Method for determining positions of targets by bistatic measurements using signals scattered by the targets

SWEDEN (12) PATENT (13) C2 di) 522 651 (19) SE ₍₅₁₎

International class ⁷

G01S 13/00, 13/87

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PATENT AND REGISTRATION (45) (41) (22) (24) (62) (86) (86) (83)

Patent issued 2004-02-24

Application generally available 2003-12-15 The patent application was filed on 14/06/2002

Running day 2002-06-14

Tribal application number

International filing day

Filing date for European patent application

Deposit of microorganism (21) Patent Application Number 0201818-2

Application received as:

Swedish patent application completed international patent application with number □ converted European patent application with number (30) Priority information (73) (72) (74) (54) (56) (57)

Assignee

INVENTOR

AGENT

NAME

Total Defense Research Institute, 172 90 Stockholm SE Magnus Herberthson, Linköping SE Defense materiel plant

Methods and systems for determining the locations of the targets through bistatic measurements with signals spread from the target

CALLED PUBLICATIONS:

US A 4 499 468 (342/126)

SUMMARY:

The present invention relates to a method of determining the location of the targets by means of bistatic measurements with signals scattered from the target. The speed of the targets can also be determined. The range of the transmitters is chosen so that a target at any point can be measured by spreading in the target of at least four interacting measuring facilities.

First, the goals are associated. This is done by calculating the sum of all distances between targets and selected stations in two different ways as sums of bistatically measured distances via the target. Thereafter, the two sums are sorted with respect to the distance and compared with each other. The sums that correspond to each other, taking into account a predetermined margin of error, are stated corresponding goals. Finally, the distance to the targets is calculated from an equation system for the bistatically measured distances.

The numbers in brackets indicate international identification code, INID code. The letter within the pinch indicates the internal time-keeping document code.

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Summary:

The present invention relates to a method of determining the location of the targets by means of bistatic measurements with signals scattered from the target. The speed of the targets can also be determined. The range of the transmitters is chosen so that a target at any point can be measured via scattering in the target of at least four interacting measuring facilities.

First, the goals are associated. This is done by calculating the sum of all distances between targets and selected stations in two different ways as sums of bistatically measured distances via the target. Thereafter, the two sums are sorted with respect to the distance and compared with each other. The sums that correspond to each other, taking into account a predetermined margin of error, are stated corresponding goals. Finally, the distance to the targets is calculated from an equation system for the bistatically measured distances.

i I »I&gt; tt

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The present invention relates to a method of determining the location of the targets and a system utilizing the method by means of bistatic measurements with scattered signals. The speed of the targets can also be determined. The method comprises a rapid bistatic association method suitable for, for example, a network of radar stations on the AASR (associative aperture synthesis radar), although the applications may be more numerous. AASR is described in i.a. the Swedish patent 0101661-7, to which reference is hereby made. In the following, the description is concentrated on the new way of associating with only bistatic measurements.

The principle problem solved by the invention is first presented. We think N_s stations (e.g. radar dito) deployed in space (R³). The stations are denoted by Sj, j = 1, ... N_s and their location vectors with Pj, j = 1, ... N_s. In addition to the stations are also N_t moving targets to be detected. These are denoted by t, i = 1 .... N_t and has corresponding time-dependent location vectors η = r, (t), i = 1, ... N_t.

Each station has the ability to measure distance and radial speed for each target (up to a certain maximum distance). Thus, station Sj, 1 &lt;j &lt;N_s to, at some point in time, measure dj (k) = | r_k-_Pj|, k = 1.2, ... N_dj&lt;N_tVj (k) = (d / dt) | r_k - p, |, k = 1,2, ... N_d) &lt;N_t

For stations that are close enough to each other, you also get bistatic measurement information, ie. one transmits from one station and registers at another. For the station pair (Sj.Sj) it means registering dij (k) = | r_k - Pi | + | r_k - p_} | = di (k) + dj (k), k = 1, 2, ...

