CN113093139A - Data association method for multi-target tracking - Google Patents

Abstract

The invention relates to a data association method for multi-target tracking, in particular to a combined probability data association method based on a loss function. According to the correlation among the wave gates and the quantity of the echoes in the crossed wave gates, the data association is divided into three major categories; on the basis, a contribution coefficient and a loss function are introduced, and expressions of the loss functions under different conditions are further given; and finally, calculating the contribution coefficient of the target corresponding to each echo when the loss function is minimum, thereby associating the targets. The method adopts a Newton iteration method to solve the contribution coefficient equation set, and simplifies the multivariate joint iteration method into the iteration of a plurality of univariates. The method does not need to split the confirmation matrix, so that the situation of combination explosion is not caused like the traditional data association method, and the method has the advantages of small operand, high tracking precision and easy engineering realization.

Description

Data association method for multi-target tracking

Technical Field

The invention relates to a data association method for multi-target tracking, and belongs to the field of data processing and data fusion.

Background

Modern radar systems generally comprise two important components, namely a signal processor and a data processor. The radar signal processing is used for processing signals received by the radar once, and has the main functions of inhibiting clutter and interference signals and finally sending target signals to a data processor for data processing. The radar data processing is used for secondary processing of information received by the radar, and mainly aims to perform correlation, smoothing, filtering, prediction and other processing on measured data, estimate various parameters of a target at the current moment and finally form a stable target track.

With the development of modern radar systems, the struggle between electronic countermeasure and objection countermeasure is intensified day by day, and the traditional radar data processing method can not meet the requirement of modern war, so that the radar target data must be processed in real time by modern data processing means. Through data processing, the target state information is extracted to the maximum extent so as to estimate the motion trail of the target in the control area, and therefore the high-precision real-time tracking of the target by the radar is achieved.

The tracking of the flight path is a key part of radar data processing, and the data association is the most important content in a target tracking system, so that whether the data association is correct or not can be said, and the efficiency is directly related to the effect and efficiency of radar data processing. In the prior art, commonly used data association methods include Nearest Neighbor (NN), Probability Data Association (PDA), Joint Probability Data Association (JPDA), Multiple Hypothesis Tracking (MHT), and empirical Joint Probability data association (cjdap). The NN method updates the state by using the measurement with the nearest distance predicted value in the wave gate, so that the method has low tracking precision and is only suitable for tracking the non-maneuvering target in the sparse echo environment. The PDA method considers all candidate echoes falling into the relevant wave gate, calculates the probability of each echo from the target according to different conditions, weights the probability to obtain an equivalent echo, and finally updates the target state by using the equivalent echo. The tracking method has the advantages of small probability of tracking errors and target loss and relatively small calculation amount, but is not suitable for multi-target environment. MHT relies heavily on prior knowledge of targets and clutter and is therefore difficult to adopt in engineering implementation. The JPDA has a good tracking effect on the targets in a multi-target environment, but the method is complex and large in calculation amount, and the situation of combined explosion can occur when the confirmation matrix is split along with the increase of the number of the targets, so that the JPDA is not easy to realize in engineering. The CJPDA method is often used in engineering, and is a simplification method of the JPDA method, so that the confirmation matrix does not need to be split, but the tracking accuracy is greatly reduced while the calculation amount of the method is reduced. Based on the above, designing a data association method which has high tracking accuracy, small operand and is easy for engineering implementation is one of the tasks to be solved urgently in the modern radar data processing.

Disclosure of Invention

The invention provides a data association method for tracking multiple targets by a radar, which can ensure that the radar can track the multiple targets with high precision and has low operation complexity.

In order to achieve the technical purpose, the technical scheme adopted by the invention is as follows:

a data association method for multi-target tracking by radar comprises the following steps:

s1, prediction of target state:

predicting a state X (k | k-1) of a target at the current moment according to the target state information filtered at the previous moment, wherein X (k | k-1) is the predicted state of the target at the current k moment;

s2, judging the relationship between the echo and the target wave gate:

calculating the innovation covariance in the state X (k | k-1) of the target at the current moment predicted in the step S1, establishing a target gate according to the innovation covariance and the gate coefficient, and further judging the relationship between all points scanned by the radar and each target gate, wherein the relationship comprises the following conditions:

in case one, the target gates do not intersect, or no echo exists in the intersecting region;

in the second case, only one echo exists in the target wave gate and falls in the intersection region;

in the third case, a plurality of echoes exist in the target wave gate and echoes exist in the intersected area;

wherein the innovation is a difference between the measured state and the predicted state, and the gate coefficient is a parameter related to the gate probability and the gate shape;

s3, calculating a weighting coefficient and a combination innovation of the target, and the steps are as follows:

