System for determining position and velocity of targets from signals scattered by the targets

(54)

PATENT INVENTOR INVENTOR'S OFFICE NAME

The total defense research institute, Hans Hellsten, Linköping SE The Swedish Defense Material Agency

System for spreading from targets and speeds for the targets

172 90 Stockholm SE signals determine locations (56) (57)

QUOTES PUBLISHED: - SUMMARY:

The present invention relates to a system for determining the locations and speeds of the targets by means of scattered signals, and comprises a plurality of transmitters and receivers of electromagnetic or acoustic signals distributed at known points. Each pair of transmitters and receivers, monostatic or bistatic, is referred to as a measuring facility. The ranges of the transmitters are chosen so that a target at any point within the location room can be measured via scattering in the target of at least four, but preferably significantly more, measuring facilities.

For each measurement facility, target detection with constant false alarm level in the form of probabilities of resolution cells with respect to distance and Doppler velocity and possible targets are placed in a 2-dimensional linear space of distance and Doppler velocities associated with the measurement facility. 3-dimensional positions and 3-dimensional Doppler velocities are represented as a 6-dimensional linear position and velocity space divided into resolution cells with the same distance and Doppler velocity resolution as found in the measurement facilities.

For each section representing detections at at least 4 measurement facilities, the probability is calculated that the section is a false alarm that is generated by averaging between subsets that originate from different targets and when the probability falls below a predetermined value, it is stated that the section contains at least one target. Target modes and target speeds are thereby extracted.

<img file="SE519089C2_D0001.tif" />

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<td>E</td><td>patent in amended version</td><td></td><td></td><td></td>

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<td>E9</td><td>corrected patent in amended version</td><td colspan="2">• published under older legislation</td><td>J</td>

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<img file="SE519089C2_D0002.tif" />

519 089

The present invention relates to a system for transmitting signals from one or more targets to determine the location and speed of the respective targets. The targets are located in a position space comprising a plurality of transmitters and receivers of electromagnetic or acoustic signals scattered at known points in the position space. The system will be discussed in the following on the basis of a radar application. However, the invention is equally suitable for use in acoustic systems and it is the applicant's stated opinion that this patent application should also cover such systems. Generally, the system can be used in case a very large number of targets are to be determined in space and assigned to their velocity vectors.

Today's radar system for monitoring and combat management consists of a small number of long-range and capable radar stations. These systems are very vulnerable, partly because the radar stations can be detected relatively easily and partly because they are so few. The invention aims to improve this situation. The improvement consists partly in that the monitoring function is distributed over a large number of scattered but relatively simple radar stations, where some can be lost without deteriorating the position picture in a decisive manner. In addition, individual radar stations are small and easily transportable and can be placed at short notice without extensive ground installations or other preparations and therefore cannot be stretched in advance.

Another motive for the need for the present new radar technology is that future generations of military aircraft are expected to receive ever-decreasing radar cross sections. Already today there are so-called stealht aircraft that have radar cross sections less than ten thousandth of conventional aircraft. In the next few years, new types of military aircraft will become operational that have equally small radar cross-sections, but which are also high-performance in terms of speed and turning ability. These aircraft will initially be few in number, but in the long term, technology will spread to many aircraft types and to many nations' weapons.

The possibility of stealth design is limited by basic physical reasons. The ideal stealth aircraft (something that cannot be constructed today and may not even be in the future) has a complete electromagnetic adaptation to the surrounding airspace so that incident radar radiation is completely absorbed by the aircraft. This means that no reflection (or, in other words, retransmission) in the -N direction occurs

519 089 regardless of the direction N of the incident radiation. However, in the case of scatter physics, even in this case, the aircraft has a non-vanishing scattering cross-section in directions Ν 'which differs from the direction of retraction -N. In fact, the scattering cross-section in the extended direction N of the illuminating radiation is independent of electromagnetic adaptation and stealth design and constitutes the square of the aircraft's projected geometry in the direction N divided by the wavelength in square. Around the energy distribution concentrated in N and at angles that may very well be close to 90 * relative to N, with suitable wavelength selection, scattering cross sections can be expected in par with those currently prevailing for conventional aircraft.

As will be explained in detail in the following, the present proposal is based on so-called bistatic radar geometries. By combining these with relatively low radar frequencies (UHF), the above-mentioned easily measurable scattering cross sections for stealth aircraft are obtained, which can thus be detected.

The proposed technology uses a large number of radar stations with relatively short range. The stations are spread over a surface, over and around which you want to be able to detect and measure targets. The stations should have overlapping coverage so that each target is detected from multiple stations. Only distance and Doppler information and thus no directional information are used for the determination of the target positions. This means that the radar antennas can be made relatively simple, without sacrificing the scanning capacity or the measurement accuracy.

By combining at least three radar stations so that at least three mono- or bistatic measurements of distance and approach speed are obtained to a target, the target's three-dimensional location and speed are uniquely determined by the measurements. A special problem is how the simultaneous presence of multiple targets can be handled. Correct determination of target states in this case requires knowing which measurements at the different radar stations correspond to one and the same target.

It will be readily apparent that if measurements at different radar stations originate from different targets, these when combined will uniquely determine a target location and target speed, but this will not correspond to any real target. In the proposed invention, it is required that at least four different mono or bistatic measurements are possible for each point in the room. Thus, it becomes possible to verify with the fourth radar measurement if the employed combination of three measurements is from one and the same target or from different targets. The latter situation thus means that it

519 089 derived position and speed does not correspond to a real target and thus the fourth station does not detect targets at this distance or at this speed. If so, the invalid association can be rejected.

Of course, it is possible that the fourth station finds a target at the position derived from the three measurement geometries, but this is solely due to the coincidence that another target happens to have the same distance and velocity projection as the false association between the first three measurement geometries resulted. cases do not take four measurement geometries for a unique determination of target states. If, instead, five measurement geometries cover each point in the room, access to a fifth measurement can be used to reject or verify the remaining associations between four measurement geometries. The likelihood that these five measurement geometries actually see different targets becomes very small, which is why it can be assumed that the associations supported by five measurement geometries give the correct target states. However, if this confidence is not sufficient, a six-fold overlay is required, etc. In the proposed system, by utilizing bistatic geometries between a variety of stations with radiant antennas, a more than 20-fold overlay is obtained. The confidence for freedom from false alarms is thereby extremely high even in the case that perhaps 1000 targets are within the measurement ranges for each radar station.

