Method of passive determination of target data

The 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.

In order to determine without self-betrayal of a carrier vehicle, such as a surface ship or submarine, position, speed and heading of a target, such as a surface ship, submarine or torpedo as the target data, are received with a sonar receiver sound waves of the target noise and bearing angle to Target measured. From these bearing angles, together with the eigenpositions of the host vehicle, a position of the target is estimated and an associated estimated bearing angle is calculated. Iteratively, the difference between the measured and the estimated bearing angle is reduced until an error limit is reached. The underlying estimated position is recognized as the target position.

Starting from an initial position of the target, which, for example, is arbitrarily chosen as the start position on a first beacon or is known by other sensors on board, positions are calculated from estimated xy components for the target and estimated bearing angles determined therefrom. The host vehicle travels for constant-level bearing angle measurements for a predetermined period of time and travels a path called Eigenleg, after a course change, the target is further targeted by this eigenlayer. The respective 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, with the exception of a residual error. The residual error depends on a predefinable threshold. Such a filter arrangement is described for example in DE 34 46 658 C2. The iteration time of this filter arrangement is significantly determined by additional inputs. By way of example, the starting position or supporting values ​​which are determined by observation or measured values ​​of other sensors on board the carrier vehicle, eg periscope observations or radar measurements, are entered. Filter coefficients are determined from these support values, which lead to an improved first estimate of the target position.

It 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 becomes comparable or even shorter when using the mentioned filter arrangement, without the need for measurement values ​​of other sensors on board the carrier vehicle as support values.

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

Receiving signals of at least one electroacoustic transducer arrangement, for example a horseshoe base or side antenna on board a submarine as a carrier vehicle and / or a towed by a surface ship or a submarine towed antenna are summarized in the sonar receiver direction selective to group signals and observed the levels of the group signals. 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 his bearing is present. The orator, for example, sets a limit for a maximum possible distance of the target, which he derives from geographic and oceanographic knowledge and the specification of the sonar receiving facility, eg sixty kilometers. A minimum distance, from eg One kilometer is derived from a possible threat situation for the carrier vehicle. Speed ​​limits are between just over zero knots to eliminate fixed targets, and speed limits for speedboats or torpedoes. Even rough prescriptions shorten the computation time and make it possible to exclude estimates of target positions that are impossible to detect with the sonar receiver. From these predetermined limits boundary conditions for position components and velocity components are determined and used as the basis for estimating the position of the target, with which the estimated bearing angle is determined to minimize the bearing angle difference.

The advantage of the inventive method according to claim 1 is that only physically and technically meaningful parameters about the position of the target, its speed and its course are entered into the iterative estimation process by the limit values. Completely illogical results, such as A speed of one hundred knots or a distance of a thousand kilometers are excluded from the outset, which could well have been incurred in the course of the iteration in the case of strongly noisy reception signals.

The advantageous development of the method according to the invention as claimed in claim 2 is that the upper limit value for the target distance is derived from on-board sound propagation programs for the sea area. Since the target is to be located only in those zones that allow sound transmission from the destination to the receiving location and correspond to the detection range of the sonar receiving system, it is advantageous to use this knowledge, since more distant targets could not be detected at all.

Alone the limitation of the course to incoming goals according to the advantageous development of the method according to claim 3 drastically increases the convergence speed of the position estimate, even if the course of the target is almost perpendicular to the direction of the beam and a slightly deviating expiring course in the position estimate is no longer considered. The first input of the limitation of the course to incoming goals already ensures that erroneous position estimates are excluded.

The limits for the target speed according to the embodiment of the method according to claim 4 are derived from the driving characteristics of different watercraft, eg surface ships, submarines and torpedoes.

By measuring the change in the bearing angle, it is possible according to the advantageous development of the method according to claim 5, determine the course direction with respect to the first beam and with this page identifier to further limit the limits for the course with which the target of the sonar receiving system approaches.

By setting limit values, the estimate of the target data is adapted to the 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 least squares constraints 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 solve the algorithm given in the book numerically. This mathematical tool is ideally suited to determine the target position from given limit values ​​with the advantage that the convergence times for the determination of the target data are almost halved even under the most difficult positioning conditions.

During the journey of the carrier vehicle on the respective Eigenleg along its course, bearing angles are continuously measured. In the advantageous development of the method according to the invention as claimed in claims 6 and 7, 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 heading is approaching. In order for the target to be able to reach just the last measured beacon beam from the maximum distance on the first beacon, it must travel there at maximum speed. From the lot length between the maximum distance and the bearing beam associated with the last bearing divided by the time interval, the upper limit of the speed is determined. The lot length to the first directional beam includes the minimum heading for the approaching heading and is the lower limit of the heading. The lower limit of speed or minimum distance is determined by the target traversing a path from the minimum distance of the target on the first beacon to the last beacon during the time interval along the lower bound for the heading. This path divided by the time interval indicates the limit for the minimum speed.

The other upper limit of the course is determined according to the advantageous development according to claim 8, in that the target reaches the second beam from the minimum distance on the first beam at maximum speed during the time interval. A distance corresponding to the maximum speed taking into account the time interval intersects the last directional beam and includes the maximum course angle.

From the limit values ​​for the speeds and the course, according to the advantageous development of the method according to the invention as claimed in claims 9, 10 and 11, the boundary conditions are calculated in an xy coordinate system for estimating a new target position. It is assumed that the target could move along the two limits for the minimum and maximum speed course within the time interval and take up new positions on the next beacon. The velocity limits are decomposed into orthogonal velocity components whose extremes span a boundary area. This border area limits all speed vectors possible for the destination in terms of magnitude and direction and indicates the associated speed components. With these velocity components and the positional components in the xy direction for all distances within the given limits on the first directional beam, a target start position and a velocity vector of the target pointing in heading direction are estimated. Target positions are estimated and estimated bearing angles are determined from the resulting target path, which crosses a bearing beam of bearing beams of the previously measured bearing angle. All estimated bearing angles are used with the measured bearing angles for determining the least square of the error and the minimum of the bearing angle differences is searched for. The advantage lies in particular in a further restriction of the uncertainty area for possible target start positions and velocity vectors and thus faster convergence of the filtering method through fewer iterations.

The advantageous developments of the method according to the invention as claimed in claims 12-14 take into account the difference between the threshold values ​​for a starting course in 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 relative to the bearing and course reference system by an optimization rotation angle which is selected as a function of the difference in the course angles defined by the limits. This limits the border area to one quadrant with either only right-pointing or only left-pointing limits and a difference of less than 90 °. If the difference between the 90 ° and 180 ° heading angles specified by the limits is selected, the optimization angle of rotation will be such that the maximum and minimum speeds along the course limits are symmetrical to the y-axis in two quadrants.

With the advantageous development of the method according to the invention, the optimization angle of rotation is chosen equal to the negative measured bearing angle for a difference of the predetermined course angle greater than 180 °, at which the course can even be estimated.

To passively determine the target data, the host vehicle travels along its own course at a constant speed and heading, and measures bearing angles to the target. When using an on-board antenna and a towed antenna further behind the host vehicle, the target data can already be determined without changing course. If the host vehicle has only a single receiving antenna for pointing, the target data may be determined only after a first self-maneuver. The advantageous development of the inventive method according to claim 16 allows a target data measurement already when driving through the first Eigenlegs when using only one receiving antenna. From DE 101 29 726 A1 it is known that the reception frequency is dependent on the own radial velocity component of the host vehicle and pointing in the same direction radial velocity of the target. Knowing one's own speed, one can eliminate the intrinsic contribution to the Doppler shift and only consider the target share. Apart from the change in frequency over time, the so-called frequency deviation, a change in the bearing position over time takes place while driving along the self-level. The time until target data can be estimated stably is called convergence time. The convergence time is shorter, the greater the frequency deviation when passing through a Eigenlegs.

After 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 highest level or the frequency spacing of adjacent spectral lines is taken as the basis for the reception frequency together with the measured bearing angle of the target data estimate. Target positions are estimated and estimated bearing angles are determined. A bearing angle difference is determined between the measured and estimated bearing angle. In addition, a Doppler shift and a transmit frequency radiated or emitted by the target are estimated from the same estimated target positions and their temporal changes. The estimated transmit frequency is frequency shifted according to the estimated Doppler shift and forms the estimated Doppler frequency from which the receive frequency is subtracted. The difference between the reception 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.

For the given limits of the speed limits of the Doppler shift are determined according to the advantageous development of the method according to claim 16 and linked to the measured reception frequency. Thus one obtains limits of the estimated transmission frequency. From the estimated target positions, Doppler shifts are determined and linked to the estimated transmission frequency and its limits. The frequency difference to the measured reception frequency is iteratively minimized for the target data determination together with the bearing angle difference. The advantage of the method according to claim 16 is in particular that the minimization of the frequency difference is based on the estimated Doppler frequencies which are determined from possible velocity components of the estimated target position and its limits. Taking into account the bearing to the target, these velocity components correspond to the limits of a radial velocity component, which in turn causes the Doppler shift of the transmission frequency of the target. By determining and involving the receiving frequency to estimate the target data, there is the advantage of determining a first target position or starting position without self-maneuvering, separating and determining multiple targets and their target data under the same bearing, and further shortening the convergence times for the target position estimates.