32) when the target wave gates are not intersected or no echo exists in the intersected region, calculating the combined innovation V of the target t according to a probability interconnection method_t(k)；

32) When only one echo in the target wave gate falls within the intersection region, the echo is subjected to data association with the target with the minimum loss function value in order to prevent track overlapping, and the combined innovation V of the target t is calculated_t(k)，

34) When a plurality of echoes exist in the target wave gate and echoes exist in the intersecting area, the steps are as follows:

a1) the square of the Mahalanobis distance (Mahalanobis distance) is taken as a loss function, and a contribution coefficient lambda is introduced_jtConstructing a contribution coefficient equation set and adding the contribution coefficient lambda_jtInitializing;

a2) solving optimal contribution coefficient lambda by Newton iteration method_jt；

a3) Using the optimum contribution factor lambda solved in step a2)_jtCalculating a combined innovation V of the weighting coefficient and the target t_t(k)；

S4, filtering to complete target tracking: the combined innovation V of the target t calculated in the step S3_t(k) And substituting the current state of the target into a filtering algorithm to carry out filtering, thereby realizing the updating of the current state of the target and completing the tracking of the target.

Preferably, the step S2 is as follows:

21) the information generated by each echo from each target is solved,

U_jt(k)＝Z_j(k)-HX_t(k|k-1)

wherein, U_jt(k) Process information, Z, indicating that the echo j at time k is from the target t_j(k) Is the observed value of the echo j at time k, H is the observation matrix, X_t(k | k-1) is a predicted value of the target t at the moment k;

22) constructing a relation matrix omega between the echo and the target, and judging whether the echo falls in each target wave gate, wherein the method comprises the following steps:

221) a matrix omega of the echo and target relationship is constructed,

wherein m is_kIs the total number of loops at time k, and ω_jtWhen the value is 1, the echo j is in the gate of the target t, otherwise, the value is 0;

222) whether the echo falls within each target wave gate is judged,

when in use

When the echo j falls within the gate of the target t, let ω be_jt＝1，

Otherwise, it indicates that the echo j is not the echo of the target t, let ω_jt＝0，

Wherein S is_t(k) The innovation covariance of the target t at the moment k is shown, eta is a wave gate coefficient related to the wave gate probability, and the value of eta is given by the used wave gate rule;

23) according to the judgment result of whether the echo in 22) falls on the target related gate, dividing the relation between the target gates into three cases, including:

in case one, the target gates do not intersect, or no echo exists in the intersecting region;

in the second case, only one echo exists in the target wave gate and falls in the intersection region;

and in the third case, multiple echoes exist in the target wave gate and echoes exist in the intersecting area.

Preferably, step a1) includes the steps of:

a10) taking the square of the mahalanobis distance as a loss function,

wherein, the

Is the square of the Mahalanobis distance, S_t(k) An innovation covariance matrix, U, for the target t at time k_jt(k)＝Z_j(k)-HX_t(k|k-1)，

Wherein, U_jt(k) Process information, Z, indicating that the echo j at time k is from the target t_j(k) Is the observed value of the echo j at time k, H is the observation matrix, X_t(k | k-1) is a predicted value of the target t at the moment k;

a11) introducing a contribution coefficient lambda_jtConstructing a real combined innovation weighting coefficient beta 'of an echo j from a target t'_jtAnd the actual combined innovation weighting coefficient beta ″)_jt，

Where T is the total number of loops in the target T-wave gate, λ_jtFor the contribution coefficient, P, of the echo j with respect to the target t_jtFor the effective likelihood function:

a12) utilizing a true combined innovation weighting coefficient beta'_jtActual combination innovation weighting coefficient beta ″_jtTarget t detection probability P_DtAnd the square of the Mahalanobis distance

Construction of the Process variable D of the equation set_jt，

Wherein M is the total wave gate number in the crossed wave gate to which the echo j belongs;

a13) passing squareSet of process variables D_jtA system of contribution coefficient equations is constructed,

wherein a is an undetermined coefficient;

a14) to the contribution coefficient lambda_jtInitialisation, i.e. ordering

I.e. when lambda_jtWhen the contribution coefficient of the echo j to be solved in the common wave gate is relative to the target t (t is 1, …, M), the initialized value is 1/M, otherwise, the initialized value is 1.