The basic of the invention is the understanding of how a plurality of transmitters and receivers should be arranged to realize this extensive overlay of independent measurement geometries as well as how computer calculations of target states, based on superimposed verifications of associations from these independent measurement geometries, are practically arranged.

In addition to being able to handle large numbers of targets and high target densities, the proposed technology allows for such performance that the system in a common function can be used for monitoring the airspace over a very large area, say the entire country, combined with direct fire management with metemog accuracy. This compensates for the short range and the associated short preheating time. The system allows immediate weapons action upon detection, e.g. by commanding air defense robots based on the relative position between the robot and the target, by measuring both the robot and the target by the system. It is noted that this would be one of the few opportunities to effectively combat a future threat from stealth aircraft, as not only conventional reconnaissance radar but also fire control radar and robotic target seekers are expected to be inactive against stealth.

IN

519 089: · ** j: = ·. · '= .. = = -. = - = *

It is again emphasized that the described measurement method is completely independent of the radar stations' ability to angle measurement. Herein lies a significant difference from conventional radar and, in fact, the prerequisite (due to the otherwise too large amounts of data) for the possibility of accurate position determination and thus among other things. the possibility of precision control of air defense robots. The principle advantage lies in the fact that while the system allows the location of the flight targets over an extremely large number of possible resolution cells in location and speed - each meter and with a resolution of a few meters per second - the corresponding large amounts of data do not need to be collected at any single station or not even be represented by the total number of stations. This is in contrast to conventional radar, which can be said to measure each resolution cell to determine whether it is empty or contains a target. The proposed method works provided that only one target is located in each speed / distance cell at each station (without the requirement for angle determination). The number of speed / distance cells can amount to 10⁵, which means that, even if more than 1,000 targets are within the reach of radams, the probability of more than one target occurring in a cell is small. Once targets have been detected as a function of velocity and distance, the target's 3-dimensional position and velocity are determined by the subsequent algorithm. Even in this subsequent step, the amount of data can be limited by the appropriate design of this algorithm.

The 6-dimensional state space of modes and velocities may contain 1O²⁰cells. This number is close enough to the same order of magnitude as the number of atoms in any gram of a substance (Avogadro's number). It follows that unless sophisticated methods are utilized to collect and signal data, this task becomes unmistakable even in all future computer equipment since computer memory is limited by being made up of a finite number of atoms. An efficient algorithm design is thus not only a desire, but a requirement for the feasibility of the proposed method.

A close-to-hand such method of effectively limiting the computational burden to determine target locations and target velocities in the corresponding state space is based on three mono- or bistatic measurement geometries and N targets detected by each of these measurement geometries. Based on this data, all conceivable target35 states for the N targets are first formed. These states will be of the order N³ to the number. In the way already mentioned, each of these candidate states can then be supported or rejected depending on whether the derived targets and speeds

519 089 are found as detections of additional measurement geometries that observe the area in which the candidates are placed.

However, this direct method has several weaknesses:

- Determining target locations and target speeds from radar data is a demanding calculation. Obtaining target locations for each of the N³ the target candidates include (for bistatic measurement geometries) the solution of a 6th degree algebraic equation. In addition, every candidate10 must then be checked for all facilities that reach the corresponding target position. This provides a processing algorithm consisting of the CN³ elementary counting steps. Unfortunately, K necessarily becomes a relatively large number (say&gt; 1000), since this includes said calculation and then, among other things, the complexity of solving the 6th degree equation. In addition, if N = 1000, the number of steps is&gt; 10¹² which may be considered impractical and ineffective, though not in principle impossible.

By initially selecting 3 out of maybe 20 coverage radar stations, there is a clear risk that none of these just happened to observe a particular target. Perhaps because the target has said stealth design or because it appears at an aspect angle inappropriate for this particular station (it has Ο-Doppler and drenched in the ground) or weather and propagation conditions happen to be unfavorable at the time of the measurements. Although in this case, perhaps all other of the 20 radar stations can detect the target, the method will, however, not measure the target. This is a crucial disadvantage, since this type of situation can very well occur and the radar system must work in this case as well.

Based on these arguments, the present invention uses a different principle for target detection.

The object of the invention is to solve problems in determining the speed and location of targets using the above method, which is based on a large number of overlapping radar stations. This is done by giving the invention a design as shown in the following independent claim. Suitable embodiments of the invention are apparent from other claims and encompass, in part, various concrete ways of placing transmitters and receivers and concrete design of calculation steps, and in part a particularly suitable antenna arrangement.

519 089

The invention will be described in more detail below with reference to the accompanying drawing, in which Fig. 1a shows the principle of coarse target positioning by superimposed radar measurements and refinement of resolution cells; the number of facilities with detections carrying is indicated in the respective resolution cell, whereby cells determined as empty cells are marked in italics and cells that are preserved for further decomposition are marked in bold type. Fig. 1b shows target positioning through three transposed cell divisions; Fig. 1c shows fine positioning with four consistent measurements for each sub-reflector; Fig. 2 shows a computer architecture for the execution of target positioning; Fig. 3 shows frequency assignment within a radar grid at increased frequency; Fig. 4 shows bistatic radar configurations covering a triangular prism of positions; Fig. 5 shows an antenna arrangement suitable for the application; 6 shows an appropriate principle diagram for a radar receiver.

Basically, the system consists of a scattered amount of transmitters and receivers at a known point in a location room, as well as an analysis equipment. The system can, as stated, work with electromagnetic or acoustic signals. A conventional radar is monostatic, which means that the pair of transmitters and receivers are co-located. However, if they are spatially separated, the equipment is called bistatic. The system assumes that measurements can be made bistatically, but also monostatically. In the following, a pair consisting of a receiver and a transmitter, whether the measurement is bistatic or monostatic, is referred to as a measurement facility.