The invention is described in more detail with reference to the drawing in an embodiment of a method for passively determining 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 limits,</dd><dt>Fig. 2.3</dt><dd>xy coordinate systems for determining the boundary conditions for orthogonal velocity components,</dd><dt>Fig. 4</dt><dd>Charts 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>

Fig. 1 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 towed antenna, a noise emitted by a target from an incident direction along a first aiming beam P_ridge at a first bearing angle B_ridge detected. The destination is on approaching course B_ridge + 90 &lt;K_min ≤ K ≤ K_Max &lt;B_ridge - 90. At the moment to the carrier vehicle is at origin 0/0. The y-axis gives the north direction N₀ as a reference direction. At time t₁ the host vehicle has the location II with constant airspeed V_own achieved while the target on his course K at a speed V takes a next target position. On the first beacon P_ridge are predetermined limits R_min and R_Max for the removal of the target with Z_0min and Z_{0 max} designates and predefined limit values ​​K_min and K_Max entered for an incoming course of the destination. If the target is located directly on the beacon P_ridge approaching the host vehicle on a collision course, is the maximum limit for the course<maths id="math0001" num="(1)."><math display="block"><mrow><msub><mrow><mtext>K</mtext></mrow><mrow><mtext>Max</mtext></mrow></msub><msub><mrow><mtext> = B</mtext></mrow><mrow><mtext>ridge</mtext></mrow></msub><mtext> + 180°</mtext></mrow></math><img file="EP1531339A2_D0001.tif" /></maths>

If the target moves across, the heading angle is<maths id="math0002" num="(2)."><math display="block"><mrow><msub><mrow><mtext>K</mtext></mrow><mrow><mtext>min</mtext></mrow></msub><msub><mrow><mtext> = B</mtext></mrow><mrow><mtext>ridge</mtext></mrow></msub><mtext> ± 90°</mtext></mrow></math><img file="EP1531339A2_D0002.tif" /></maths>

An emigration of the bearing from the bearing angle B_ridge to the bearing angle B_load shows that the target is not on a collision course. The temporal change of the bearing limits the course by a page identifier to the right or left of the beacon P_ridge and thus limits the course:<maths id="math0003" num="(3)."><math display="block"><mrow><msub><mrow><mtext>B</mtext></mrow><mrow><mtext>ridge</mtext></mrow></msub><msub><mrow><mtext> + 90 ° ≤ K &lt;B</mtext></mrow><mrow><mtext>ridge</mtext></mrow></msub><mtext> + 180°</mtext></mrow></math><img file="EP1531339A2_D0003.tif" /></maths>

There will be a limit for the maximum speed V_Max given and provided that the target Z moves so that the lower limit of the velocity V_min &gt; 0 is:<maths id="math0004" num="(4)."><math display="block"><mrow><msub><mrow><mtext>0 &lt;V ≤ V</mtext></mrow><mrow><mtext>Max</mtext></mrow></msub></mrow></math><img file="EP1531339A2_D0004.tif" /></maths>

With the maximum speed, the goal of Z_{0 max} at R_Max or from Z_0min at R_min around the path V_Max dt below a heading angle B_ridge + 90 ° ≤ K &lt;B_ridge + 180 ° to a location on the arcs 10 and 11 indicated by dashed lines. If the velocity V is smaller, the target is within the specified circle segments. The boundary conditions for the coordinates for the estimated target position are calculated taking into account the limit values ​​R_min, R_Max, K_min, K_Max and V_Max calculated.

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

In Fig. 2a is given as a further example, a starting course of the target of eg 100 &lt;K &lt;260 as limits for the course. The bearing angle is B_ridge = 0 °. Observations, for example, limit the velocity V_min &lt;V &lt;V_Max determined with 5Kn &lt;V &lt;20Kn. The difference between maximum heading angle K_Max &lt;260 ° and minimum heading angle K_min &gt; 100 °<maths id="math0005" num=""><math display="block"><mrow><msub><mrow><mtext>Kmax - K</mtext></mrow><mrow><mtext>min</mtext></mrow></msub><mtext> = 160°</mtext></mrow></math><img file="EP1531339A2_D0005.tif" /></maths> and is less than 180 °.

Fig. 2a shows for this example in a Cartesian coordinate system the decomposition of the limit values ​​of the speed along the maximum and minimum course angle K_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. The xy velocity components, in addition to the xy position components for the limits of the distance, are the boundary conditions for input to the iteration calculation for determining the minimum of the bearing angle difference or the squared bearing angle difference from the measured and estimated beam angle. The limit values ​​V pointing in minimum and maximum course directions_Max and V_min of velocity are calculated in velocity components ± V_xmax/ ± V_ymax and ± V_xmin/ ± V_ymin disassembled. A hatched rectangle enclosed by the maximum and minimum velocity components in the x and y directions encloses a boundary area within which the target can move at a given velocity, due to the boundary conditions<maths id="math0006" num=""><math display="block"><mrow><msub><mrow><mtext>- V</mtext></mrow><mrow><mtext>xmax</mtext></mrow></msub><msub><mrow><mtext> &lt;V</mtext></mrow><mrow><mtext>x</mtext></mrow></msub><msub><mrow><mtext> &lt;+ V</mtext></mrow><mrow><mtext>xmax</mtext></mrow></msub></mrow></math><img file="EP1531339A2_D0006.tif" /></maths><maths id="math0007" num=""><math display="block"><mrow><msub><mrow><mtext>- V</mtext></mrow><mrow><mtext>Max</mtext></mrow></msub><msub><mrow><mtext> &lt;V</mtext></mrow><mrow><mtext>y</mtext></mrow></msub><msub><mrow><mtext> &lt;- V</mtext></mrow><mrow><mtext>ymin</mtext></mrow></msub></mrow></math><img file="EP1531339A2_D0007.tif" /></maths> are limited. From the six limit values, eight boundary conditions are determined, which are processed in the calculation algorithm. With these speed constraints from the heading and speed limits and the position constraints from the distance limits, target positions are determined and an associated bearing angle estimated. These associated estimated bearing angles are compared with the measured bearing angle. The smallest bearing angle difference then identifies the estimated position on the measured bearing beam with the associated velocity vector in the direction of the heading. At the beginning of the determination of the target data, the position and velocity vector for each determined minimum bearing angle difference are very different until they converge and come back calculated to a starting position on the first beam with the same values. The convergence times are the lower, the better the limit values ​​which are effective for the calculation coincide with the preset limit values ​​for speed V and course K.

The effective limits V *_min, V *_Max for the speed that the preset limits V_min and V_Max include, according to FIG. 2:<maths id="math0008" num=""><math display="block"><mrow><mtext mathvariant="italic">V</mtext><msub><mrow><mtext>*</mtext></mrow><mrow><mtext>min</mtext></mrow></msub><mtext> &lt; </mtext><mtext mathvariant="italic">V</mtext><mtext> &lt; </mtext><mtext mathvariant="italic">V</mtext><msub><mrow><mtext>*</mtext></mrow><mrow><mtext>Max</mtext></mrow></msub></mrow></math><img file="EP1531339A2_D0008.tif" /></maths><maths id="math0009" num=""><math display="block"><mrow><mtext>- </mtext><msub><mrow><mtext mathvariant="italic">V</mtext></mrow><mrow><mtext mathvariant="italic">y</mtext></mrow></msub><msub><mrow><mtext></mtext></mrow><mrow><mtext>min</mtext></mrow></msub><mtext> &lt; </mtext><mtext mathvariant="italic">V</mtext><mtext> &lt; </mtext><msqrt><msub><mrow><mtext mathvariant="italic">V</mtext></mrow><mrow><mtext mathvariant="italic">x</mtext></mrow></msub><msub><mrow><mtext></mtext></mrow><mrow><mtext>Max</mtext></mrow></msub><msup><mrow><mtext>​</mtext></mrow><mrow><mtext>2</mtext></mrow></msup><mtext> + </mtext><msub><mrow><mtext mathvariant="italic">V</mtext></mrow><mrow><mtext>Max</mtext></mrow></msub><msup><mrow><mtext>​</mtext></mrow><mrow><mtext>2</mtext></mrow></msup></msqrt></mrow></math><img file="EP1531339A2_D0009.tif" /></maths> With<maths id="math0010" num=""><math display="block"><mrow><msub><mrow><mtext>V</mtext></mrow><mrow><mtext>ymin</mtext></mrow></msub><msub><mrow><mtext> = V</mtext></mrow><mrow><mtext>min</mtext></mrow></msub><msub><mrow><mtext> sin (K</mtext></mrow><mrow><mtext>min</mtext></mrow></msub><mtext> - 90°)</mtext></mrow></math><img file="EP1531339A2_D0010.tif" /></maths> and<maths id="math0011" num=""><math display="block"><mrow><msub><mrow><mtext>V</mtext></mrow><mrow><mtext>xmax</mtext></mrow></msub><msub><mrow><mtext> = V</mtext></mrow><mrow><mtext>Max</mtext></mrow></msub><msub><mrow><mtext> • COS (K</mtext></mrow><mrow><mtext>min</mtext></mrow></msub><mtext> - 90°).</mtext></mrow></math><img file="EP1531339A2_D0011.tif" /></maths>

The effective limits K *_min, K *_Maxwhich include the predetermined limits for K are:<maths id="math0012" num=""><math display="block"><mrow><mtext mathvariant="italic">K</mtext><msub><mrow><mtext>*</mtext></mrow><mrow><mtext>min</mtext></mrow></msub><mtext> &lt; </mtext><mtext mathvariant="italic">K</mtext><mtext> &lt; </mtext><mtext mathvariant="italic">K</mtext><msub><mrow><mtext>*</mtext></mrow><mrow><mtext>Max</mtext></mrow></msub></mrow></math><img file="EP1531339A2_D0012.tif" /></maths><maths id="math0013" num=""><math display="block"><mrow><mtext>90 + tan </mtext><mfrac><mrow><msub><mrow><mtext mathvariant="italic">V</mtext></mrow><mrow><mtext mathvariant="italic">y</mtext></mrow></msub><msub><mrow><mtext></mtext></mrow><mrow><mtext>min</mtext></mrow></msub></mrow><mrow><msub><mrow><mtext mathvariant="italic">V</mtext></mrow><mrow><mtext mathvariant="italic">x</mtext></mrow></msub><msub><mrow><mtext></mtext></mrow><mrow><mtext>Max</mtext></mrow></msub></mrow></mfrac><mtext> &lt; </mtext><mtext mathvariant="italic">K</mtext><mtext> &lt;270 - tan</mtext><mfrac><mrow><msub><mrow><mtext mathvariant="italic">V</mtext></mrow><mrow><mtext mathvariant="italic">y</mtext></mrow></msub><msub><mrow><mtext></mtext></mrow><mrow><mtext>min</mtext></mrow></msub><mtext></mtext></mrow><mrow><msub><mrow><mtext mathvariant="italic">V</mtext></mrow><mrow><mtext mathvariant="italic">x</mtext></mrow></msub><msub><mrow><mtext></mtext></mrow><mrow><mtext>Max</mtext></mrow></msub></mrow></mfrac></mrow></math><img file="EP1531339A2_D0013.tif" /></maths>