Vjj (k) = (d / dt) | r_k - pi | + (d / dt) | r_k - p, | = Vi (k) + Vj (k), k = 1, 2,

N_dij &lt;N, N_djj &lt;N,

Note that with these designations you become (k) = 2di (k), Vji (k) = 2Vj (k), i = 1.2, ... k = 1.2, ....

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Thus, for each sensor (monostatic or bistatic geometry), targets for distance and doppler are recorded. A priori it is not possible to know which registration from one sensor is associated with a certain registration from another sensor, ie. derives from the same goal. If registrations from different sensors are incorrectly paired with false targets, ghost targets will be created. The association problem is that, among all conceivable possibilities of combining sensor data, corresponding to conceivable target candidates, to discriminate between correct combinations (targets) and false combinations (ghosts).

Perhaps the most straightforward method is to consider three nearby stations and their monostatic recordings, which we for simplicity assume is N to the number. These measurements can be combined on N³ way, where each combination corresponds to a target position determined up to reflection in the plane containing the three stations. (Some combinations may be incompatible, corresponding to false candidates.) These ~ N³ candidates can then be compared one by one with the bistatic measurements and either rejected or accepted. The problem with such a method is that it becomes very slow if the number of targets, N, is large. For this reason, more efficient association algorithms have been developed.

Each target must be determined at both location and speed, ie. they must be positioned in a six-dimensional state space. The number of cells in the state space can be very large (~ 10¹⁸), which is why traditional projection methods become incredibly slow.

In Swedish patent 0101661-7 there is disclosed a way to attack the association problem by designing a sensor network so that each target is registered by many sensors (monostatic and bistatic), ie. a high degree of redundancy is achieved in the system. Thereafter, the state space is divided into manageably many relatively large cells.

If the cells are sufficiently large, many of them will be rejected. they cannot contain any goals, for the following reasons. If the cell contains a target, all (or almost all) of the possible sensors that can detect targets in the current cell will display such a record. If, on the other hand, the cell is empty, some, but still not too many sensors will still show registrations (from other targets) that are compatible with the cell in question. Through the redundancy, enough sensors will point to the cell as empty, and it can be depreciated. When the number of cells on this

522 651 ways are reduced by dividing the surviving cells into smaller cells and repeating the procedure. The process is repeated until the cells in the state space have reached the desired size. As the cells become smaller, fewer and fewer ghosts will survive, so that when you interrupt, you almost only have true targets left. What argues for this method is that it utilizes (but also requires) the redundancy of the sensor network. On the other hand, it is not yet clear how fast the method can eventually be.

An alternative method is disclosed in the Swedish patent 0101662-5, to which reference is hereby made, and means that certain symmetries of the combination sensors measurement data are used. Given two stations, the two monostatic measurements together with the bistatic dito will share a symmetry, namely that the three measurement geometries are all insensitive to rotation of the targets around the axis passing through the two stations. This means, but can make an initial quick screening of the candidates and erase many false associations (ghosts). The subsequent definitive association then becomes considerably faster. The disadvantage, on the other hand, is that the monostatic measurements become important, which can be disadvantageous when scouting for sneak-adjusted targets.

The present method according to the invention is based on the use of a fast method where only bistatic measurements are used. In addition, the method manages a certain sensor failure better than the method discussed in the preceding section. The method solves the current association problem in that it is designed in the manner stated in the first independent claim. A system utilizing the method is set out in the second independent claim. Advantageous embodiments of the invention are apparent from other claims.

Prior to a more detailed description of the invention, we first consider a multistatic network of ground-based radar stations, where each radar station transmits radar pulses that are propagated toward flight targets and then received by the surrounding stations. You then get a situation with a lot of bistatic measurements (ie the transmitting and receiving station are in different locations) and in addition monostatic measurements, which are not used in the invention, however. The bistatic measurements contain information about the total distance of the transmitter-target receiver and the corresponding doppler information. From all these measurements it is important to create a coherent air position picture. This problem, the association problem, is non-trivial if there are many goals.