The analysis equipment determines the timing of transmission and received signals are parameterized as a function of walkway and walkway change between transmitting point and receiving point according to accepted principles for radar. Walkway change is thereby estimated through Doppler estimation. Furthermore, the analysis equipment stores and analyzes received signals throughout the system in ways that will be described in more detail below. This requires communication between the various transmitters and receivers and the analysis equipment. The communication technology necessary for the invention is established and thus does not in itself form part of the invention and will not be discussed explicitly.

519 089

<img file="SE519089C2_D0003.tif" />

Necessary for the invention is that the ranges of the transmitters are selected so that a target at any point within the location space can be measured via scattering in the target of at least four measuring facilities. As already discussed, this is not a choice of suitability but an absolute prerequisite for the function of the invention. This is explored in more detail below in the 5 more detailed review. It also shows that the invention works even better with more measuring facilities.

The following designation conventions continue to be used: Vectors are indicated by an arrow over the symbol, e.g. N. Affine points e.g. in the position room is indicated by a dash over the symbol e.g. X. Quantities are indicated in bold, e.g. X.

Measurement facilities (mono- or bistatic) are indicated by lowercase Greek letters.

At each measuring facility φ, target detection with constant false alarm risk - "Constant False Alarm Rate", CFAR - is performed by comparing the signal intensity with the noise intensity of each resolution cell with respect to distance and Doppler speed.

Noise may be thermal or caused by signals that are not available to the radar function, but satisfy any given statistical distribution. The cells where the measured signal intensity exceeds the expected noise intensity with any given probability are stated to contain targets, those below the value are stated to be empty.

To move from detections to actual target locations, the analysis equipment uses a target positioning algorithm that includes each measuring facility φ placing n_t target candidates in_in of N resolution cells in a 2-dimensional linear space of distance and Doppler velocities SJ, and 3-dimensional positions and 3-dimensional Doppler velocities are represented in a 6-dimensional linear position and velocity space S⁶ subdivided into N³ resolution cells XcS⁶ with the same distance and Doppler velocity resolution as found in the measurement facilities.

Given a cell XcS⁶ there are a number of facilities = Φ (Χ) carrying the cell. The facilities to be included in Φ (Χ) are mainly dependent on the facilities' range and proximity to the position of X but also wave propagation conditions and can thus depend on e.g. weather. However, it is assumed that Φ (Χ) is always known for each XcS⁶. In addition, for each facility ^ e Φ (Χ) there is a known image

X c S⁶ -&gt; ^ (x) c SJ which relates target states to measured values ​​at each facility φ e d&gt; (X). Let n (X) be the size of the quantity Φ (Χ) ie. the number of measuring facilities that carry X.

519 089

Now, at some point, let ′ ′ (X) be the number of facet tenses φ e Φ (för) for which ^ (X) contains a detection, i.e. the number of measurement facilities that detect targets that could hypothetically lie in X. Consider the ratio a (X) = w '(X) / «(X). In an ideal case, all facilities carrying the cell X also always detect the target located in X, where a (X) = 1 would apply in all cases where X contains a target. In reality, however, it may occur that only a fraction of the facilities in Φ (Χ) perceive the target, in which case a (X) &lt;1 The reasons for this may be different, mainly that the propagation conditions for radar signals are not assumed or that the target has less radar10 cross-section than assumed.

Sold as a target positioning criterion in S⁶ For example, it is utilized that a (X) exceeds a predetermined value selected in view of such a limited probability of discovery and thus may be less than one. On the other hand, an excessively small threshold value for a (X) may involve the risk of false alarms caused by the fact that for any cell X that does not in fact contain any target m ^ (X) nevertheless contains targets for sufficient facilities φ e Φ (Χ). This risk of false alarms can be calculated by probability calculation. A useful approximate formula is p^BEAST{_n'^^^UIN

The formula indicates the probability of a false target occurring in any cell, given that r measurements are sufficient for detection, M is the expected number of targets and N the number of resolution cells. The formula is based on the fact that false alarms arise entirely through associations between detections of different targets at the various facilities. The assumption can be assumed to be correct if M »n '&gt; 3. For example, if om -10³applies

N = io², n '= 4 =&gt; p^FA («') = 0,99999...

N = 10², w '= 20 =&gt; p^FA(n ') = 0.99

N = 10³, h '= 4 =&gt; p^FA(n ') = 0.1 tV = 10³, m '= 20 =&gt; ^ (^) = 10^-21N = 10⁵, n '= 4 =&gt; p^FA (ri) = 10⁸N = 10⁵ , ri = 20 =&gt; p^FA (»') = 1O⁴⁰

We see that about the number of resolution cells in S² is less than the number of targets N &lt;M then almost all cells are in S⁶ covered by false alarms. About the number of resolution cells in S² is in par with the number of targets N, the degree of occupancy depends largely on the degree of

519 089 overlay. While the number of resolution cells is significantly greater than the number of targets N »M, the probability of a target in any cell is small but because the state space S⁶ contains N³ resolution cells (i.e. 10¹⁵ cells of N = 10⁵) then the total probability that a false target exists in any cell to a corresponding degree is greater. Obviously, with selected parameters, n '= 4 is insufficient to eliminate false targets from the state space while n' = 20 is more than sufficient.

In fact, the large redundancy in the form of many superimposed measurement geometries is a crucial opportunity to quickly carry out the signal processing for association between the measurement geometries. This rapid procedure assumes that a preliminary association can be carried out with a resolution coarser than the final one. These coarse cells become relatively few in number, but the multiple redundancy nevertheless makes a certain number of cells empty and contains neither targets nor false alarms.

These cells can thus be deleted in the preliminary association and the remaining cells maintained to a finer cell division. This is the basis for the computer implementation of the target positioning algorithm described below, see also Figure 1a.

In Figure 1a, the left part of Figure A shows a distribution of empty cells and cells containing flight targets. These cells are coarse and for this reason there are many measuring facilities for each cell that detect targets that may in principle lie in the cell. The numbers indicate how many such facilities are available for each cell. The fact that the number for a particular cell is italicized means that the number of facilities is below the fraction of the possible number of facilities required for it to be likely that the cell contains a target. Cells that are preserved for further disintegration are marked in bold.