In order to achieve the symmetrical ratios shown in Fig. 2a for the determination of the boundary conditions from the limits for speed and heading, so that the deviation of the components breaking down into components is the smallest of the predetermined limits, the coordinate system becomes an optimization turning angle α rotated as shown in FIG. 2b against the north direction N for the bearing and the course. The optimization rotation angle α is dependent on the limit values ​​for the course K<maths id="math0014" num=""><math display="block"><mrow><msub><mrow><mtext>180 - (K</mtext></mrow><mrow><mtext>Max</mtext></mrow></msub><msub><mrow><mtext> + K</mtext></mrow><mrow><mtext>min</mtext></mrow></msub><mtext>) / 2 = α.</mtext></mrow></math><img file="EP1531339A2_D0014.tif" /></maths>

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

FIG. 3 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 the course K are given:<maths id="math0015" num=""><math display="block"><mrow><msub><mrow><mtext>90 &lt;K &lt;K</mtext></mrow><mrow><mtext>Max</mtext></mrow></msub><mtext>,</mtext></mrow></math><img file="EP1531339A2_D0015.tif" /></maths> With<maths id="math0016" num=""><math display="block"><mrow><msub><mrow><mtext>K</mtext></mrow><mrow><mtext>Max</mtext></mrow></msub><msub><mrow><mtext> - K</mtext></mrow><mrow><mtext>min</mtext></mrow></msub><mtext> &lt; 90°.</mtext></mrow></math><img file="EP1531339A2_D0016.tif" /></maths>

The limits for the speed V are given:<maths id="math0017" num=""><math display="block"><mrow><msub><mrow><mtext>V</mtext></mrow><mrow><mtext>min</mtext></mrow></msub><msub><mrow><mtext> &lt;V &lt;V</mtext></mrow><mrow><mtext>Max</mtext></mrow></msub><mtext>.</mtext></mrow></math><img file="EP1531339A2_D0017.tif" /></maths>

This results in the boundary conditions<maths id="math0018" num=""><math display="block"><mrow><msub><mrow><mtext>V</mtext></mrow><mrow><mtext>xmin</mtext></mrow></msub><msub><mrow><mtext> &lt;V</mtext></mrow><mrow><mtext>x</mtext></mrow></msub><msub><mrow><mtext> &lt;V</mtext></mrow><mrow><mtext>Max</mtext></mrow></msub></mrow></math><img file="EP1531339A2_D0018.tif" /></maths><maths id="math0019" num=""><math display="block"><mrow><msub><mrow><mtext>- V</mtext></mrow><mrow><mtext>ymax</mtext></mrow></msub><msub><mrow><mtext> &lt;V</mtext></mrow><mrow><mtext>y</mtext></mrow></msub><mtext> &lt; 0</mtext></mrow></math><img file="EP1531339A2_D0019.tif" /></maths> in which<maths id="math0020" num=""><math display="block"><mrow><msub><mrow><mtext>V</mtext></mrow><mrow><mtext>xmin</mtext></mrow></msub><msub><mrow><mtext> = V</mtext></mrow><mrow><mtext>min</mtext></mrow></msub><msub><mrow><mtext> cos (K.</mtext></mrow><mrow><mtext>Max</mtext></mrow></msub><msub><mrow><mtext> - K</mtext></mrow><mrow><mtext>min</mtext></mrow></msub><mtext>)</mtext></mrow></math><img file="EP1531339A2_D0020.tif" /></maths> and<maths id="math0021" num=""><math display="block"><mrow><msub><mrow><mtext>V</mtext></mrow><mrow><mtext>ymax</mtext></mrow></msub><msub><mrow><mtext> = V</mtext></mrow><mrow><mtext>Max</mtext></mrow></msub><msub><mrow><mtext> sin (K</mtext></mrow><mrow><mtext>Max</mtext></mrow></msub><msub><mrow><mtext> - K</mtext></mrow><mrow><mtext>min</mtext></mrow></msub><mtext>)</mtext></mrow></math><img file="EP1531339A2_D0021.tif" /></maths>

The hatched rectangle indicates the border area within which the target can reach the next position below the respective heading at the respective speed.

The effective limits V *_min, V *_Max for the speed V amount<maths id="math0022" num=""><math display="block"><mrow><msub><mrow><mtext>V *</mtext></mrow><mrow><mtext>min</mtext></mrow></msub><msub><mrow><mtext> &lt;V &lt;V *</mtext></mrow><mrow><mtext>Max</mtext></mrow></msub></mrow></math><img file="EP1531339A2_D0022.tif" /></maths><maths id="math0023" num=""><math display="block"><mrow><msub><mrow><mtext>V</mtext></mrow><mrow><mtext>xmin</mtext></mrow></msub><mtext> &lt;V &lt; </mtext><msqrt><msub><mrow><mtext mathvariant="italic">V</mtext></mrow><mrow><mtext>Max</mtext></mrow></msub><msup><mrow><mtext>​</mtext></mrow><mrow><mtext>2</mtext></mrow></msup><mtext> + </mtext><msub><mrow><mtext mathvariant="italic">V</mtext></mrow><mrow><mtext mathvariant="italic">y</mtext></mrow></msub><msub><mrow><mtext></mtext></mrow><mrow><mtext>Max</mtext></mrow></msub><msup><mrow><mtext>​</mtext></mrow><mrow><mtext>2</mtext></mrow></msup></msqrt></mrow></math><img file="EP1531339A2_D0023.tif" /></maths> and for effective limits K *_min, K *_Max for the course K result from:<maths id="math0024" num=""><math display="block"><mrow><msub><mrow><mtext mathvariant="italic">K</mtext></mrow><mrow><mtext>min</mtext></mrow></msub><mtext> &lt; </mtext><mtext mathvariant="italic">K</mtext><mtext> &lt;180 - tan </mtext><mfrac><mrow><msub><mrow><mtext mathvariant="italic">V</mtext></mrow><mrow><mtext mathvariant="italic">x</mtext></mrow></msub><msub><mrow><mtext></mtext></mrow><mrow><mtext>min</mtext></mrow></msub><mtext></mtext></mrow><mrow><msub><mrow><mtext mathvariant="italic">V</mtext></mrow><mrow><mtext mathvariant="italic">y</mtext></mrow></msub><msub><mrow><mtext></mtext></mrow><mrow><mtext>Max</mtext></mrow></msub></mrow></mfrac></mrow></math><img file="EP1531339A2_D0024.tif" /></maths>

The effective limits include the preset limits for V and K.

FIG. 4 shows the convergence process in the passive determination of the target data in chronologically successive diagrams FIG. 4.1 to FIG. 4.4. Starting from a bearing B_ridge According to FIG. 4.1, the predetermined limit values ​​for the distance R with R_Max and R_min applied on the first beam. Predetermined limits for the course K are with K_Max and K_min and predetermined limits for the velocity V with V_Max and V_min are at the maximum distance R_Max and the minimum distance R_min plotted as velocity vectors. The target can be any starting distance between R_Max and R_min with the given limits for V and K. It is assumed that the target moves at a constant speed and heading during its journey. After several time intervals and bearing angle measurements, at time t₁ according to FIG. 4.2 the bearing angle B₁ measured. The boundary conditions for the distance and the speed are entered as position components and velocity components according to the explanations in the context of FIGS. 2a and 2b in the calculation algorithm. It is the minimum between all measured bearing angles to the bearing angle B₁ and the estimated bearing vector of the target, namely the starting position, speed and heading of the target. 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 destination railway V₁ t of the target, starting at the first beam under the measured bearing angle B_ridge , cuts a Peilstahlenfächer, which is spanned under all measured bearing angles, and marks on the beam at the last measured bearing angle B₁ the target position Z₁.

After another time t₂ is a last bearing angle B in FIG. 4.3₂ 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. In the now determined Peilwinkeldifferenzen between measured and estimated bearing angles, the position Z₂ and determines the associated velocity vector of the target. The associated course K₂ and the speed V₂ let to a starting position R₀₂ conclude. This starting position is between R_Max and R_min on the first beam and is other than the starting position R₀₁ according to FIG. 4.2.

The next measurements of the bearing angle including the last bearing angle B_load at the time t₃ confirm the starting position R₀₂, the speed V₂ and the heading angle K₂because the last state estimate also lies 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.

