><mi mathvariant="italic">REigen</mi></msub></mrow></mfrac></math><img file="EP1531339B1_D0068.tif" /></maths>

0076The limit values ​​for the transmission frequency are used when determining the error ΔF_s to estimate the transmission frequency and thus also to minimize the frequency difference ΔF between the measured reception frequency F_mess and estimated Doppler frequency F_est considered.

0077Further measurement uncertainties for the reception frequency and the speed of sound c can also be taken into account.

0078FIG. 7 shows a block diagram of a sonar reception system for determining the target data P with an adaptive filter arrangement for evaluating measured bearing angles B._imess and reception frequencies F_imess. Received signals from a converter arrangement 10 are combined in a directional generator 11 by delay or phase compensation to form group signals and a target at a bearing angle B_imess detected with a measuring circuit 12. The measuring circuit 12 is a control circuit 13 at intervals of time Δt_i controlled. The entire signal processing takes place at intervals of the time intervals Δt. An estimation circuit 15 receives the north direction as input data from a compass device 16 as a reference direction N.₀, the autoposition x_E, y_E the converter arrangement 10 from an on-board navigation system 17 and from a start state circuit 18 boundary conditions for the position estimation, which are determined from limit values ​​for the distance R, the speed V, and the course K of the target. From the last measured bearing angle B_first and the limit value for the distance R become the boundary conditions for the position components x₀ / y₀ certainly: <maths id="math0069" num=""><math display="block"><mtable><mtr><mtd><msub><mi mathvariant="normal">R</mi><mi>min</mi></msub><mo>⁢</mo><msub><mrow><mspace width="1em" /><mi>sin B</mi></mrow><mi>first</mi></msub><mo mathvariant="normal">≤</mo><msub><mi mathvariant="normal">X</mi><mn mathvariant="normal">0</mn></msub><mo mathvariant="normal">≤</mo><msub><mi mathvariant="normal">R</mi><mi>Max</mi></msub><mo>⁢</mo><msub><mrow><mspace width="1em" /><mi>sin B</mi></mrow><mi>first</mi></msub></mtd></mtr><mtr><mtd><msub><mi>minX</mi><mn mathvariant="normal">0</mn></msub><mo mathvariant="normal">≤</mo><msub><mi mathvariant="normal">X</mi><mn mathvariant="normal">0</mn></msub><mo mathvariant="normal">≤</mo><msub><mi>maxX</mi><mn mathvariant="normal">0</mn></msub></mtd></mtr></mtable></math><img file="EP1531339B1_D0069.tif" /></maths><maths id="math0070" num=""><math display="block"><mtable><mtr><mtd><msub><mi mathvariant="normal">R</mi><mi>min</mi></msub><mo>⁢</mo><msub><mrow><mspace width="1em" /><mi>cos B</mi></mrow><mi>first</mi></msub><mo mathvariant="normal">≤</mo><msub><mi mathvariant="normal">Y</mi><mn mathvariant="normal">0</mn></msub><mo mathvariant="normal">≤</mo><msub><mi mathvariant="normal">R</mi><mi>Max</mi></msub><mo>⁢</mo><msub><mrow><mspace width="1em" /><mi>cos B</mi></mrow><mi>first</mi></msub></mtd></mtr><mtr><mtd><msub><mi>minY</mi><mn mathvariant="normal">0</mn></msub><mo mathvariant="normal">≤</mo><msub><mi mathvariant="normal">Y</mi><mn mathvariant="normal">0</mn></msub><mo mathvariant="normal">≤</mo><msub><mi>laxY</mi><mn mathvariant="normal">0</mn></msub></mtd></mtr></mtable></math><img file="EP1531339B1_D0070.tif" /></maths>