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To give an intuitive understanding of the invention, we look at a simple case with only one target, πη, and four stations Si, s₂, s₃, s₄. Suppose we have the measurements di₂, d₃₄, d₁₃, d₂₄, where dy means the total distance s, - - Sj. It is recognized that d₁₂+ d₃₄= d₁₃+ d₂₄, since both expressions mean the total distance from the target to the four stations.

If there are now N targets instead, the above observation can be used to correctly associate data as follows. All conceivable combinations of type d data are formed₁₂ and D₃₄; they become N² to the number. Similarly, N is formed² combinations of data of type d₁₃ and D₂₄. These combinations are sorted and compared, whereby only sums from both quantities that are equal (within a given tolerance) can correspond to real goals. The same reasoning can be used about the doppler speeds, so that they provide a further screening. In this way, one can quickly and easily make an association of measurement data.

In general, the transmitters and receivers must be positioned and the range of the transmitters selected so that a target at any point within the location room can be measured by spreading in the target by at least four cooperating bistatic pairs of transmitters and receivers. The number of transmitters and receivers can be large. Among these bistatic pairs, at least four such cooperating pairs are selected to perform the association and determination of distance.

The following is a more systematic presentation of the calculations. For a simple description, we make the following (non-critical) assumptions. Suppose there are four stations and N targets, all of which are seen by all sensors (monostatic as well as bistatic).

Thus, the input data (monostatic measurements) dj (k) = | r_k - _Pj |, k = 1, 2, ... N, j = 1,2,3,4

Vj (k) = (d / dt) | r_k - pj |, k = 1,2, ... N, j = 1,2,3,4 and (bistatic measurements) di / k) = | r_k - pj | + | rk - Pj | = d | (k) + d / k), k = 1.2, ... N, j = 1,2,3,4

Vij (k) = (d / dt) | r_k - p | + (d / dt) | r_k - _Pj |= _vj(k) + v / k), k = 1, 2, ... N, j = 1,2,3,4

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where i = j in the bistatic case corresponds to monostatic measurements, i. i 4 = j can be assumed if desired.

Note that, for example, station j, with the monostatic measurement d, (k), k = 1,2, ... N, cannot know which measurement belongs to a certain target, ie. the measurements should be considered as a quantity that is proposed to be sorted by distance. In this way, there is no connection between a certain index k belonging to two different sensor registrations.

The method is now based on the following observation: For each registered target (not candidate, but real target) there must be a k, a k ', an I and a Γ, all between 1 and N so that d₁₂(K) + d₃₄(L) = d₁₃(k^,) + D₂₄(L ')

For the same k, k ', I, Γ we also apply₂(K) + v₃₄(L) = we₃(K ') + V₂₄(L ')

The reason is that if the target has the location vector r_t, then, for the case, d₁₂(K) + d₃₄(l) = | r_t - ρ_ή | + | r, - p₂| + | r, - p₃| + | r, - p₄| and in the same way that di₃(K) + d₂₄(l) = | r_t - p! | + | R_t - p₃| + | R_t - p₂| + | R_t - p₄| so they are equal. The argument for the velocities is identical. The proposed method 30 is now as follows.

Step 1. Form the N² the sums di₂(K) + d₃₄(l), 1 &lt;l, ​​k &lt;N 35

Sort them by total distance and label them

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d₁₂₊₃₄(m), 1 &lt;m &lt;N²

Step 2. Proceed in the same way with d₁₃(K ') + d₂₄(l '), 1 &lt;r, k' &lt;N so that we also get (sorted) d₁₃₊24 (m '), 1 &lt;m' &lt;N²

Step 3. Associate goals from {d₁₂₊₃4 (m)}_{m = 1},₂... N2 with target clock {d₁₃₊₂₄(M ')}_m.=₁₂.. n2 om

I d₁₂₊₃₄(m) - d₁₃₊₂₄(M ') | &lt;appropriate tolerance

Step 4. Investigate, and keep associated goals if they additionally meet

I v₁₂₊3₄(m) - v₁₃₊₂₄(M ') | &lt;appropriate tolerance ”Appropriate tolerance in step 3 is determined, among other things. of transmitted signal bandwidth, the purpose of the processing and hypotheses about the size and number of the targets. Usually it is from a few meters to a few tens of meters. Correspondingly, the "appropriate tolerance" in step 4 is normally a few meters / second.