FIG. 5 illustrates the geometric relationship of the position determination from the boundary conditions for the velocity components and the distance components. Starting from FIG. 1, after the time interval dt, the carrier vehicle has assumed location II. The target is under a bearing angle B_load gepeilt. With this bearing and the bearing angle B_load The boundary conditions for estimating the next target position can be further restricted. Currently t₀ the bearing angle B_ridge measured, a minimum target distance R_min ≤ R and an approaching course<maths id="math0025" num=""><math display="block"><mrow><msub><mrow><mtext mathvariant="italic">B</mtext></mrow><mrow><mtext mathvariant="italic">ridge</mtext></mrow></msub><mtext mathvariant="italic"> +</mtext><mtext> 90 &lt; </mtext><mtext mathvariant="italic">K</mtext><mtext> &lt; </mtext><msub><mrow><mtext mathvariant="italic">B</mtext></mrow><mrow><mtext mathvariant="italic">ridge</mtext></mrow></msub><mtext> - 90</mtext></mrow></math><img file="EP1531339A2_D0025.tif" /></maths> specified.

Currently t₁ the bearing angle B_load measured and thus the price limits:<maths id="math0026" num="(3)"><math display="block"><mrow><msub><mrow><mtext>B</mtext></mrow><mrow><mtext>ridge</mtext></mrow></msub><msub><mrow><mtext> + 90 ° ≤ K &lt;B</mtext></mrow><mrow><mtext>ridge</mtext></mrow></msub><mtext> + 180°</mtext></mrow></math><img file="EP1531339A2_D0026.tif" /></maths>

Limits are assumed for the speed<maths id="math0027" num="(4),"><math display="block"><mrow><msub><mrow><mtext>0 &lt;V ≤ V</mtext></mrow><mrow><mtext>Max</mtext></mrow></msub><mtext>,</mtext></mrow></math><img file="EP1531339A2_D0027.tif" /></maths> with which the target has moved until it is below the bearing angle B_load is being targeted. For this it must be from a R_Max on the first beam P_ridge at the speed V_Max just the last beam P_load reachable. This condition, the upper limit of the speed, leads to the limit R_Max on the first beam P_ridge and is as a way piece V_Max dt marked. This path V_Max dt is in Z_0min plotted and cut with the beam P_load brought. This route forms the limit of the maximum course K_Maxwith which the target the second beam P_load at maximum speed V_Max reached:<maths id="math0028" num="(7)."><math display="block"><mrow><msub><mrow><mtext>B</mtext></mrow><mrow><mtext>ridge</mtext></mrow></msub><msub><mrow><mtext> + 90 ° ≤ K ≤ K</mtext></mrow><mrow><mtext>Max</mtext></mrow></msub></mrow></math><img file="EP1531339A2_D0028.tif" /></maths>

A movable limit for the minimum speed results from the intersection of the perpendicular bisector to the first beam P_ridge at Z_0min and the intersection with the last beam P_loadwhen the target is at minimum speed V_min along the minimum course angle to the beacon P_load moves. The limit values ​​for the speed are now specified with:<maths id="math0029" num="(8)."><math display="block"><mrow><msub><mrow><mtext>V</mtext></mrow><mrow><mtext>min</mtext></mrow></msub><msub><mrow><mtext> ≤ V ≤ V</mtext></mrow><mrow><mtext>Max</mtext></mrow></msub></mrow></math><img file="EP1531339A2_D0029.tif" /></maths>

The limits of the velocity are in velocity component V_x, V_y converted and per coordinate extreme values ​​as boundary conditions for V_x and V_y certainly:<maths id="math0030" num="(9)"><math display="block"><mrow><msub><mrow><mtext>V</mtext></mrow><mrow><mtext>Max</mtext></mrow></msub><msub><mrow><mtext> • sin K</mtext></mrow><mrow><mtext>Max</mtext></mrow></msub><msub><mrow><mtext> ≤ V</mtext></mrow><mrow><mtext>x</mtext></mrow></msub><msub><mrow><mtext> ≤ V</mtext></mrow><mrow><mtext>min</mtext></mrow></msub><msub><mrow><mtext> cos K</mtext></mrow><mrow><mtext>min</mtext></mrow></msub></mrow></math><img file="EP1531339A2_D0030.tif" /></maths><maths id="math0031" num="(10)"><math display="block"><mrow><msub><mrow><mtext>V</mtext></mrow><mrow><mtext>min</mtext></mrow></msub><msub><mrow><mtext> • Sin K</mtext></mrow><mrow><mtext>min</mtext></mrow></msub><msub><mrow><mtext> ≤ V</mtext></mrow><mrow><mtext>y</mtext></mrow></msub><msub><mrow><mtext> ≤ V</mtext></mrow><mrow><mtext>Max</mtext></mrow></msub><msub><mrow><mtext> COS K</mtext></mrow><mrow><mtext>Max</mtext></mrow></msub></mrow></math><img file="EP1531339A2_D0031.tif" /></maths>

From the velocity 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_{0 max} (maxX₀/ maxY₀) sum components are calculated and used to determine boundary conditions for the estimation of the position of the target on the last beam.

At the limits for the distance R boundary conditions for the position Z₀ of the destination:<maths id="math0032" num=""><math display="block"><mrow><msub><mrow><mtext>R</mtext></mrow><mrow><mtext>min</mtext></mrow></msub><msub><mrow><mtext> sin B</mtext></mrow><mrow><mtext>ridge</mtext></mrow></msub><msub><mrow><mtext> ≤ X</mtext></mrow><mrow><mtext>0</mtext></mrow></msub><msub><mrow><mtext> ≤ R</mtext></mrow><mrow><mtext>Max</mtext></mrow></msub><msub><mrow><mtext> sin B</mtext></mrow><mrow><mtext>ridge</mtext></mrow></msub></mrow></math><img file="EP1531339A2_D0032.tif" /></maths> or<maths id="math0033" num=""><math display="block"><mrow><msub><mrow><mtext>minx</mtext></mrow><mrow><mtext>0</mtext></mrow></msub><msub><mrow><mtext> ≤ X</mtext></mrow><mrow><mtext>0</mtext></mrow></msub><msub><mrow><mtext> ≤ maxX</mtext></mrow><mrow><mtext>0</mtext></mrow></msub></mrow></math><img file="EP1531339A2_D0033.tif" /></maths><maths id="math0034" num=""><math display="block"><mrow><msub><mrow><mtext>R</mtext></mrow><mrow><mtext>min</mtext></mrow></msub><msub><mrow><mtext> COS B</mtext></mrow><mrow><mtext>ridge</mtext></mrow></msub><msub><mrow><mtext> ≤Y</mtext></mrow><mrow><mtext>0</mtext></mrow></msub><msub><mrow><mtext> ≤ R</mtext></mrow><mrow><mtext>Max</mtext></mrow></msub><msub><mrow><mtext> COS B</mtext></mrow><mrow><mtext>ridge</mtext></mrow></msub></mrow></math><img file="EP1531339A2_D0034.tif" /></maths> or<maths id="math0035" num="(12)"><math display="block"><mrow><msub><mrow><mtext>minY</mtext></mrow><mrow><mtext>0</mtext></mrow></msub><msub><mrow><mtext> ≤Y</mtext></mrow><mrow><mtext>0</mtext></mrow></msub><msub><mrow><mtext> ≤ maxY</mtext></mrow><mrow><mtext>0</mtext></mrow></msub></mrow></math><img file="EP1531339A2_D0035.tif" /></maths>

The velocity components multiplied by the time interval dt in accordance with the 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="math0036" num=""><math display="block"><mrow><msub><mrow><mtext>R</mtext></mrow><mrow><mtext>min</mtext></mrow></msub><msub><mrow><mtext> sin B</mtext></mrow><mrow><mtext>ridge</mtext></mrow></msub><msub><mrow><mtext> - V</mtext></mrow><mrow><mtext>Max</mtext></mrow></msub><msub><mrow><mtext> sin K</mtext></mrow><mrow><mtext>Max</mtext></mrow></msub><msub><mrow><mtext> dt ≤ X</mtext></mrow><mrow><mtext>1</mtext></mrow></msub><msub><mrow><mtext> ≤ R</mtext></mrow><mrow><mtext>Max</mtext></mrow></msub><msub><mrow><mtext> sin B</mtext></mrow><mrow><mtext>ridge</mtext></mrow></msub><mspace linebreak="newline" /><msub><mrow><mtext> + V</mtext></mrow><mrow><mtext>min</mtext></mrow></msub><msub><mrow><mtext> COS K</mtext></mrow><mrow><mtext>min</mtext></mrow></msub><mtext> dt</mtext></mrow></math><img file="EP1531339A2_D0036.tif" /></maths><maths id="math0037" num="(13)"><math display="block"><mrow><msub><mrow><mtext>minx</mtext></mrow><mrow><mtext>1</mtext></mrow></msub><msub><mrow><mtext> ≤ X</mtext></mrow><mrow><mtext>1</mtext></mrow></msub><msub><mrow><mtext> ≤ maxX</mtext></mrow><mrow><mtext>1</mtext></mrow></msub></mrow></math><img file="EP1531339A2_D0037.tif" /></maths><maths id="math0038" num=""><math display="block"><mrow><msub><mrow><mtext>R</mtext></mrow><mrow><mtext>min</mtext></mrow></msub><msub><mrow><mtext> COS B</mtext></mrow><mrow><mtext>ridge</mtext></mrow></msub><msub><mrow><mtext> - V</mtext></mrow><mrow><mtext>Max</mtext></mrow></msub><msub><mrow><mtext> COS K</mtext></mrow><mrow><mtext>Max</mtext></mrow></msub><msub><mrow><mtext> dt ≤ Y</mtext></mrow><mrow><mtext>1</mtext></mrow></msub><msub><mrow><mtext> ≤ R</mtext></mrow><mrow><mtext>Max</mtext></mrow></msub><msub><mrow><mtext> cos B</mtext></mrow><mrow><mtext>ridge</mtext></mrow></msub><mspace linebreak="newline" /><msub><mrow><mtext> - V</mtext></mrow><mrow><mtext>Max</mtext></mrow></msub><msub><mrow><mtext> COS K</mtext></mrow><mrow><mtext>Max</mtext></mrow></msub><mtext> dt</mtext></mrow></math><img file="EP1531339A2_D0038.tif" /></maths><maths id="math0039" num="(14)"><math display="block"><mrow><msub><mrow><mtext>minY</mtext></mrow><mrow><mtext>1</mtext></mrow></msub><msub><mrow><mtext> ≤Y</mtext></mrow><mrow><mtext>1</mtext></mrow></msub><msub><mrow><mtext> ≤ maxY</mtext></mrow><mrow><mtext>1</mtext></mrow></msub><mtext>,</mtext></mrow></math><img file="EP1531339A2_D0039.tif" /></maths> on the last beam P_load below the last measured bearing angle B_load lies. With these constraints, the target start position is again determined by means of an iterative process by minimizing the differences in the tracks.