0079From the given limit values ​​for the speed V and the course K, the boundary conditions for the speed components V_x / V_y certainly: <maths id="math0071" num=""><math display="block"><msub><mi mathvariant="normal">V</mi><mi>xmin</mi></msub><mo>≤</mo><msub><mi mathvariant="normal">V</mi><mi mathvariant="normal">x</mi></msub><mo>≤</mo><msub><mi mathvariant="normal">V</mi><mi>xmax</mi></msub></math><img file="EP1531339B1_D0071.tif" /></maths><maths id="math0072" num=""><math display="block"><msub><mi mathvariant="normal">V</mi><mi>ymin</mi></msub><mo>≤</mo><msub><mi mathvariant="normal">V</mi><mi mathvariant="normal">y</mi></msub><mo>≤</mo><msub><mi mathvariant="normal">V</mi><mi>ymax</mi></msub><mo>,</mo></math><img file="EP1531339B1_D0072.tif" /></maths>as is in connection with FIGS. 2 and 3 for the cases <maths id="math0073" num=""><math display="block"><mn mathvariant="normal">90</mn><mo mathvariant="normal">&lt;</mo><mfenced open="|" close="|" separators=""><msub><mi mathvariant="normal">K</mi><mi>Max</mi></msub><mo mathvariant="normal">-</mo><msub><mi mathvariant="normal">K</mi><mi>min</mi></msub></mfenced><mo mathvariant="normal">&lt;</mo><mn mathvariant="normal">180</mn><mspace width="1em" /><mi>and</mi><mspace width="1em" /><mo mathvariant="normal">|</mo><msub><mi mathvariant="normal">K</mi><mi>Max</mi></msub><mo mathvariant="normal">-</mo><msub><mi mathvariant="normal">K</mi><mi>min</mi></msub><mo mathvariant="normal">|</mo><mo mathvariant="normal">&lt;</mo><mn mathvariant="normal">90</mn></math><img file="EP1531339B1_D0073.tif" /></maths>was explained.

0080The estimated transmission frequency F_s and the limits <maths id="math0074" num=""><math display="block"><mi>F</mi><mo>⁢</mo><mfrac><mrow><mi>c</mi><mo>-</mo><msub><mi>V</mi><mi>Max</mi></msub></mrow><mrow><mi>c</mi><mo>+</mo><msub><mi>V</mi><mi mathvariant="italic">REigen</mi></msub></mrow></mfrac><mo>≤</mo><msub><mi>F</mi><mi>s</mi></msub><mo>≤</mo><mi>F</mi><mo>⁢</mo><mfrac><mrow><mi>c</mi><mo>-</mo><msub><mi>V</mi><mi>min</mi></msub></mrow><mrow><mi>c</mi><mo>+</mo><msub><mi>V</mi><mi mathvariant="italic">REigen</mi></msub></mrow></mfrac></math><img file="EP1531339B1_D0074.tif" /></maths>are determined in a frequency circuit 19 which is connected on the input side to the start state circuit 18. The group signals at the output of the direction generator 11 are analyzed in a frequency analysis circuit 24. The received frequency determined is fed to the frequency circuit 19 and a differential circuit 23.

0081The start state circuit 18 supplies position components x_i and y_i, Speed ​​components v_ix and V_iy in the x and y directions, the frequency circuit 19 transmission frequencies F_s, an error estimation arrangement 20 an error vector ΔP₀ = (Δ_x0, Δ_y0, Δ_vx, Δ_vy, ΔF_s). From this input data, path components R are calculated in the estimation circuit 15 in accordance with the estimation equations (A) and (B)_xiest, R_yiest and path error ΔR_xi, ΔR_yi an estimated position. From the estimated path components R_xiest, R_yiest and their changes over time R_xiest and R_yiest and the errors ΔR_xi, ΔR_yi and ΔR_xi and ΔR_yi becomes the frequency difference AF_i determined within the limits for the transmission frequency specified by the frequency circuit 19. From these estimated values ​​within the limit values, the bearing angle B estimated in an arctangent circuit 21_iest calculated according to equation I.

0082the differential circuit 23, which is arranged downstream of the measuring circuit 12, the estimation circuit 15 and the frequency analysis circuit 24, are determined within the predetermined limit values ​​bearing angle differences and frequency differences.

0083About i = l_k Measurements per self-laying, the number l_k is specified in a control circuit 60, the measured and estimated bearing angles B_imess and B_iest evaluated. The time period l_k • Δt indicates the filter length.

0084The start state circuit 18 determines an optimization rotation angle α from the limit values ​​for the course, as was explained in connection with FIG. 2b. This optimization rotation angle α is taken into account when determining the boundary conditions for the speed components and also when estimating the position in the estimation circuit 15.