The upper high portion, B, shows a disintegration of a cell that does not contain targets, whereas the lower right portion, C, shows disintegration of a cell containing target. This shows how during further decomposition the original number of detections is shown to be in a certain position, which is determined with good precision as the cell division becomes finer.

In the analysis one selects the original cell division such that S⁶ indelas im₀ disjunct but congruent cells X_ly. The cells here are believed to be parallelepipeds.

However, other cell geometries may also be conceivable. The number m₀ should not be greater than adding to each cell a number of coefficients (of the order of 100 at 20-fold

519 089 overlay, see below) which determines the images w_p(X) can be stored in a fast memory in the computer that performs the target positioning. Thus

<img file="SE519089C2_D0004.tif" />

where μ () represents the volume of an area in the 6-dimensional position and velocity space. Now suppose that a certain fraction of the original cells X_vare empty according to the previously discussed target positioning criterion. We then divide the remaining cells into subcells so that we get as many new cells as possible in the original subdivision. This achieves that the computer's memory is again loaded to the same extent and the next level calculation flows identical to the original.

It must be taken into account that cells should be divided so that each original cell is evenly divided into new cells because otherwise we will not fully utilize the previous knowledge of which cells are empty and which may contain targets. Denote with Ω_ί the total volume of cells that the target positioning method designates as non-empty at the subdivision level. Thus, the subdivision ratio is selected by rounding the ratio Ω_ο / Ω_γ to the nearest larger integer h- = int-2² Ω_λ

Note that in the initial divisions the false alarm probability can be very large, e.g.

Ω_λ = Ο, 999 ... Ω_ο. In this case, however, h₂ = 2. Cells are now also divided according to

<img file="SE519089C2_D0005.tif" />

It is thus not important how cells are divided, but only how the volume is reduced. Cells can be divided either by fine-tuning the velocity distribution in one or more dimensions or by refining the spatial resolution instead.

Now suppose to recapture a certain fraction of the refined cells X_2&gt; are empty according to the target positioning criterion. We divide the remaining cells into subcells so that we get as many subcells as possible in the original subdivision. Thus, it is achieved that the computer memory is again loaded to the same degree and

519 089 the next level calculation can run identical to the original. This occurs if we assume the volume Ω₂ of remaining subcells select the volume of the refined cells ω₃ according to

<img file="SE519089C2_D0006.tif" />

6^

<img file="SE519089C2_D0007.tif" />

Generally, a recursive process of refined cell divisions is obtained

<img file="SE519089C2_D0008.tif" />

which continues until a velocity resolution is reached which corresponds to the measured Doppler resolution.

Regarding spatial resolution, the interruption criterion is more subtle. Two complications that arise from the finite extent of a target should be noted:

A. The intention is to obtain a resolution that is finer than the extent of the objectives. The target positioning criterion given by a (X_y), that facilities measuring the target in different geometries measure the same distance to the target, cannot be applied to this fine resolution, since an airliner's sub-reflectors cannot normally be detected from anything other than certain viewing geometries (for example, a wing root on an aircraft can only be detected from one side ). Measurements derived from dissolution cells X_y which only includes parts of a target will thus not create sufficiently large values ​​of z? '(X,_;).

B. Even when the spatial cell division into S⁶ is greater than the extent of the target, the target positioning criterion may be inapplicable if a target lies on the border between two adjacent cells X_y and X_(&gt;.. In this case, some of the target's sub-reflectors will be attributed to one cell and the remaining reflectors to the other. There is then a risk that neither a (X_y) or «(X_y.) becomes large enough for the target to be detected. The risk of this happening is small about the cells

519 089 is significantly larger than the targets, but increases and becomes unacceptably large as the spatial cell size approaches the target size.

To address these complications, goal setting is performed in three steps:

1st Resolution of false alarms. In this first step, it is used by a (X)_island ) given the target positioning criterion and is carried out according to the previously described procedure until resolution volumes are reduced to as small a spatial cell volume as possible.

This level should still be sufficiently fine for false alarms to occur only in a few.

2nd Final rough positioning. In this, the solution is further refined by said method with the difference that more cell divisions Χ⁽¹ζ, X⁽²\ ·, ... by S⁶ considered. The cells Χ^(Ιζ, Χ⁽²⁾ί,, ... are congruent but differ for each level in translational fraction of the cell length in the spatial domain. Since few false targets are presumed and only cells in the immediate vicinity of the targets are taken into account, an overlapping cell division is not computationally difficult to handle. The given target positioning criterion is used on all cell divisions Χ ^ ζ-, Χ ^ ζ ·, .... Suppose we take into account cell divisions, which differ in half the cell length. If a target does not have a wider distribution than half the cell size, they will then safely be enclosed in at least one cell Χ⁽* ζ, according to Figure 1b. The target modes can then be interpolated to positions within half the cell size. This is because the target is wholly or partly in Χ ^ ζ - X ^ V if it is detected in Χ ^ ζ but not in X⁽* V as well as being completely in X^(T)y nX ^ V if it is detected in Χ as well⁽* ζ as in X⁽* V. For cell divisions with finer overlap, targets with size approaching the entire cell can be considered and positioning becomes correspondingly better.

Figure 1b shows a target A which is entirely within cell a. If the target is translated to B so that it intersects an edge of the cell, it is surely located in one of four cell halves of the original cell, and thus lies in a cell b that separates itself from a through translation half the cell length along a border. If the target is translated to C and intersects two edges, it is enclosed in one of four cell quadrants c that differs from a by translation along two edges. In three dimensions, seven cell divisions take half the cell length to safely enclose targets no larger than half the cell length.

519 089

3rd Fine positioning. In this final step, a cell division X is performed_{n + 1;} in which individual reflectors in the target are resolved by utilizing the full bandwidth and resolution capability of the radar facilities. It is thus assumed, in principle, that the target is within a cell X obtained according to paragraph 2, which cell is approximately the expected size of the target. According to point A, earlier target positioning criterion, given that the plurality of facet tones carrying a point reflector in X_{+ v}, does not apply. However, it is now perfectly acceptable to require only, for example, verification with four measuring facilities when positioning partial reflectors, ie.