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

6 shows by way of example 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_est, which for all measurements B_imess of the bearing angle simultaneously with the same boundary conditions for the x- and y-speed components and x- and y-position components starting from an initial position Z.₀within the limits for R₀ is, is carried out.<maths id="math0040" num="(15)"><math display="block"><mrow><msub><mrow><mtext>(B</mtext></mrow><mrow><mtext>mess</mtext></mrow></msub><msub><mrow><mtext> - B</mtext></mrow><mrow><mtext>est</mtext></mrow></msub><mtext>) = min</mtext></mrow></math><img file="EP1531339A2_D0040.tif" /></maths>

In the xy-coordinate system of FIG. 1, at a time t₁ the carrier vehicle with the own position x_e, y_e, shown at the origin of the xy coordinate system. At this time, the target is at position Z_true, It has its starting or starting position Z₀ at the coordinates x_0true, y_0true that are within the boundary conditions for the starting position min x₀/ miny₀ and max x₀/ max y₀ lie, with the speed v_XTRUE, v_ytruewithin the boundary conditions for the velocity v_xmin and V_ymin lie, leave and the way components v_xtru · Δt and v_ytrue · Δt covered. The new true position Z_true of the target leads to the measurement of a bearing angle B_measured. 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 given effective limits.

It is assumed that the target is from the coordinate x_0true with a path error Δx₀ to the coordinate R_Xest in the x direction at a speed v_x and a velocity component error Δv_x in a time interval .DELTA.t moves. In the y-direction, the target has the time interval Δt of the coordinate y_0true to the coordinate R_yest with a path error Δy₀ and a speed v_yest with a velocity component error Δv_y emotional. The coordinates of the destination are estimated to:<maths id="math0041" num="(A)"><math display="block"><mrow><msub><mrow><mtext>R</mtext></mrow><mrow><mtext>x est</mtext></mrow></msub><msub><mrow><mtext> = x</mtext></mrow><mrow><mtext>0 true</mtext></mrow></msub><msub><mrow><mtext> + v</mtext></mrow><mrow><mtext>x</mtext></mrow></msub><msub><mrow><mtext> · Δt + (ΔX</mtext></mrow><mrow><mtext>0</mtext></mrow></msub><msub><mrow><mtext> + Δv</mtext></mrow><mrow><mtext>x</mtext></mrow></msub><msub><mrow><mtext> · Δt) = R</mtext></mrow><mrow><mtext>x true</mtext></mrow></msub><msub><mrow><mtext> + ΔR</mtext></mrow><mrow><mtext>x</mtext></mrow></msub></mrow></math><img file="EP1531339A2_D0041.tif" /></maths><maths id="math0042" num="(B)"><math display="block"><mrow><msub><mrow><mtext>R</mtext></mrow><mrow><mtext>y est</mtext></mrow></msub><msub><mrow><mtext> = y</mtext></mrow><mrow><mtext>0 true</mtext></mrow></msub><msub><mrow><mtext> + v</mtext></mrow><mrow><mtext>y</mtext></mrow></msub><msub><mrow><mtext> · Δt + (Δy</mtext></mrow><mrow><mtext>0</mtext></mrow></msub><msub><mrow><mtext> + Δv</mtext></mrow><mrow><mtext>y</mtext></mrow></msub><msub><mrow><mtext> · Δt) = R</mtext></mrow><mrow><mtext>y true</mtext></mrow></msub><msub><mrow><mtext> + ΔR</mtext></mrow><mrow><mtext>y</mtext></mrow></msub></mrow></math><img file="EP1531339A2_D0042.tif" /></maths> with the errors ΔR_x, ΔR_y, After forming one obtains<maths id="math0043" num="(a)"><math display="block"><mrow><msub><mrow><mtext>R</mtext></mrow><mrow><mtext>XTRUE</mtext></mrow></msub><msub><mrow><mtext> = R</mtext></mrow><mrow><mtext>Xest</mtext></mrow></msub><msub><mrow><mtext> - ΔR</mtext></mrow><mrow><mtext>x</mtext></mrow></msub><msub><mrow><mtext> = R</mtext></mrow><mrow><mtext>Xest</mtext></mrow></msub><msub><mrow><mtext> - (Δx</mtext></mrow><mrow><mtext>0</mtext></mrow></msub><msub><mrow><mtext> + Δv</mtext></mrow><mrow><mtext>x</mtext></mrow></msub><mtext> · Δt)</mtext></mrow></math><img file="EP1531339A2_D0043.tif" /></maths><maths id="math0044" num="(b)"><math display="block"><mrow><msub><mrow><mtext>R</mtext></mrow><mrow><mtext>ytrue</mtext></mrow></msub><msub><mrow><mtext> = R</mtext></mrow><mrow><mtext>yest</mtext></mrow></msub><msub><mrow><mtext> - ΔR</mtext></mrow><mrow><mtext>y</mtext></mrow></msub><msub><mrow><mtext> = R</mtext></mrow><mrow><mtext>yest</mtext></mrow></msub><msub><mrow><mtext> - (Δy</mtext></mrow><mrow><mtext>0</mtext></mrow></msub><msub><mrow><mtext> + Δv</mtext></mrow><mrow><mtext>y</mtext></mrow></msub><mtext> · Δt)</mtext></mrow></math><img file="EP1531339A2_D0044.tif" /></maths>

From this, the estimated bearing angle B_est calculated:<maths id="math0045" num="I"><math display="block"><mrow><msub><mrow><mtext>B</mtext></mrow><mrow><mtext>est</mtext></mrow></msub><mtext> = arctane </mtext><mfrac><mrow><msub><mrow><mtext>R</mtext></mrow><mrow><mtext>Xest</mtext></mrow></msub><msub><mrow><mtext> - ΔR</mtext></mrow><mrow><mtext>x</mtext></mrow></msub></mrow><mrow><msub><mrow><mtext>R</mtext></mrow><mrow><mtext>yest</mtext></mrow></msub><msub><mrow><mtext> - ΔR</mtext></mrow><mrow><mtext>y</mtext></mrow></msub></mrow></mfrac></mrow></math><img file="EP1531339A2_D0045.tif" /></maths>

The true position Z_true is determined when the errors ΔR_x = Δx₀ + Δv_x · Δt and ΔR_y = Δy₀ + Δv_y · Δt are equal to zero. Then the velocity components v_x and V_y correctly estimated that to take the new true position Z_true of the target. The associated estimated bearing angle B_est is equal to the true bearing angle B_true and is:<maths id="math0046" num=""><math display="block"><mrow><msub><mrow><mtext>B</mtext></mrow><mrow><mtext>est</mtext></mrow></msub><msub><mrow><mtext> = B</mtext></mrow><mrow><mtext>true</mtext></mrow></msub><mtext> = arctane </mtext><mfrac><mrow><msub><mrow><mtext>x</mtext></mrow><mrow><mtext>0true</mtext></mrow></msub><msub><mrow><mtext> + y</mtext></mrow><mrow><mtext>XTRUE</mtext></mrow></msub><msub><mrow><mtext> · Δt - x</mtext></mrow><mrow><mtext>e</mtext></mrow></msub><mtext></mtext></mrow><mrow><msub><mrow><mtext>y</mtext></mrow><mrow><mtext>0true</mtext></mrow></msub><msub><mrow><mtext> + v</mtext></mrow><mrow><mtext>ytrue</mtext></mrow></msub><msub><mrow><mtext> · Δt - y</mtext></mrow><mrow><mtext>e</mtext></mrow></msub></mrow></mfrac><msub><mrow><mtext>= B</mtext></mrow><mrow><mtext>mess</mtext></mrow></msub></mrow></math><img file="EP1531339A2_D0046.tif" /></maths>

The target data P = (x₀, y₀, v_x, v_y) are correctly estimated when the error vector equals zero:<maths id="math0047" num=""><math display="block"><mrow><msub><mrow><mtext>ΔP = (Δx</mtext></mrow><mrow><mtext>0</mtext></mrow></msub><msub><mrow><mtext>, Δy</mtext></mrow><mrow><mtext>0</mtext></mrow></msub><msub><mrow><mtext>, Δv</mtext></mrow><mrow><mtext>x</mtext></mrow></msub><msub><mrow><mtext>, Δv</mtext></mrow><mrow><mtext>y</mtext></mrow></msub><mtext>) = 0</mtext></mrow></math><img file="EP1531339A2_D0047.tif" /></maths> With<maths id="math0048" num=""><math display="block"><mrow><msub><mrow><mtext>.DELTA.P</mtext></mrow><mrow><mtext>1</mtext></mrow></msub><msub><mrow><mtext> = Δx</mtext></mrow><mrow><mtext>0</mtext></mrow></msub><msub><mrow><mtext>, Δp</mtext></mrow><mrow><mtext>2</mtext></mrow></msub><msub><mrow><mtext> = Δy</mtext></mrow><mrow><mtext>0</mtext></mrow></msub><msub><mrow><mtext>, Δp</mtext></mrow><mrow><mtext>3</mtext></mrow></msub><msub><mrow><mtext> = Δv</mtext></mrow><mrow><mtext>x</mtext></mrow></msub><msub><mrow><mtext>   and Δp</mtext></mrow><mrow><mtext>4</mtext></mrow></msub><msub><mrow><mtext> = Δv</mtext></mrow><mrow><mtext>y</mtext></mrow></msub><mtext>.</mtext></mrow></math><img file="EP1531339A2_D0048.tif" /></maths>

For the target data determination, the sum of the bearing angle differences between the estimated bearing positions estimated under the same limit values ​​for the starting position, the speed and the course and the measured bearing angles is minimized for all measurements:<maths id="math0049" num=""><img file="EP1531339A2_D0049.tif" /></maths>

The initial position Z₀ and target positions Z_itrue are then determined except for a residual error which is determined by a minimum determining threshold. Then<maths id="math0050" num=""><math display="block"><mrow><msub><mrow><mtext>B</mtext></mrow><mrow><mtext>iest</mtext></mrow></msub><msub><mrow><mtext> ≈ B</mtext></mrow><mrow><mtext>itrue</mtext></mrow></msub></mrow></math><img file="EP1531339A2_D0050.tif" /></maths>

The inclusion of an estimated Doppler frequency makes possible a position estimation without self-maneuver by simultaneously minimizing a frequency difference between measured reception frequency and estimated Doppler frequency taking into account the bearing angle estimation according to I.