Preferably, step a2) Newton iteration method solves the optimal contribution coefficient lambda_jtThe method comprises the following steps:

a21) solving a fixed constant in an iterative process, namely a real combined innovation weighting coefficient beta 'of an echo j from a target t'_jt，

a22) Solving for process variable value beta' in iterative process_jt、D_jtAnd

wherein the content of the first and second substances,

as a process variable D_jtWith respect to the contribution coefficient lambda_jtPartial derivatives of (d);

a23) by the value of the process variable beta ″)_jt、D_jtAnd

calculating an update value of the contribution coefficient after a single iteration

Wherein in the formula

Updating the value of the contribution coefficient after iteration;

a24) judging whether a target t exists₀So that

If present, let

Constantly equal to 0, go to the next step a 25);

otherwise, go directly to the next step a 25);

a25) judgment of

Whether or not it is less than the threshold value sigma,

if so, let

At this time λ_jtThe optimal contribution coefficient is obtained, and the iteration is ended;

otherwise, it orders

Repeating a22) to a25) until the conditions in a25) are met or the upper iteration limit is reached.

Preferably, the step of step a3) is as follows:

optimum contribution factor lambda according to step a2)_jtSolving for the weighting coefficient beta_jtCombined innovation V with target t_t(k)；

Wherein, beta_jtAre weighting coefficients.

Preferably, the step S1 is as follows:

the state information X (k | k-1) of the target current time is predicted,

X(k|k-1)＝F·X(k-1|k-1)

wherein X (k | k-1) is the predicted state of the target at the k-th time, X (k-1| k-1) is the updated state of the target at the k-1 th time, and F is the state transition matrix.

The invention has the beneficial effects that:

1. compared with other joint probability data association methods, the method provided by the invention combines the ideas of joint probability and loss function, calculates the effect of each effective echo on target state estimation when the loss function is minimum, and gives a target estimation value by taking the effect as weight, unlike other joint probability data association methods which calculate the effect of each effective echo on target state estimation in a statistical sense. Therefore, the invention has the characteristic of high tracking precision.

2. According to the invention, the confirmation matrix does not need to be split, so that the situation of combined explosion is not caused like the traditional data association method, a large amount of storage space is occupied, excessive target prior information is not needed, when the optimal contribution coefficient equation set is solved, a Newton iteration method is adopted to carry out iterative solution on the multivariate nonlinear equation set, and the single iteration operand is as follows: the multiplication is performed for T +17 times, the division is performed for 3 times, and the addition is performed for T +9 times, so that compared with other high-tracking-precision data association methods, the method has the advantages of small calculation amount and easiness in engineering realization, and the specific embodiment part also proves that the calculation efficiency is improved by more than 10 times compared with the data association method on the premise of ensuring the tracking precision.

Drawings

FIG. 1 is a schematic diagram of a data association method for multi-target tracking according to the present invention.

FIG. 2 is a single-cycle flow chart of the data association method for multi-target tracking according to the present invention.

FIG. 3 is a first diagram illustrating a relationship between a target gate and an echo.

FIG. 4 is a diagram illustrating a relationship between a target gate and an echo.

Fig. 5 is a third schematic diagram of the relationship between the target gate and the echo.

Fig. 6 is a diagram of the rms position error of the target, where fig. 6(a) is the rms position error of the target 1 and fig. 6(b) is the rms position error of the target 2.

Detailed Description

In order to further illustrate the present invention, the following embodiments are given by way of examples, and it should be understood that the following is only exemplary of the present invention and is not intended to limit the present invention, and all equivalent modifications, equivalents and improvements made within the spirit and principle of the present invention should be included in the scope of the present invention.