^A(X_v) = 4 / n (X_island). This is because erroneous associations between detections are very likely to result in positions outside X_n;. and thus already found to be empty. These four measurement facilities will have similar viewing geometry, with the assumption that the target positioning criterion is met by enough actual sub-reflectors in flight destinations. This is shown in Figure 1c, which partly shows a target entirely in a single cell A after coarse positioning and partly reflects reflexes from the target divided into subcells B.

With the determination of the location of the sub-reflectors, the radar measurement procedure is considered completed. In the application of precision control of flight targets, additional data20 handling remains in the form of target tracking, target recognition and target point selection. The basis for these procedures can be found in the radar data collected. It is, for example. it is possible to use established pattern recognition methods to determine the orientation and extent of flight targets based on the location of the sub-reflectors. Important prior knowledge is found in the common velocity vector of the sub-reflectors, which provides a dimension for orientation determination. In addition, the diversity of radar facilities provides a genuinely 3-dimensional image of aerial targets, The normal right / left symmetry of an airplane becomes an indication for the final determination of orientation and the indication of the main dimensions of the airplane.

We now describe in greater detail the images m_v(X) to be implemented in computer. Assume that measurement data from all facilities carrying a common volume P_O of positions are stored in a computer. The 6-dimensional state space S⁶here refers to this volume combined with a velocity volume V_O, thus

S⁶ = (P_O, V_O). Let Χ_ϋ = (P +, V_v) be a cell entrapment of S⁶ in parallel pipettes in position and speed room. It is noted that the cell division is entirely given by a rectangular grid of vertices Xy = (Py, Vy) for the parallel piped. The images w ^ (X_v) is defined by maximum and minimum distance and Doppler speed 519 089 values ​​and vU, respectively._/;. for each cell X,_y = (P_&amp; , V₀ ) and with respect to each facility φ e Φ (Χ,_;). Thus, where [ώτ, Ζ&gt;] is defined as the interval from the number a to the number b.

As previously mentioned, the number of cells in S⁶ be so large that storing the numbers Τφ ^, τφ, ^ and v ^ jj, νφ ^ for each cell and facility is an impossibility. Instead of calculating 10 and vj, ij, v &amp; y individually for each cell, as also mentioned, involves the complicated procedure of solving a 6th degree equation. However, it is possible to find and νφ, α, νφ, η quickly by linear interpolation. This assumes an initial cell division Xiy = (Piy, Vv) of S⁶ which is not greater than the necessary interpolation coefficients for the continued refinement of this cell division can be stored for each cell and facility. Highlights X_{t, J} = (P_in} , Vy) for the refined cell division is easily calculated from X_{} j} = (Ρ_υΛ_ν). The numbers rfa, rfä and follow from the knowledge of the points X_in} = (Ρ_ν,7₉) and the unit norms Χ_φ,_νfor the intersection with Ry of the distance surfaces corresponding to constant (mono- or bistatic) distance with respect to the facility φ. The unit normal, in so far as the cells are not too large, can be determined with good accuracy from a fixed but characteristic value for the main curvature radii and the unit normal

Ν_φλΙ for cutting the distance surfaces with Piy. Thus, for the interpolation, four numbers are required (of which two angles are described) for each facility carrying each initial cell Xiy = (Pl;, Vy).

The transfer of the above procedure to a computer processing scheme is relatively obvious, see Figure 2. Assume that measurement data from all facilities carrying a common volume P_O of positions are stored in a computer, and that data in a computer memory B is sorted into memory banks by facility and within each such bank at 30 distances and speeds. The spatial cells P_ly. forms address areas in another memory

A in which the coefficients are stored for interpolation calculation of the images τη_φ for cells X,_y· = (P, /, V,_z), where X, y is a subcell within X_1;.. Except for coefficients, address area A contains pointers to the memory banks for data derived from facilities carrying cell X_1; and thus at least some of its sub-35 cells. Coefficients are obtained from A to form the images m_p(x_y.) for bank after bank. A third memory C contains counters, so that there is a counter for each cell X,. and that it counts a unit for each time a target is detected via ηι_φ (x_y) then a (x_v) is evaluated. A certain number of cells will then

519 089 is stated to be empty on target. Based on the extent to which this occurs, the solution is refined in the non-empty cells and new counters are initiated in C for the refined cells. The process is repeated in a similar manner until final dissolution has been reached. It is noted that the above method of refining cell division so that the total number of cells is kept constant as far as possible guarantees high efficiency in memory occupancy by this type of computer scheme.

An advantageous way of placing transmitters and receivers is to co-locate them at each grid point in a regular parallel grid, with e.g. common antenna. By a regular equilateral lattice is hereby understood a plurality of points in a plane, which constitute the corners of an equilateral polygon which, through translations, just covers the plane. An equilateral grid can be rhombic, quadratic, or hexagonal from the selected polygon. A rhombic lattice made up of equilateral triangles is called equidistant because the possible lattice translations are all multiples of one and the same lattice15, see Figure 3.

For the proposed monitoring system, the equidistant network is preferred because it results in the smoothest possible spread of the radar stations over the surface. The square grid is also conceivable and does not really pose any significant disadvantages compared to the equidistant. Here, we concentrate the discussion on the equidistant network, which may thus constitute a concrete embodiment of the monitoring system. It should be emphasized that the placement of stations in an equidistant grid only needs to be approximate and may well deviate more or less from the regular pattern in order to adapt to external conditions such as topography etc.

When bistatic geometries are included, the number of possible measurement configurations becomes large and so does the desired overlay of independent measurement geometries. For each station, the number of bistatic facilities in which this station is included becomes 12 if the other station of the bistatic pair is within a grid distance d and 36 if the other station is allowed to lie within two grid distances 2d. Note that each facility provided by one transmitter in one grid point and one receiver in another has a reverse facility where the receiver is in the first grid point and the transmitter in the other. Both facilities measure under the same geometrical conditions and provide the same data so that only 6 and 18 configurations can provide independent data for the respective 35 grid spacings. Especially in this latter case, the desired degree of multiple overlay is achieved, so the continued discussion of the range of radar stations assumes that the separation between transmitters and receivers in bistatic geometries is allowed to extend up to 2d.