To see that this really provides a quick method, we can use the following rough estimate. Suppose we have many goals, so they are of the same order of magnitude as the number of distance traps and the number of doppler traps. We denote this common number again with N. It is then estimated that since the total number of cells (= number of distance traps times the number of doppler traps) is equal to the number of candidates in, for example, {d₁₂₊34 (m)}_m= I₂... n2, each such candidate will be paired with typically a fake candidate from {d₁₃₊₂₄(RRI)}_m'=_1i2.. _N2nd Thus, the number of candidates following the above procedure is ~ N² (fewer at fewer targets), which is a sharp reduction compared to N³. Further processing can then be done by comparison with the remaining bistatic geometry {d₁₄₊₂₃(M)} m₌₁,_{2 N}2, the monostatic measurements or measurements involving other stations.

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Also note that you can also involve {d₁₄₊2₃(M)}_rn»= I, 2 ... n2 from the beginning. This provides an opportunity to get a redundancy, ie. an opportunity to manage a certain lapse in the registrations, as follows. The condition that | d₁₂₊₃4 (m) - d₁₃₊24 (m ') | &lt;"Appropriate tolerance" can be seen as both di₂₊₃₄(m) as d₁₃₊2₄(m ') should be close to some given value. By instead requiring that two of d₁₂₊₃4 (m), d₁₃₊₂4 (m ') and d₁₄₊₂₃(m ") should be close to the specified value (for some values ​​of m, m 'and m"), discrimination still exists between false candidates (ghosts) and targets. One can, however, tolerate that any of the measurements will be dropped.

The bills as a whole require 0 (N² log N) operations, and there are simple methods to really get the position and speed from the candidates, ie. after processing, you know four bistatic distances for a particular candidate according to:

| r - pi | + | rp₂| = d₁₂ | rp₃| + | rp₄| = d₃₄ | R p | + | rp₃| = d₁₃ | rp₂| + | rp₄| = d₂₄

Of course, one is interested in knowing the value of r (the position of the target), ie. any way to solve the above equation system, (p, ·, i = 1,2,3,4, is the known positions / location vectors of the stations and d₁₂, d₃₄, d₁₃, d₂₄ are the measured bistatic distances.) Generally, intersections between ellipsoids give rise to relatively complicated algebraic equation systems, but in this case the equation system can be solved by simpler methods.

If you look at the equation system as a 4x4 system you see that it is degenerate. At the same time, the condition guarantees d_i2 + d₃₄ = di₃ + d₂₄ that there is a parameter solution. By choosing origo ip₄ so that | r - p₄| = | r | = r, and entering r as a parameter, we obtain the following equations | r-pi | = d₁₂ - d₂4 + r

I rp₂1 = d₂₄ - r | rp₃1 = d₃₄ - r

Here you can square the three equations, where r² can be ironed, and get (for some a, b, c, a, p, 7)

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r ρ_ή = ar + α r · p₂ = br + β r · pi = cr + γ

The latter equation system can then be solved fairly straight forward. However, two different cases are obtained depending on whether {Pi} j = i, 2.3 is linearly dependent or not.

The case of the velocities is similar, we get the equation system if-v + u₂v = v₁₂ ύ₃· Ν + ΰ₄· Ν = v₃₄ΰ, -ν + ΰ₃ν = v₁₃ ύ₂ v + u₄-v = v_2A

Γ — Γ _ »where Z7, =, v = r, i = 1,2,3,4. The equation system can be treated in the same principle as the previous equation system.

The invention can be implemented in high-level languages ​​suitable for calculations, such as MatLab, C, Pascal, Fortran and others.

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