As shown in fig. 1, a data association method for radar to track multiple targets includes the following steps:

step 1, predicting the target state, namely predicting the state information of the target at the current time by using a formula X (k | k-1) ═ F · X (k-1| k-1), wherein X (k | k-1) is the predicted state of the target at the kth time, X (k-1| k-1) is the updated state of the target at the kth-1 time, and F is a state transition matrix.

And 2, judging the relation between each echo and the target wave gate.

21) First, using formula U_jt(k)＝Z_j(k)-HX_t(k | k-1) solving for the information that each echo is coming from each target,

wherein, U_jt(k) Process information, Z, indicating that the echo j at time k is from the target t_j(k) Is the observed value of the echo j at time k, H is the observation matrix, X_t(k | k-1) is a predicted value of the target t at time k.

22) A matrix omega of the echo and target relationship is constructed,

wherein m is_kIs the total number of loops at time k, and ω_jtWhen the value is 1, the echo j is in the gate of the target t, otherwise, the value is 0;

then, whether the echo falls in the target wave gate is judged, and an inequality is utilized

The judgment is carried out, and the judgment is carried out,

when the inequality is satisfied, it is stated that the echo j falls within the gate of the target t, let ω be_jt＝1，

Otherwise, it indicates that the echo j is not the echo of the target t, let ω_jt＝0，

Wherein S is_t(k) The innovation covariance of the target t at time k is represented by η, which is a gate coefficient related to the gate probability, and in this example, when an elliptic gate is used and the gate probability is 0.987 (two-dimensional measurement detection probability), η is 9.

Then, the effective likelihood function P of the echo j from the target t is calculated respectively_jtAnd mahalanobis distance

The square of the square,

23) according to the judgment result of whether the echo in 22) falls on the target related gate, the relationship between the target gates can be divided into three cases, and the steps are as follows:

firstly, calculating 2201) the sum of each row and each column of elements in the constructed echo and target relation matrix omega; secondly, finding out a row with the sum of row elements in omega larger than 1, and judging and processing according to the sum of columns where the non-zero elements of the row are located;

when the sum of the columns where the non-zero elements are located is 1, dividing the columns into two cases, namely only one echo in the target wave gate falls in the intersection region;

when the sum of the columns of the non-zero elements is not 1, indicating that a plurality of echoes exist in the target number wave gate corresponding to the column number and echoes exist in the intersection area; it is drawn into case three, i.e. there are multiple echoes within the target wave gate and echoes within the intersection region.

Secondly, removing the distributed echoes and the rows and columns corresponding to the targets from the echo-target relation matrix omega to obtain a simplified echo-target relation matrix omega₁This is the case-one, i.e. no echo in the disjoint or intersecting regions of the respective gates.

For example, assume that the echo-target relationship matrix Ω is:

where the rows represent echoes and the columns represent targets.

Firstly, calculating the sum of each row and each column of elements; secondly, finding out a row (such as the 4 th and 5 th rows in the assumption of omega) with the sum of row elements in omega larger than 1, and judging and processing according to the sum of columns of the non-zero elements in the row;

when the sum of the columns of the non-zero elements is 1, dividing the non-zero elements into two cases, namely only one echo in the target wave gate falls in the intersection region (if the non-0 column in the fourth row is the 3 rd column and the 4 th column, and the sum of the columns is 1, only one echo 4 in the target 3 and the target 4 wave gate is shown to fall in the intersection region of the two targets);

when the sum of the columns of the non-zero elements is not 1, indicating that a plurality of echoes exist in the target number wave gate corresponding to the column number and echoes exist in the intersection area; it is drawn into case three, i.e. there are multiple echoes within the target wave gate and echoes within the intersection region. (for example, the column in the fifth row in which the element other than 0 is located, that is, the sum of the 5 th column and the 6 th column is 1, 2, respectively, which indicates that there is an echo (echo 5) in the intersection region of the target 5 and the target 6, and there are a plurality of echoes (echo 5, echo 6) in the gate, and these are divided into cases three).

Secondly, removing the distributed echoes and the rows and columns corresponding to the targets from the echo-target relation matrix omega to obtain a simplified echo-target relation matrix omega₁This is the case-one, i.e. no echo in the disjoint or intersecting regions of the respective gates. Thus, the echoes 4, 5, 6, and the targets 3, 4, 5, 6 in the example are removed, resulting in a simplified echo-target relationship matrix Ω₁As shown below;

that is, targets 1, 2 belong to case one, and echoes 1, 3 are within the gate of target 1 and echo 2 is within the gate of target 2.