The target has the starting position Z₀ leave at the speed v of FIG. 6. With knowledge of the true bearing angle B_true are the velocity components v_x and V_y of the target into a radial velocity component V_R converted in the direction between the eigenposition x_e, y_e and the true target position P_true has.<maths id="math0051" num="(1c)"><math display="block"><mrow><msub><mrow><mtext>V</mtext></mrow><mrow><mtext>R</mtext></mrow></msub><msub><mrow><mtext> = V</mtext></mrow><mrow><mtext>R</mtext></mrow></msub><msub><mrow><mtext>'+ V</mtext></mrow><mrow><mtext>R</mtext></mrow></msub><msub><mrow><mtext>"= v</mtext></mrow><mrow><mtext>y</mtext></mrow></msub><msub><mrow><mtext> • COS B</mtext></mrow><mrow><mtext>true</mtext></mrow></msub><msub><mrow><mtext> + v</mtext></mrow><mrow><mtext>x</mtext></mrow></msub><msub><mrow><mtext> sin B</mtext></mrow><mrow><mtext>true</mtext></mrow></msub></mrow></math><img file="EP1531339A2_D0051.tif" /></maths>

This radial velocity component V_R takes into account the correct radial added velocity components of the target V_RZ and the host vehicle V_RE<maths id="math0052" num="(d)"><math display="block"><mrow><msub><mrow><mtext>V</mtext></mrow><mrow><mtext>R</mtext></mrow></msub><msub><mrow><mtext> = V</mtext></mrow><mrow><mtext>RE</mtext></mrow></msub><msub><mrow><mtext> - V</mtext></mrow><mrow><mtext>RZ</mtext></mrow></msub></mrow></math><img file="EP1531339A2_D0052.tif" /></maths>

Because of the radial velocity component V_R is a transmission frequency F contained in the transmission signal or in the sound of the target and transmitted_strue shifted in frequency and a Doppler transmission frequency as receiving frequency F_true as described in Chapter 7.4 "The Doppler Effect", page 334, 335 in the textbook "Experimental Physics I", Part 2, Edgar Lüscher, University Book, Bibliographic Institute, Mannheim. Described in 1967, applies to the Doppler frequency:<maths id="math0053" num=""><img file="EP1531339A2_D0053.tif" /></maths>

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

The velocity components v_x and V_y are equal to the temporal change of the xy coordinates of the target:<maths id="math0054" num=""><math display="block"><mrow><msub><mrow><mtext>v</mtext></mrow><mrow><mtext>x</mtext></mrow></msub><mtext> = </mtext><mfrac><mrow><msub><mrow><mtext>dR</mtext></mrow><mrow><mtext>XTRUE</mtext></mrow></msub><mtext></mtext></mrow><mrow><mtext>dt</mtext></mrow></mfrac><mtext> = </mtext><msub><mrow><mover accent="true"><mrow><mtext>R</mtext></mrow><mo>̇</mo></mover></mrow><mrow><mtext>XTRUE</mtext></mrow></msub></mrow></math><img file="EP1531339A2_D0054.tif" /></maths><maths id="math0055" num=""><math display="block"><mrow><msub><mrow><mtext>v</mtext></mrow><mrow><mtext>y</mtext></mrow></msub><mtext> = </mtext><mfrac><mrow><msub><mrow><mtext>dR</mtext></mrow><mrow><mtext>ytrue</mtext></mrow></msub></mrow><mrow><mtext>dt</mtext></mrow></mfrac><mtext> = </mtext><msub><mrow><mover accent="true"><mrow><mtext>R</mtext></mrow><mo>̇</mo></mover></mrow><mrow><mtext>ytrue</mtext></mrow></msub></mrow></math><img file="EP1531339A2_D0055.tif" /></maths>

Equations (a) and (b) give:<maths id="math0056" num="(e)"><math display="block"><mrow><msub><mrow><mtext>v</mtext></mrow><mrow><mtext>x</mtext></mrow></msub><mtext> = </mtext><msub><mrow><mover accent="true"><mrow><mtext>R</mtext></mrow><mo>̇</mo></mover></mrow><mrow><mtext>XTRUE</mtext></mrow></msub><mtext> = </mtext><msub><mrow><mover accent="true"><mrow><mtext>R</mtext></mrow><mo>̇</mo></mover></mrow><mrow><mtext>Xest</mtext></mrow></msub><mtext> - Δ</mtext><msub><mrow><mover accent="true"><mrow><mtext>R</mtext></mrow><mo>̇</mo></mover></mrow><mrow><mtext>x</mtext></mrow></msub></mrow></math><img file="EP1531339A2_D0056.tif" /></maths><maths id="math0057" num="(f)"><math display="block"><mrow><msub><mrow><mtext>v</mtext></mrow><mrow><mtext>y</mtext></mrow></msub><mtext> = </mtext><msub><mrow><mover accent="true"><mrow><mtext>R</mtext></mrow><mo>̇</mo></mover></mrow><mrow><mtext>ytrue</mtext></mrow></msub><mtext> = </mtext><msub><mrow><mover accent="true"><mrow><mtext>R</mtext></mrow><mo>̇</mo></mover></mrow><mrow><mtext>yest</mtext></mrow></msub><mtext> - Δ</mtext><msub><mrow><mover accent="true"><mrow><mtext>R</mtext></mrow><mo>̇</mo></mover></mrow><mrow><mtext>y</mtext></mrow></msub></mrow></math><img file="EP1531339A2_D0057.tif" /></maths>

Using the true bearing angle B_true between the reference direction N₀ and the direction to the true target position Ptrue<maths id="math0058" num="(g)"><math display="block"><mrow><msub><mrow><mtext>sin B</mtext></mrow><mrow><mtext>true</mtext></mrow></msub><mtext> = </mtext><mfrac><mrow><msub><mrow><mtext>R</mtext></mrow><mrow><mtext>XTRUE</mtext></mrow></msub></mrow><mrow><msub><mrow><mtext>R</mtext></mrow><mrow><mtext>true</mtext></mrow></msub></mrow></mfrac></mrow></math><img file="EP1531339A2_D0058.tif" /></maths><maths id="math0059" num="(h)"><math display="block"><mrow><msub><mrow><mtext>cos B</mtext></mrow><mrow><mtext>true</mtext></mrow></msub><mtext> = </mtext><mfrac><mrow><msub><mrow><mtext>R</mtext></mrow><mrow><mtext>ytrue</mtext></mrow></msub><mtext></mtext></mrow><mrow><msub><mrow><mtext>R</mtext></mrow><mrow><mtext>true</mtext></mrow></msub></mrow></mfrac></mrow></math><img file="EP1531339A2_D0059.tif" /></maths> one obtains with the equations (a) and (b) for the true distance R_true to the goal<maths id="math0060" num=""><math display="block"><mrow><msub><mrow><mtext>R</mtext></mrow><mrow><mtext>true</mtext></mrow></msub><mtext> = </mtext><msqrt><msub><mrow><mtext>R</mtext></mrow><mrow><mtext>x</mtext></mrow></msub><msubsup><mrow><mtext>​</mtext></mrow><mrow><mtext>true</mtext></mrow><mrow><mtext>2</mtext></mrow></msubsup><msub><mrow><mtext> + R</mtext></mrow><mrow><mtext>y</mtext></mrow></msub><msubsup><mrow><mtext>​</mtext></mrow><mrow><mtext>true</mtext></mrow><mrow><mtext>2</mtext></mrow></msubsup></msqrt></mrow></math><img file="EP1531339A2_D0060.tif" /></maths><maths id="math0061" num="(i)"><math display="block"><mrow><msub><mrow><mtext>R</mtext></mrow><mrow><mtext>true</mtext></mrow></msub><mtext> = </mtext><msqrt><msub><mrow><mtext>(R</mtext></mrow><mrow><mtext>Xest</mtext></mrow></msub><msub><mrow><mtext> - ΔR</mtext></mrow><mrow><mtext>x</mtext></mrow></msub><msup><mrow><mtext>)</mtext></mrow><mrow><mtext>2</mtext></mrow></msup><msub><mrow><mtext>(R</mtext></mrow><mrow><mtext>yest</mtext></mrow></msub><msub><mrow><mtext> - ΔR</mtext></mrow><mrow><mtext>y</mtext></mrow></msub><msup><mrow><mtext>)</mtext></mrow><mrow><mtext>2</mtext></mrow></msup></msqrt></mrow></math><img file="EP1531339A2_D0061.tif" /></maths> is there<maths id="math0062" num=""><math display="block"><mrow><msub><mrow><mtext>.DELTA.R</mtext></mrow><mrow><mtext>x</mtext></mrow></msub><msub><mrow><mtext> = Δx</mtext></mrow><mrow><mtext>0</mtext></mrow></msub><msub><mrow><mtext> + Δv</mtext></mrow><mrow><mtext>x</mtext></mrow></msub><mtext> · Δt</mtext></mrow></math><img file="EP1531339A2_D0062.tif" /></maths><maths id="math0063" num=""><math display="block"><mrow><msub><mrow><mtext>.DELTA.R</mtext></mrow><mrow><mtext>y</mtext></mrow></msub><msub><mrow><mtext> = Δy</mtext></mrow><mrow><mtext>0</mtext></mrow></msub><msub><mrow><mtext> + Δv</mtext></mrow><mrow><mtext>x</mtext></mrow></msub><mtext> · Δt.</mtext></mrow></math><img file="EP1531339A2_D0063.tif" /></maths>