519 089

Consider a position space in the form of a triangular prism with a triangle of radar stations separated a grid distance as a base and with height h (the expected maximum target height). Triangle is superimposed (in whole or in part) by 3x36 = 108 bi5 static facets, given that the radar stations have pulse repetition frequency and transmit power selected according to accepted principles. Only those configurations that have e.g. receiver in the corner of the triangle, ie 54 of the 108 facilities, however, can provide independent bistatic data from each other. In fact, among these 54 configurations, the bistatic facilities between Triangle's homes are counted twice, so only 51 of the 54 facilities provide independent data. In addition to this bistatic data, monostatic data is also collected covering the triangular prism. The extent to which this occurs is not a dimension for the selection of radar parameters and is therefore only described somewhat later in the following.

The following suggestions for transmission / reception patterns for the radar stations provide the opportunity to utilize the desired bistatic geometries in the grid. The radar bandwidth B required for a certain distance resolution is divided into as many sub-bands as the number of stations located within a subset Ψ (2ά, Ρ) of the grating, which is a regular hexagon with radius 2d, centered around the grid point P.

Thus, the number of sub-bands is 19, see also Figure 3. Radar transmission and radar reception is performed with the known technique called stepped frequency according to which technique each sub-band is completely transmitted and received before the same procedure is repeated for the next sub-band following a predetermined turn order. For the present application, the receivers of each station are performed so that reception can occur over the entire bandwidth during each frequency step. Furthermore, by assigning each station within 'P (2d, P') one and only one subband, the received signal for the station at the point P will cover the entire radar band B, while each subband can be uniquely attributed to some of the 19 stations in P (2d , P). In addition, if the same order of the subbands is applied to all stations in Ψ (2ά, Ρ), data for the entire radar band will have been obtained for all bistatic configurations in Ψ (2ά, P) that have reception in P. A transmission pattern is established over the entire grid by utilizing the transmission pattern in P (2d, P) in Ψ (2ά, Ρ ^ mG ^ where m and i are integers and G_t is a vector with length 3d and direction ix 60 ', cf. Figure 3. They realize that just as at point P, the transmission pattern involves data for the entire radar band for all bistatic configurations in Ψ (2ά, Ρ '} that have reception in each grid point P'.

519 089

That the signal recorded in each grid point P can be uniquely attributed to one of the transmitters in Ψ (2ά, Ρ) assumes that listening at each radar station does not last longer than a time

3d ^tsUg ~ c after the start of the shipment. In fact, the simplest embodiment of the monitoring system is that the listening time is limited to the rise time minus the transmission time. In this way, the desired reflected signals can be received completely before the hearing. A more advanced method is to modulate the transmitter signal by e.g. linear frequency sweep. This allows the overheating signal to be received at the same time as radar reflexes, after which both signals can be separated in distance and the step time is fully utilized. Several known methods can be applied to suppress overheating from pulse to pulse and thus the emergence of ambiguous echoes. Such methods include changing the modulation of the transmission signal between frequency steps as well as changing the order of frequencies from step period to step period.

With the specified time limit, the 51 independent bistatic geometries can all be used for superimposed measurements within the triangular prism. However, we can simplify the ongoing discussion by considering only configurations that cover the entire triangular prism, see Figure 4. Let C be its center and A_O any arbitrary of the grid points that form corners in its base. Name all grid points within two grid distances from C through the angle they have relative to the vector Ä₀C. Thus, the vertices of the base, while the grid points Α ^, Α ^, Α ^, Α ^, Α ^, Α ^, Α ^, Α ^ are found within an additional grid distance.

Consider first the situation h = 0. As shown in Figure 4, however, in this case 12 independent mono / bistatic measurements with A_O as a reception point that covers the entire prism. The bistatic angles are approximately scattered throughout the revolution, ie. the angular increments between the geometries are on average 40 '. Assuming that all three homes 4&gt;, 4₂₀&gt; A «o contains recipients, the triangular prism will be superimposed by 36 measurements. Among these, bistatic measurements return between the hay A₀, A₁₂₀, A₂₄₀ twice each so 34 of the measurements are independent. Some of these measurements will only cover the entire prism when h = 0. Such is the case with transmissions from ^_2O, 4oo, 44o&gt; A2o&gt; ΑβοΆ »· Thus, 18 of the 34 measurements created by Α ^, Α ^, Α ^, Α ^, Α ^, Α ^ in combination with

519 089

Å_O, 4₂o&gt; A40 ^only their lot ·¹ coverage. In Figure 4, where a target exists between center C and A_]20, however, shipments will come from A₂₀, A_ioo, A₁₄₀, A₂₂₀ with reception in A₀, A₁₂₀, A₂₄₀ even reaching such targets (even up to targets at heights slightly higher than the grid spacing). It follows that the overlaying of measurements in these cases is at least 28-fold (in fact, there are additional monostatic and bistatic measurements of the target including the stations in Α ^, Α ^, Α ^, Α, ^ which we ignore here). The symmetry gives the same at least 28-fold coverage for alternative target positions between C and the triangle corner h₂₄₀ and a_O, ie the whole prism apart from the most extreme target heights.

Of course (although we will not continue to study this case explicitly) it is possible to increase the step time according to a general formula

Thus, the signal recorded at each grid point P can be uniquely attributed to one of the transmitters in P [(k - 1) J, P]. It is required that the transmitter signal be divided into 3k (k + 1) + 1 frequency step.