Step 3, calculating a weighting coefficient and a target combination innovation:

301) when the target wave gates are not intersected or no echo exists in the intersected region, calculating the combined innovation V of the target t according to a probability interconnection method_t(k),

Wherein in the formula

Weighting factors, U, for echoes j in relation to the target t_jt(k) Process information, P, indicating that the echo j at time k originates from the target t_jtFor the effective likelihood function, T is the number of effective echoes in the gate T, and B is a constant dependent on the clutter density, where B is 0 in this example.

302) When only one echo is in the target wave gate and falls within the intersection region, the echo is data-correlated with the target with the smallest loss function value in order to prevent track overlap, i.e. the echo is assigned to the target

Minimum target t₀I.e. using the formula

Is obtained, where m is the number of intersecting gates, P_DnIs the probability of detection of the target n,

is the square of the immediate distance of the echo 1 with respect to the target n.

At this time, the combined innovation V of the target t_t(k) Comprises the following steps:

303) when a plurality of echoes exist in the target wave gate and echoes exist in the intersecting area, the steps are as follows:

a1) introducing a contribution coefficient lambda by taking the square of the Mahalanobis distance (Mahalanobis distance) as a loss function_jtConstructing a contribution coefficient equation set and adding the contribution coefficient lambda_jtInitializing, specifically comprising the following steps:

a10) taking the square of the mahalanobis distance as a loss function,

wherein, the

Is the square of the Mahalanobis distance, U_jt(k) Process information, S, indicating that the echo j at time k originates from the target t_t(k) The innovation covariance of the target t at time k;

a11) introducing a contribution coefficient lambda_jtConstructing a real combined innovation weighting coefficient beta 'of an echo j from a target t'_jtAnd the actual combined innovation weighting coefficient beta ″)_jt，

Wherein λ is_jtAnd the contribution coefficient of the echo j relative to the target T is shown, T is the number of echoes in the wave gate of the target T, and M is the number of the wave gates of the target where the echo j is located.

a12) Utilizing a true combined innovation weighting coefficient beta'_jtActual combination innovation weighting coefficient beta ″_jtTarget t detection probability P_DtAnd the square of the Mahalanobis distance

Construction of the Process variable D of the equation set_jt，

a13) Process variable D by equation set_jtA system of contribution coefficient equations is constructed,

wherein a is undetermined coefficient and lambda_jtThe contribution coefficient of the echo j relative to the target t is obtained, and M is the number of target waves where the echo j is located;

a14) to the contribution coefficient lambda_jtInitializing to obtain contribution coefficient lambda_jtInitialization is 1/M.

a2) Solving optimal contribution coefficient lambda by Newton iteration method_jt；

a21) Solving fixed constant beta 'in iterative process'_jt，

Wherein, P_jtFor an effective likelihood function, T is the number of echoes within the target gate T.

a22) Solving for process variable value beta' in iterative process_jt、D_jtAnd

wherein in the formula

As a process variable D_jtWith respect to the contribution coefficient lambda_jtPartial derivatives of (d);

a23) by the value of the process variable beta ″)_jt、D_jtAnd

calculating the contribution coefficient after iteration

Wherein in the formula

Is the contribution coefficient after iteration;

a24) judging whether a target t exists₀So that

If present, let

Constantly equal to 0, go to the next step a 25);

otherwise, go directly to the next step a 25);

a25) judgment of

Whether or not it is less than the threshold value sigma,

if so, let

At this time

The optimal contribution coefficient is obtained, and the iteration is ended;

otherwise, it orders

Repeating a22) to a25) until the conditions in a25) are met or the upper iteration limit is reached. a3) Optimum contribution factor lambda according to step a2)_jtSolving the combined innovation V of the weighting coefficient and the target t_t(k)；

Wherein the content of the first and second substances,

are weighting coefficients.

And 4, completing target tracking by filtering: combining innovation V of the target t obtained by calculation in the step 3_t(k) And filtering by substituting into a filtering algorithm (in the example, a Kalman filtering method is adopted), so that the current state of the target is updated, and the target is tracked.