In equation (c) for the radial velocity component V_R Now the equations (e), (f), (g), (h) and (i) are used, and for the Doppler shift ΔP = (Δx₀, Δy₀, Δv_x, Δv_y):<maths id="math0064" num=""><img file="EP1531339A2_D0064.tif" /></maths>

The transmission frequency F_swhich is emitted from the target is rejected with an error .DELTA.F_s valued<maths id="math0065" num=""><math display="block"><mrow><msub><mrow><mtext>F</mtext></mrow><mrow><mtext>sest</mtext></mrow></msub><msub><mrow><mtext> = F</mtext></mrow><mrow><mtext>strue</mtext></mrow></msub><msub><mrow><mtext> + ΔF</mtext></mrow><mrow><mtext>s</mtext></mrow></msub></mrow></math><img file="EP1531339A2_D0065.tif" /></maths><maths id="math0066" num=""><math display="block"><mrow><msub><mrow><mtext>F</mtext></mrow><mrow><mtext>strue</mtext></mrow></msub><msub><mrow><mtext> = F</mtext></mrow><mrow><mtext>sest</mtext></mrow></msub><msub><mrow><mtext> - ΔF</mtext></mrow><mrow><mtext>s</mtext></mrow></msub></mrow></math><img file="EP1531339A2_D0066.tif" /></maths> and, together with the Doppler shift Q, provides the reception frequency F_mess.

The Doppler frequency F_true is estimated as an error with an error difference ΔF.<maths id="math0067" num=""><math display="block"><mrow><msub><mrow><mtext>F</mtext></mrow><mrow><mtext>true</mtext></mrow></msub><msub><mrow><mtext> = F</mtext></mrow><mrow><mtext>est</mtext></mrow></msub><mtext> - ΔF</mtext></mrow></math><img file="EP1531339A2_D0067.tif" /></maths>

Since the transmission frequency F_s is unknown, the error vector ΔP is another error term ΔF_s for the estimation of the transmission frequency F_sest to expand:<maths id="math0068" num=""><math display="block"><mrow><msub><mrow><mtext>.DELTA.P</mtext></mrow><mrow><mtext>1</mtext></mrow></msub><msub><mrow><mtext> = (Δx</mtext></mrow><mrow><mtext>0</mtext></mrow></msub><msub><mrow><mtext>, Δy</mtext></mrow><mrow><mtext>0</mtext></mrow></msub><msub><mrow><mtext>, Δv</mtext></mrow><mrow><mtext>x</mtext></mrow></msub><msub><mrow><mtext>, Δv</mtext></mrow><mrow><mtext>y</mtext></mrow></msub><msub><mrow><mtext>, ΔF</mtext></mrow><mrow><mtext>s</mtext></mrow></msub><mtext>)</mtext></mrow></math><img file="EP1531339A2_D0068.tif" /></maths>

Here, the estimated Doppler frequency F_iest equal to the measured reception frequency F_imess for ΔP = 0, namely, if the transmission frequency was correctly estimated.

One obtains for the estimated Doppler frequency F_iest a sum equal to the measured received frequency F_imess plus the frequency difference ΔF_i is.<maths id="math0069" num=""><math display="block"><mrow><msub><mrow><mtext>F</mtext></mrow><mrow><mtext>imess</mtext></mrow></msub><msub><mrow><mtext> + ΔF</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><msub><mrow><mtext> = F</mtext></mrow><mrow><mtext>iest</mtext></mrow></msub></mrow></math><img file="EP1531339A2_D0069.tif" /></maths><maths id="math0070" num=""><math display="block"><mrow><msub><mrow><mtext>.DELTA.F</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><msub><mrow><mtext> = F</mtext></mrow><mrow><mtext>imess</mtext></mrow></msub><msub><mrow><mtext> - F</mtext></mrow><mrow><mtext>iest</mtext></mrow></msub><mtext>.</mtext></mrow></math><img file="EP1531339A2_D0070.tif" /></maths>

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

The determination of the target data is improved for the transmission frequency F radiated from the target_S Limits are given and added to the algorithm. The emitted from the target transmission frequency F_S experienced by 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_ridge measured:<maths id="math0071" num="(16)"><math display="block"><mrow><mtext mathvariant="italic">F</mtext><mtext> = </mtext><msub><mrow><mtext mathvariant="italic">F</mtext></mrow><mrow><mtext mathvariant="italic">s</mtext></mrow></msub><mfrac><mrow><mtext mathvariant="italic">C</mtext><mtext> + </mtext><msub><mrow><mtext mathvariant="italic">V</mtext></mrow><mrow><mtext mathvariant="italic">roundelay</mtext></mrow></msub><mtext></mtext></mrow><mrow><mtext mathvariant="italic">C</mtext><mtext> - </mtext><msub><mrow><mtext mathvariant="italic">V </mtext></mrow><mrow><mtext mathvariant="italic">RZiel</mtext></mrow></msub></mrow></mfrac></mrow></math><img file="EP1531339A2_D0071.tif" /></maths>

Taking into account the Doppler shift, the transmission frequency Fs is:<maths id="math0072" num="(17)."><math display="block"><mrow><msub><mrow><mtext mathvariant="italic">F</mtext></mrow><mrow><mtext mathvariant="italic">s</mtext></mrow></msub><mtext> = </mtext><mtext mathvariant="italic">F</mtext><mfrac><mrow><mtext mathvariant="italic">C</mtext><mtext> - </mtext><msub><mrow><mtext mathvariant="italic">V</mtext></mrow><mrow><mtext mathvariant="italic">RZiel</mtext></mrow></msub><mtext></mtext></mrow><mrow><mtext mathvariant="italic">C</mtext><mtext> + </mtext><msub><mrow><mtext mathvariant="italic">V</mtext></mrow><mrow><mtext mathvariant="italic">roundelay</mtext></mrow></msub></mrow></mfrac></mrow></math><img file="EP1531339A2_D0072.tif" /></maths>

From the limit values ​​for the speed V_min ≤ V ≤ V_Max are limits for the transmission frequency F_S determined:<maths id="math0073" num="(18)"><math display="block"><mrow><mtext mathvariant="italic">F</mtext><mtext></mtext><mfrac><mrow><mtext mathvariant="italic">C</mtext><mtext> - </mtext><msub><mrow><mtext mathvariant="italic">V</mtext></mrow><mrow><mtext>Max</mtext></mrow></msub><mtext></mtext></mrow><mrow><mtext mathvariant="italic">C</mtext><mtext> + </mtext><msub><mrow><mtext mathvariant="italic">V</mtext></mrow><mrow><mtext mathvariant="italic">roundelay</mtext></mrow></msub></mrow></mfrac><mtext> ≤ </mtext><msub><mrow><mtext mathvariant="italic">F</mtext></mrow><mrow><mtext mathvariant="italic">s</mtext></mrow></msub><mtext> ≤ </mtext><mtext mathvariant="italic">F</mtext><mtext></mtext><mfrac><mrow><mtext mathvariant="italic">C</mtext><mtext> - </mtext><msub><mrow><mtext mathvariant="italic">V</mtext></mrow><mrow><mtext>min</mtext></mrow></msub><mtext></mtext></mrow><mrow><mtext mathvariant="italic">C</mtext><mtext> + </mtext><msub><mrow><mtext mathvariant="italic">V</mtext></mrow><mrow><mtext mathvariant="italic">roundelay</mtext></mrow></msub></mrow></mfrac></mrow></math><img file="EP1531339A2_D0073.tif" /></maths>

The limits for the transmission frequency are used in determining the error ΔF_S for estimating the transmission frequency and thus also for minimizing the frequency difference ΔF between measured reception frequency F_mess and estimated Doppler frequency F_est considered.