The design of radar sensors for the proposed sensor grating follows in most respects conventional radar principles. Thus, transmitter power is selected according to the bistatic radar equation_n . _λ Ρ ^ χΡ ^ χ kTQ

PA = 4π ™ ^TX--^σΝ ^ int

The left side consists of the size parameters of the radar in the form of the average power of the transmitter P, and the effective area of ​​the receiver antenna A. The right side defines the radar function for noise equivalent radar measuring surface σ_Ν, distance between target and receiver R_K , distance between transmitter and target R_TX, noise temperature T, integration time for Doppler estimation of (bistatic) approach speed ζ *, and angular volume

Ω which needs to be illuminated by the radar transmitter. The most demanding cases in terms of power are when R_PJr 2d and r_TX «D or vice versa. We get it

Ρ4 «16π

<img file="SE519089C2_D0009.tif" />

519 089

An upper limit for t_int put off by the uncertainty about target maneuvers. This requires that Doppler measurements be renewed at a certain rate and that t_INL is limited to this rate. The indeterminacy is caused partly by the target's vector of velocity changing during maneuvers and partly by the target's orientation in the room changing, which changes the position of the phase center for radar signal propagation in the target. The limitations due to the respective effect are expressed by the differences

<img file="SE519089C2_D0010.tif" />

where a is the characteristic acceleration characteristic of target maneuvers and v_n Characteristic man tic target speed during maneuver, AR is the distance resolution and λ is the radar wavelength.

A lower limit for t_int is set by the requirement for Doppler clarity. The proposed sensor grille operates according to the above with frequency steps, which are received during fixed time intervals._step determined by the grid spacing d. Since 19 such steps must pass between transmissions of the same frequency, Doppler ambiguities arise in the manner well known in radar when the repetition frequency becomes too low in relation to the transmitted frequency and expected target speeds.

These ambiguities can be resolved in the present case, since the distance resolution is high. Namely, according to well-known principles of matched filtering, Doppler speeds can be sorted into traps with different degrees of linear distance migration during the integration time. These traps are then sorted with matched filtration in different Doppler shifts. If Doppler ambiguities thus obtained are outside the resolution of the linear distance travel, they can be sorted out, whereby the Doppler speed is unambiguously determined. The speed resolution obtained when sorting by distance walking is = 2AR / h_int. Since ambiguous Doppler velocity is λ / ^ / 2, where fsw is the signal repetition rate, the condition for unambiguous Doppler velocity determination is obtained.

<img file="SE519089C2_D0011.tif" />

λ

519 089

It is clear that the resolution must be good in relation to the wavelength as well as the integration time must be sufficient. Since = \ / 19h_3teg and step = 3d / c is obtained&gt; 228 dAR

CA

Based on the constraints implied by accelerations, two conditions for the necessary radar wavelength are obtained.²ARE²_my &gt; 3 103968 -: = 2 = ---- mm M 2 λ

VJ

For example, in an embodiment relevant for scouting over large areas, grid distance d = 20 km. In addition, if α „= 100 m / s², = 100 ms¹ and AR = 2.5 m is obtained ⁼ θ "? ^m respectively 2_my = 0.3 m. Consequently, relatively low radar frequencies are suitable, which harmonizes well with not requiring any angular resolution and, consequently, that the aperture does not need to be large in relation to the wavelength.

The integration time with 2 ^ = 0.7 m becomes t_int = 0.06 s. If for the example we choose that the transmitter antenna only illuminates the airport ie. the upper hemisphere and this isotropic is Ω - 2π steroid. In addition, use σ_Ν = 0.1 m² and A = 1 m². The required average power according to the radar equation thus becomes P = 36 W.

In another embodiment for battlefield surveillance, d - lkm is selected. In this case, it is relevant to look at operating robots as well as projectiles why = 100 m / s²= 300 ms¹ and AR = 0.5 m. We get λ = 0.03 m and λ respectively. = 0.01 m for the two wavelength criteria. The integration time with Amine = 0.03 m becomes = 0.01 5. Assume again that Ω = 2π stered and that σ_Ν = 10 µm² and A = 0.1 m². The necessary mean power according to the radar equation then becomes P = 10 W.

A further aspect that must be considered is self-glare, ie. the phenomenon that for a bistatic radar facility the transmitter signal directly illuminates the receiver antenna and adversely affects the receiver function. One method of avoiding mixing may be to

519 089 appropriately design the directional characteristics of the antennas. It is, for example, it is possible to design vertical directional characteristics, so that both ground interaction i is minimized, and that the antennas neither transmit nor are sensitive to signals that propagate horizontally and thus between adjacent radar stations. On the other hand, a capacity to measure low-flying targets is highly desirable, which places demands on antenna action at the horizontal level (a certain vertical lobe formation is also desirable and will be discussed in more detail below). It is also possible to shape the directional characteristics in bearing joints with zero antenna action in bearings directed to adjacent radar stations. This is also not a suitable method to eliminate the glare effect since the sectors with zero antenna effect must be very narrow in order to avoid a significant reduction in system performance. Low frequencies, which were found to be suitable for larger scouting systems above, make demands on large antennas, which is hardly possible for a system based on many co-operating stations.

Consequently, the antenna directional action can hardly be utilized to avoid glare. However, the limitation in performance due to this effect can be minimized by appropriate design of the transmitter and receiver function. There are two relatively opposite approaches. One is based on a careful maintenance of an equi distant grid. Hereby it is achieved that during the step time t_step = The 3dlc transmitter signal only affects the received signal during certain specific times namely

<img file="SE519089C2_D0012.tif" />

<img file="SE519089C2_D0013.tif" />

where Δί is the transmission time and Z_O some time for a new broadcast step. If now the transmission time is selected briefly and then based on resolution ie.

<img file="SE519089C2_D0014.tif" />

it becomes perfectly acceptable that measurement data is not available during glare. Admittedly, due to glare in the grid point P, the measurement data room S *, where P is included in the facilities φ, does not lack data for some resolution cells in the distance. These

519 089 resolution cells respond through the projections ηι_φ against volumes in S⁶ where the facility φ does not add measurement values. However, due to the multiple overlay of independent measurement geometries, only isolated resolution cells X cz S⁶ lack three metrics and essentially no cells miss more than three metrics despite the glare effect. The target positioning criterion given by a (X) = n '(X) / n (X) can be easily adjusted for this effect without significant degradation of performance.

However, in most cases, the requirement for a strict and accurate maintenance of an equidistant grid is inappropriate. From a military point of view, the grating is easy to fight with precision when the grid points are exactly known. It may also be inappropriate from a wave propagation point of view or from a purely practical point of view to place radar stations in a predefined configuration. Since radar equation determines average power, short pulses imply a high peak power requirement, which is device-wise. Preferably, instead of using a suitable coding of the transmit signal, a working factor is used

<img file="SE519089C2_D0015.tif" />

which is reasonably large, e.g. η = 10%. One way of dealing with the glare problem that fulfills all these wishes is based on the observation that the glare signal is coherent with the signal reflected from the target. Thus, they can be discriminated against by Doppler and distance analysis. However, the Doppler analysis can be done with sufficient dynamics for this discrimination, which requires a highly linear radar receiver.