Test verification:

the target gate relationship is case one, as shown in FIG. 3: in the planar space there are two moving objects, the state of the object at a moment ([ x; v)_x；y；v_y]) Respectively as follows: target 1[ -29459 m; 400 m/s; 34553 m; 400m/s](ii) a Target 2[ -26095 m; -200 m/s; 34515 m; 400m/s](ii) a MiningThe sample interval T is 1s, and there is a certain clutter interference and measurement error in the space. After adding the clutter and the measurement noise, the trace points scanned by the radar at the current time are shown in table 1.

Table 1 shows radar scanning traces at current moment by considering influence of clutter and noise

Point trace	1	2	3	4	5	6	7
								X coordinate (m)	-28998	-25875	-29039	-29281	-29219	-29406	-27327
Y coordinate (m)	34247	34177	33200	33757	35146	35545	33265

Associating each trace point with two targets respectively to obtain its innovation U_jt(k) And by the above formula

Performing a determination, wherein S (k) is given by the filtering result and the measurement error at the previous time; ignoring process noise, the innovation covariance s (k) of the target current time [ 226500; 022650](ii) a When target wave gate probability P_GWhen it is 0.987, η is 9. At this time, only the traces 1, 2, and 4 satisfy the conditions and fall within the gates of the targets 1, 2, and 1, respectively, and then the effective likelihood function and the square of the mahalanobis distance of each trace with respect to the target are obtained, as shown in table 2.

TABLE 2 trace points and target associated information

At this time, the combined innovation V of the target t is calculated by using a probabilistic interconnection (PDA) method_t(k) Calculating the weighting coefficients as shown in the last column of table 2; the weighting coefficients are used to obtain the combined information of the target, and the state information of the target at the current moment obtained by filtering (here, kalman filtering) is respectively: target 1[ -29059m,400m/s,34154m, -400m/s]Target 2[ -25895m,200m/s,34115m, -400m/s]。

If the target gate relationship is determined to be case two at a certain time, as shown in fig. 4: by the formula

And finding the target with the minimum loss generation and associating the target with the minimum loss generation.

The target gate relationship is determined to be case three, as shown in FIG. 5: at a certain time, the state of the target at the previous time is respectively as follows: target 1[ -24172 m; 400 m/s; 29351 m; -400m/s ]; target 2[ -23522 m; -200 m/s; 29351 m; 400m/s ] and there are measurement errors and clutter, and the trace information in the gate is shown in Table 3.

TABLE 3 Point trace information in target wave gate at present time

Point trace	Number of target wave	X coordinate (m)	Y coordinate (m)
				1	1、2	-23821	28915
2	1、2	-23347	29017
				3	1、2	-23489	29001

At this time, by solving the square of the effective likelihood function and mahalanobis distance of each point trace relative to the target,as shown in table 4. Since the point traces 1, 2 and 3 are all in the intersection region of the targets 1 and 2, the contribution coefficient lambda of each point trace with respect to the target is also determined₁₁、λ₁₂、λ₂₁、λ₂₂、λ₃₁、λ₃₂Initialized to 1/2, and calculating a real combined innovation weighting coefficient beta'_jtAnd the actual combined innovation weighting coefficient beta ″)_jtRecalculating the process variable D_jtAnd

the contribution coefficients were solved using the constructed newton iteration formula, with the results shown in column 5 of table 4.

Finally, the combination information of the target is obtained by using the weighting coefficient, and the current time state information of the target obtained by filtering is respectively as follows: target 1[ -23772m,400 m/s; 28951m, -400m/s ], target 2[ -23322m,200 m/s; 28952m, -400m/s ].

TABLE 4 trace points and target associated information

Target	Point trace	Effective likelihood function Pjt	Mahalanobis distance squared	Coefficient of contribution	Weighting coefficient
							1	1	1.62E-05	0.165	1	0.914
1	2	3.03E-07	8.127	0.324	0.005
						1	3	2.86E-06	3.638	0.494	0.079
2	1	6.98E-08	11.061	0	0
						2	2	1.58E-05	0.221	0.675	0.701
2	3	9.00E-06	1.343	0.505	0.299

In order to further illustrate the performance of the method, the invention utilizes Matlab simulation environment to compare with the currently recognized JPDA method with high tracking precision, wherein the PC end is configured as follows: windows10, CPU is i5-3210m @2.5GHz, and memory is 8 GB. The tracking precision and time consumption of the two methods for the two crossed targets are mainly compared, and the mean square error graph after simulation tracking and the performance results of the two methods are shown in fig. 6 and table 5.