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

7 shows a block diagram of a sonar receiving system for determining the target data P with an adaptive filter arrangement for the evaluation of measured bearing angles B_imess and reception frequencies F_imess, Receive signals of a transducer array 10 are combined in a direction generator 11 by runtime or phase compensation to group signals and a target at a bearing angle B_imess detected with a measuring circuit 12. The measuring circuit 12 is controlled by a control circuit 13 at intervals of time intervals .DELTA.t_i driven. The entire signal processing takes place at intervals of the time intervals .DELTA.t. An estimation circuit 15 receives as input data the north direction from a compass 16 as the reference direction N₀, the eigenposition x_e, y_e the transducer assembly 10 from an on-board navigation system 17 and from a start state circuit 18 boundary conditions for the position estimate, which are determined from limits for the distance R, the speed V, and the course K of the target. From the last measured bearing angle B_ridge and the limit for the distance R, the boundary conditions for the position components x₀ / y₀ certainly:<maths id="math0074" num=""><math display="block"><mrow><msub><mrow><mtext>R</mtext></mrow><mrow><mtext>min</mtext></mrow></msub><msub><mrow><mtext> Sin B</mtext></mrow><mrow><mtext>ridge</mtext></mrow></msub><msub><mrow><mtext> ≤ X</mtext></mrow><mrow><mtext>0</mtext></mrow></msub><msub><mrow><mtext> ≤ R</mtext></mrow><mrow><mtext>Max</mtext></mrow></msub><msub><mrow><mtext> Sin B</mtext></mrow><mrow><mtext>ridge</mtext></mrow></msub></mrow></math><img file="EP1531339A2_D0074.tif" /></maths><maths id="math0075" num=""><math display="block"><mrow><msub><mrow><mtext>minx</mtext></mrow><mrow><mtext>0</mtext></mrow></msub><msub><mrow><mtext> ≤ X</mtext></mrow><mrow><mtext>0</mtext></mrow></msub><msub><mrow><mtext> ≤ maxX</mtext></mrow><mrow><mtext>0</mtext></mrow></msub></mrow></math><img file="EP1531339A2_D0075.tif" /></maths><maths id="math0076" num=""><math display="block"><mrow><msub><mrow><mtext>R</mtext></mrow><mrow><mtext>min</mtext></mrow></msub><msub><mrow><mtext> cos B</mtext></mrow><mrow><mtext>ridge</mtext></mrow></msub><msub><mrow><mtext> ≤Y</mtext></mrow><mrow><mtext>0</mtext></mrow></msub><msub><mrow><mtext> ≤ R</mtext></mrow><mrow><mtext>Max</mtext></mrow></msub><msub><mrow><mtext> COS B</mtext></mrow><mrow><mtext>ridge</mtext></mrow></msub></mrow></math><img file="EP1531339A2_D0076.tif" /></maths><maths id="math0077" num=""><math display="block"><mrow><msub><mrow><mtext>minY</mtext></mrow><mrow><mtext>0</mtext></mrow></msub><msub><mrow><mtext> ≤Y</mtext></mrow><mrow><mtext>0</mtext></mrow></msub><msub><mrow><mtext> ≤ maxY</mtext></mrow><mrow><mtext>0</mtext></mrow></msub></mrow></math><img file="EP1531339A2_D0077.tif" /></maths>

From the given limit values ​​for the speed V and the course K, the boundary conditions for the velocity components V_x / V_y certainly:<maths id="math0078" num=""><math display="block"><mrow><msub><mrow><mtext>V</mtext></mrow><mrow><mtext>xmin</mtext></mrow></msub><msub><mrow><mtext> ≤ V</mtext></mrow><mrow><mtext>x</mtext></mrow></msub><msub><mrow><mtext> ≤ V</mtext></mrow><mrow><mtext>xmax</mtext></mrow></msub></mrow></math><img file="EP1531339A2_D0078.tif" /></maths><maths id="math0079" num=""><math display="block"><mrow><msub><mrow><mtext>V</mtext></mrow><mrow><mtext>ymin</mtext></mrow></msub><msub><mrow><mtext> ≤ V</mtext></mrow><mrow><mtext>y</mtext></mrow></msub><msub><mrow><mtext> ≤ V</mtext></mrow><mrow><mtext>ymax</mtext></mrow></msub><mtext>,</mtext></mrow></math><img file="EP1531339A2_D0079.tif" /></maths> as related to Figs. 2 and 3 for the cases<maths id="math0080" num=""><math display="block"><mrow><msub><mrow><mtext>90 &lt;| K</mtext></mrow><mrow><mtext>Max</mtext></mrow></msub><msub><mrow><mtext> - K</mtext></mrow><mrow><mtext>min</mtext></mrow></msub><msub><mrow><mtext>| &lt;180 and | K</mtext></mrow><mrow><mtext>Max</mtext></mrow></msub><msub><mrow><mtext> - K</mtext></mrow><mrow><mtext>min</mtext></mrow></msub><mtext>|&lt;90</mtext></mrow></math><img file="EP1531339A2_D0080.tif" /></maths> was explained.

The estimated transmission frequency F_s and the limits<maths id="math0081" num=""><math display="block"><mrow><mtext mathvariant="italic">F</mtext><mfrac><mrow><mtext mathvariant="italic">C</mtext><mtext> - </mtext><msub><mrow><mtext mathvariant="italic">V</mtext></mrow><mrow><mtext>Max</mtext></mrow></msub><mtext></mtext></mrow><mrow><mtext mathvariant="italic">C</mtext><mtext> + </mtext><msub><mrow><mtext mathvariant="italic">V</mtext></mrow><mrow><mtext mathvariant="italic">roundelay</mtext></mrow></msub></mrow></mfrac><mtext> ≤ </mtext><msub><mrow><mtext mathvariant="italic">F</mtext></mrow><mrow><mtext mathvariant="italic">s</mtext></mrow></msub><mtext> ≤ </mtext><mtext mathvariant="italic">F</mtext><mfrac><mrow><mtext mathvariant="italic">C</mtext><mtext> - </mtext><msub><mrow><mtext mathvariant="italic">V</mtext></mrow><mrow><mtext>min</mtext></mrow></msub><mtext></mtext></mrow><mrow><mtext mathvariant="italic">C</mtext><mtext> + </mtext><msub><mrow><mtext mathvariant="italic">V</mtext></mrow><mrow><mtext mathvariant="italic">roundelay</mtext></mrow></msub></mrow></mfrac></mrow></math><img file="EP1531339A2_D0081.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 determined reception frequency is supplied to the frequency circuit 19 and a differential circuit 23.

The start state circuit 18 supplies position components x_i and y_i, Velocity components v_ix and V_iy in the x and y direction, the frequency circuit 19 transmission frequencies F_s, an error estimator 20 has an error vector ΔP₀ = (Δ_x0, Δ_y0, Δ_vx, Δ_vy, ΔF_s). From these 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 temporal changes Ṙ_xiest and Ṙ_yiest and the errors ΔR_xi, ΔR_yi and ΔṘ_xi and ΔṘ_yi becomes the frequency difference AF_i determined within the limits for the transmission frequency, which specifies the frequency circuit 19. From these estimates within the limits, estimated bearing angles B are determined in an arctangent circuit 21_iest calculated according to equation I.

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

About i = l_k Measurements per eigenleg whose number l_k in a control circuit 60, the measured and estimated bearing angles B_imess and B_iest evaluated. The duration l_k • Δt indicates the filter length.

The start state circuit 18 determines from the limit values ​​for the heading an optimization turning angle α, as explained in connection with FIG. 2b. This optimization rotation angle α is taken into account in the determination of the boundary conditions for the velocity components and also in the estimation of the position in the estimation circuit 15.

The 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 formed iteratively. The minimization is carried out until the error vector ΔP₁ a lower threshold ΔP₁ less than or equal to ΔP_min below.

At each measured bearing angle B_imess in the estimation circuit 15 path components R_Xest and R_yest as well as path error ΔR_x and ΔR_y 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 has converged to a value. Except for a residual error determined by the threshold, the estimated bearing angle B is then_est equal to the true measured bearing angle B_true and the estimated path and velocity components R_Xest, R_yest, V_Xest, Vyest equal to the true path and velocity components R_ytrue, R_ytrue, v_XTRUE, v_ytrue and the estimated Doppler frequency F_iest equal to the received, true Doppler frequency F_true, The threshold circuit 31 used for this purpose is connected downstream of the iteration circuit 30 and activates the error estimation arrangement 20. When falling below the threshold ΔP_min the target data P is displayed in a display 100.

FIGS. 8 and 9 show results for the evaluation of the method according to the invention. Limits are specified for an incoming target:<maths id="math0082" num=""><math display="block"><mrow><mtext>1 km ≤ R ≤ 60 km</mtext></mrow></math><img file="EP1531339A2_D0082.tif" /></maths><maths id="math0083" num=""><math display="block"><mrow><mtext>100 ° ≤ K ≤ 260 °</mtext></mrow></math><img file="EP1531339A2_D0083.tif" /></maths><maths id="math0084" num=""><math display="block"><mrow><mtext>0 m / s ≤ V ≤ 10 m / s</mtext></mrow></math><img file="EP1531339A2_D0084.tif" /></maths>

Among the diagrams, the length L of the self-level in (m), the speed V in (kn) and the heading K in (degree) of the host vehicle are indicated.

Fig. 8 shows the convergence of the method in the case where the target is at a first bearing angle of B_ridge = 0 ° and an initial distance of 30 kilometers. The target is traveling at a speed of 10 knots on a course of K = 170 °. Horizontal is the measuring time, vertical is 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 starts to converge after 10 minutes and after approx. 20 min is the error ΔK &lt;± 5 °, while in the conventional method this value is reached only after 30 min. The distance estimation shows an error of less than 10% after only 12 minutes and less than 5% after 16 minutes. The velocity estimate begins to converge after 11 min. After 20 minutes, the estimate shows an error of ΔV = ± 1.5 m / s. The target data estimation was done without frequency analysis and determining a reception frequency so that transmission frequency limits are not used.

Fig. 9 shows the errors over time for a target which is below B at the beginning of the measurements_ridge = 0 ° in and an initial distance of 20 km. The target is traveling at a speed of 10 knots on a course of 180 °. The course error is less than 5 ° after only 11 minutes, the distance error is less than 10% after 11 minutes and less than 5% after 16 minutes. The velocity estimate begins to converge after 7 min. After 20 minutes, the error is less than 1 m / s.

Comparing these results with an estimation of the target data without limits, it is found that the convergence times are much shorter, and still decrease, although the Doppler shift of a fixed transmission frequency by comparison with a measured reception frequency to minimize the bearing angle and frequency difference after Least-square algorithm is used.