In order to investigate the requirement for receiver dynamics, it is noted that the signal strength from the signal reflected by the target is determined by the radar equation and is kT / i_mt in each Doppler cell from a target with the target surface σ_Ν. Maximum glare at any grid point occurs due to transmission from the six adjacent grid points ie. during the time interval t «tq -i— r₀ -i — i · zlz cc

The strength of the blended signal is thus estimated

<img file="SE519089C2_D0016.tif" />

519 089

The necessary dynamics in Doppler analysis are thus

Rf. _tf^mt kT Ω d^{2 mt} kT

Required dynamics at reception becomes c pkT Ω d² c or

<img file="SE519089C2_D0017.tif" />

&lt;384π²

AR 1 d² where c HAR is the receiver's full filter bandwidth. In both of the above examples, the requirement for receiver dynamics is at most about 70 dB at 7 = 10%. It is a fully possible and well-known technique to adapt the receiver function to handle this dynamic, at least with regard to the example utilizing the low radar frequencies. Also note that 70 dB receiver dynamics is an extreme case. Among other things, For example, the maximum aperture signals occur at the beginning of the reception period and then only coincide with the targets adjacent to the receiving station. For distant targets and with these hearing weak signals, only interference signals from transmitters are found at greater distances. In these cases, the aperture signal is attenuated, e.g. in that the terrain offers a significant shield. The necessary instantaneous receiver dynamics will therefore be around 50 - 60 dB. The receiver function can thus be simplified with so-called

Automatic Gain Control (AGC) which allows instantaneous adjustment of the dynamics to the level of the incoming signal.

Regarding the methods of coherently suppressing the glare signal, it is noted that the work factor should be large as opposed to the first described method. Also note that the coherent glare suppression method itself involves receiving the direct transmission signals between facilities. This provides an obvious method of synchronization between stations, which is necessary for the bistatic function.

One last aspect that needs to be highlighted regarding sensor design is antenna construction. An important advantage of conventional radar technology based on high degree of directional sensitivity is that it can naturally be combined with an ability to suppress interferences by zeroing directional sensitivity in interfering directions. The

519 The proposed 089 radar grille requires a corresponding functionality of the individual radar stations. Once such a function is present, the very fact that radar stations across the surface interact bistatically will increase the interference strength, since this grid structure of stations requires interference to be carried out simultaneously in a variety of directions.

Figure 5 illustrates in A, viewed from the side, a suitable antenna structure for the radar station in a single grid point for the low frequency radar system. The views below mainly concern this system. The antenna structure combines the necessary, bearing-bearing uniform directional characteristics with the appropriate vertical directional characteristics. It also has the desired noise suppression capability. The antenna consists of two parts. The first part consists of a vertical column of a number of identical simple antenna elements, e.g. dipoles. The number of elements is selected so that sufficient antenna gain is obtained vertically. The directional characteristic of bearing remains isotropic. The second part consists of a concentric ring relative to the column consisting of a number of simple antenna elements. If there are N antenna elements in the ring, it is well known that N -1 linear combinations of the signals from antenna elements can be formed, each of which is only sensitive to the signal from one of N -1 optional directions. In addition, by linearly combining the signal from the ring 20 and the pillar, a directional characteristic can be obtained where the directional sensitivity is zeroed in these N-1 optional directions. IB shows such a weighting which is insensitive in one direction due to the ring antenna being made sensitive only to this direction.

Combinations of signals from ring and pillar are used to suppress interference at reception, then primarily those which are intended to degrade radar function in the event of a military conflict. When transmitting, only the antenna elements of the column are utilized, which are weighted together to a directional characteristic which substantially aligns the transmission lobe horizontally, so that it reaches the intended distance with spread up to the intended height. At reception, more reception channels are necessary for simultaneous monitoring of all elevation directions. The assumed antenna surface A = 1 m²at wavelength = 0.7 m requires approx. 10 antenna elements at height (the antenna column becomes 3.5 m high). Ideally, each antenna element has its own receiver. However, such a construction is unnecessary as the antenna aperture projected in the elevation direction decreases and the vertical direction characteristic becomes less pronounced. 10 Antenna elements therefore provide only about 5 uncorrelated vertical antenna directions, with an analog signal forming network making a maximum of five independent receiver channels necessary.

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For interference suppression, additional receiver channels are connected to the antenna ring. As many receivers are needed as the number of elements in the ring, the number mentioned must be greater than the expected number of disturbed directions. Again, note that no requirement for extreme receiver dynamics is needed, since the purpose of noise suppression is to roughly suppress most of the noise energy. Thus, it is not necessary that receivers connected to the ring have sufficient sensitivity to detect targets, but that the receivers connected to the pillar have this capability.

Fig. 6 shows an example of a suitable principle diagram for a radar station in a grid point. The radar station is built around the antenna system described in Figure 5. The pillar antenna is used for transmitting and receiving, whereby transmitting signals are generated according to the stepped frequency transmission pattern described in Figure 4. A signal combining system contains the necessary switching functions between transmission and reception and delay filters for the formation of vertical directions that are separately received by different receivers and converted into digital signals.

Additional receiver channels are needed for noise suppression. For these, it is advantageous to make signal combinations after digital conversion, AD, to form narrow antenna lobes in the interfering directions, which can be obtained by delay and summation to correspond to the total interference signal arriving at the pillar antenna. By essentially a subtraction (in fact a weighted one with different weight factors for different elevation directions), noise-reduced radar signals are obtained. Through matched filtering, MF, with respect to the transmit signal, a distribution of the received signals is obtained over distance and near speed. Thereafter, target detection, Det, is performed through CFAR threshold for each elevation direction. Knowledge of elevation directions is not inherently necessary for continued treatment. Further, distance and near misses can be merged to reduce data in communication with the analysis equipment.

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