FIG. 6 shows that the tracking method (LJPDA) of the present invention has similar tracking accuracy to the JPDA method which is known to have high tracking accuracy, and can effectively track the target; meanwhile, as can be seen from table 5, the tracking method of the present invention has high tracking accuracy and excellent timeliness, and the time consumption efficiency is improved by more than 10 times compared with the JPDA, because the tracking method of the present invention does not need to split the confirmation matrix, the phenomenon of combination explosion does not occur, and excessive target prior information is not needed, the method is easy to implement in engineering, the time consumption of the method is not exponentially multiplied, and the method has the advantages that the JPDA method cannot compare with.

TABLE 5 method Performance comparison Table

Method	Time consuming single step (ms)	Position root mean square error (m)
			LJPDA	0.977	72.74
JPDA	10.2	73.36

The above description is only a preferred embodiment of the application and is illustrative of the principles of the technology employed. It will be appreciated by a person skilled in the art that the scope of the invention as referred to in the present application is not limited to the embodiments with a specific combination of the above-mentioned features, but also covers other embodiments with any combination of the above-mentioned features or their equivalents without departing from the inventive concept. For example, the above features may be interchanged with other features disclosed in this application, but not limited to those having similar functions.

Claims (6)

1. The data association method for multi-target tracking is characterized by comprising the following steps of:

s1, prediction of target state:

predicting a state X (k | k-1) of a target at the current moment according to the target state information filtered at the previous moment, wherein X (k | k-1) is the predicted state of the target at the current k moment of the target;

s2, judging the relationship between the echo and the target wave gate:

calculating innovation according to the state X (k | k-1) of the target at the current time predicted in the step S1, establishing target gates according to the innovation covariance and the gate coefficients, and further judging the relation between all points scanned by the radar and each target gate, wherein the relation comprises the following conditions:

in case one, the target gates do not intersect, or no echo exists in the intersecting region;

in the second case, only one echo exists in the target wave gate and falls in the intersection region;

in the third case, a plurality of echoes exist in the target wave gate and echoes exist in the intersected area;

wherein the innovation is a difference between the measured state and the predicted state, and the gate coefficient is a parameter related to the gate probability and the gate shape;

s3, calculating a weighting coefficient and a combination innovation of the target, and the steps are as follows:

31) when the target wave gates are not intersected or no echo exists in the intersected region, calculating the combined innovation V of the target t according to a probability interconnection method_t(k)；

32) When only one echo in the target wave gate falls within the intersection region, the echo is subjected to data association with the target with the minimum loss function value in order to prevent track overlapping, and the combined innovation V of the target t is calculated_t(k)，

33) When a plurality of echoes exist in the target wave gate and echoes exist in the intersecting area, the steps are as follows:

a1) the square of the Mahalanobis distance (Mahalanobis distance) is taken as a loss function, and a contribution coefficient lambda is introduced_jtConstructing a contribution coefficient equation set and adding the contribution coefficient lambda_jtInitializing;

a2) solving optimal contribution coefficient lambda by Newton iteration method_jt；

a3) Using the optimum contribution factor lambda solved in step a2)_jtCalculating a combined innovation V of the weighting coefficient and the target t_t(k)；

S4, filtering to complete target tracking: the combined innovation V of the target t calculated in the step S3_t(k) And substituting the current state of the target into a filtering algorithm to carry out filtering, thereby realizing the updating of the current state of the target and completing the tracking of the target.

2. The data association method for multi-target tracking according to claim 1, wherein the step S2 is as follows:

21) the information generated by each echo from each target is solved,

U_jt(k)＝Z_j(k)-HX_t(k|k-1)

wherein, U_jt(k) Process information, Z, indicating that the echo j at time k is from the target t_j(k) Is the observed value of the echo j at time k, H is the observation matrix, X_t(k | k-1) is a predicted value of the target t at the moment k;

22) constructing a relation matrix omega between the echo and the target, and judging whether the echo falls in each target wave gate, wherein the method comprises the following steps:

221) a matrix omega of the echo and target relationship is constructed,

wherein m is_kIs the total number of loops at time k, and ω_jtWhen the value is 1, the echo j is in the gate of the target t, otherwise, the value is 0;