0085The outputs of the differential circuit 23 are connected to an iteration circuit 30, in which the minimum of the sum of the bearing angle difference and the frequency difference or their squared difference values ​​is iteratively formed. The minimization is carried out until the error vector ΔP₁ a lower threshold ΔP₁ less than or equal to ΔP_min falls below.

0086For every measured bearing angle B_imess 15 path components R_xest and R_yest and path error ΔR_x and ΔR_y determined within the limit values ​​for the distance, the speed and the course and the transmission frequency until the error vector ΔP₁ a lower threshold ΔP₁ ≤ ΔP_min falls below and the target data have converged to a value. Except for a residual error determined by the threshold, the estimated bearing angle B is then_est is the true measured bearing angle B_true and the estimated path and speed components R_xest, R_yest, V_xest, V_yest equal to the true path and speed components R_ytrue, R_ytrue, V_xtrue, V_ytrue and the estimated Doppler frequency F_iest equal to the true Doppler frequency F received_true. The threshold circuit 31 used for this is connected downstream of the iteration circuit 30 and controls the error estimation arrangement 20. If the threshold ΔP is undershot_min the target data P are shown in a display 100.

00878 and 9 show results for evaluating the method according to the invention. Limits are given for a starting goal:<maths id="math0075" num=""><math display="block"><mn mathvariant="normal">1</mn><mspace width="1em" /><mi>km</mi><mo mathvariant="normal">≤</mo><mi mathvariant="normal">R</mi><mo mathvariant="normal">≤</mo><mn mathvariant="normal">60</mn><mspace width="1em" /><mi>km</mi></math><img file="EP1531339B1_D0075.tif" /></maths><maths id="math0076" num=""><math display="block"><mn mathvariant="normal">100</mn><mo>⁢</mo><mi mathvariant="normal">°</mi><mo mathvariant="normal">≤</mo><mi mathvariant="normal">K</mi><mo mathvariant="normal">≤</mo><mn mathvariant="normal">260</mn><mo>⁢</mo><mi mathvariant="normal">°</mi></math><img file="EP1531339B1_D0076.tif" /></maths><maths id="math0077" num=""><math display="block"><mn mathvariant="normal">0</mn><mspace width="1em" /><mi mathvariant="normal">m</mi><mo mathvariant="normal">/</mo><mi mathvariant="normal">s</mi><mo mathvariant="normal">≤</mo><mi mathvariant="normal">V</mi><mo mathvariant="normal">≤</mo><mn mathvariant="normal">10</mn><mspace width="1em" /><mi mathvariant="normal">m</mi><mo mathvariant="normal">/</mo><mi mathvariant="normal">s</mi></math><img file="EP1531339B1_D0077.tif" /></maths>

0088Below the diagrams are the length L of the self-laying in (m), the speed V in (kn) and the course K in (degrees) of the carrier vehicle.

0089FIG. 8 shows the convergence of the method in the event that the target is at a first bearing angle of B_first = 0 ° and an initial distance of 30 kilometers. The target travels at a speed of 10 knots on a course of K = 170 °. The measurement time is indicated horizontally, vertically the respective error in the upper diagram for the course, in the middle diagram for the distance, in the lower diagram for the speed. You can see that the course begins to converge after 10 minutes and after approx. 20 min the course error ΔK &lt;± 5 °, whereas in the conventional method this value is only reached after 30 min. The distance estimate already shows an error that is less than 10% after 12 minutes and less than 5% after 16 minutes. The speed estimate begins to converge after 11 minutes. After 20 minutes, the estimate shows an error of ΔV = ± 1.5 m / s. The target data was estimated without frequency analysis and determination of a reception frequency, so that limit values ​​for the transmission frequency are not used.

0090FIG. 9 shows the errors over time for a target that was found under B at the start of the measurements_first = 0 ° in and an initial distance of 20 km. The target travels at a speed of 10 knots on a course of 180 °. The course error is already less than 5 ° after 11 minutes, the distance error is less than 10% after 11 minutes and less than 5% after 16 minutes. The speed estimate begins to converge after 7 minutes. After 20 minutes the error is less than 1 m / s.

0091If one compares these results with an estimate of the target data without limit values, it is found that the convergence times are considerably shorter, and still decrease, even if the Doppler shift of a transmission frequency specified within limits by comparison with a measured reception frequency to minimize the bearing angle and frequency difference according to the Least Square algorithm.