222) whether the echo falls within each target wave gate is judged,

when in use

When the echo j falls within the gate of the target t, let ω be_jt＝1，

Otherwise, it indicates that the echo j is not the echo of the target t, let ω_jt＝0，

Wherein S is_t(k) The innovation covariance of the target t at the moment k is shown, and eta is a wave gate coefficient related to the wave gate probability and the wave gate shape;

23) according to the judgment result of whether the echo in 22) falls on the target related gate, dividing the relation between the target gates into three cases, including:

in case one, the target gates do not intersect, or no echo exists in the intersecting region;

in the second case, only one echo exists in the target wave gate and falls in the intersection region;

and in the third case, multiple echoes exist in the target wave gate and echoes exist in the intersecting area.

3. The data association method for multi-target tracking according to claim 1, wherein the step a1) includes the steps of:

a10) taking the square of the mahalanobis distance as a loss function,

wherein, the

Is the square of the Mahalanobis distance, S_t(k) An innovation covariance matrix, U, for the target t at time k_jt(k)＝Z_j(k)-HX_t(k|k-1)，

U_jt(k) Process information, Z, indicating that the echo j at time k is from the target t_j(k) Is the observed value of the echo j at time k, H is the observation matrix, X_t(k | k-1) is a predicted value of the target t at the moment k;

a11) introducing a contribution coefficient lambda_jtConstructing a real combined innovation weighting coefficient beta 'of an echo j from a target t'_jtAnd the actual combined innovation weighting coefficient beta ″)_jt，

Where T is the total number of loops in the target T-wave gate, λ_jtIs the contribution coefficient of the echo j with respect to the target t, B is a constant dependent on the clutter density, P_jtIn order to be an effective likelihood function,

a12) utilizing a true combined innovation weighting coefficient beta'_jtActual combination innovation weighting coefficient beta ″_jtTarget t detection probability P_DtAnd the square of the Mahalanobis distance

Construction of the Process variable D of the equation set_jt，

Wherein M is the total wave gate number in the crossed wave gate to which the echo j belongs;

a13) process variable D by equation set_jtA system of contribution coefficient equations is constructed,

wherein a is an undetermined coefficient;

a14) to the contribution coefficient lambda_jtInitialisation, i.e. ordering

4. The data correlation method for multi-target tracking according to claim 1, characterized in that step a2) Newton's iteration method solves for the optimal contribution coefficient λ_jtThe method comprises the following steps:

a21) solving a fixed constant in an iterative process, namely a real combined innovation weighting coefficient beta 'of an echo j from a target t'_jt，

a22) Solving for process variable value beta' in iterative process_jt、D_jtAnd

wherein the content of the first and second substances,

as a process variable D_jtWith respect to the contribution coefficient lambda_jtPartial derivatives of (d);

a23) by the value of the process variable beta ″)_jt、D_jtAnd

after a single iteration of the calculationIs updated with the contribution coefficient of

Wherein in the formula

Updating the value of the contribution coefficient after iteration;

a24) judging whether a target t exists₀So that

If present, let

Constantly equal to 0, go to the next step a 25);

otherwise, go directly to the next step a 25);

a25) judgment of

Whether or not less than a threshold value sigma, satisfying the condition

Namely the optimum contribution coefficient is obtained by the method,

if so, let

End iteration, λ at this time_jtThe optimal contribution coefficient is obtained;

otherwise, it orders

Repeating a22) to a25) until the conditions in a25) are met or an iteration is reachedAnd (4) limiting.

5. The data association method for multi-target tracking according to claim 1, wherein the step a3) is as follows:

optimum contribution factor lambda solved according to step a2)_jtSolving for the weighting coefficient beta_jtCombined innovation V with target t_t(k)；

Wherein, beta_jtAre weighting coefficients.

6. The data association method for multi-target tracking according to any one of claims 2 to 5, wherein the step of step S1 in claim 1 is as follows:

the state information X (k | k-1) of the target current time is predicted,

X(k|k-1)＝F·X(k-1|k-1)

wherein X (k | k-1) is the predicted state of the target at the k-th time, X (k-1| k-1) is the updated state of the target at the k-1 th time, and F is the state transition matrix.

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