A topology-aided robust joint association and registration method

Abstract

The application discloses a kind of topological auxiliary robust joint association and registration method, can realize the accurate association and registration of multiple sensor measurement in dense target and large false alarm environment.The application realizes mutual optimization by the alternate iteration of association and registration steps, in each iteration, first, based on registration result, a composite association cost function based on Euclidean distance and topological partial matching similarity is used to construct linear assignment problem to solve association matrix;Then, based on the association result, Gauss-Seidel iteration method is used to solve nonlinear least square problem, and combined with the least median square estimator to obtain robust bias estimation, so as to reduce the influence of error association on bias estimation;Finally, when the bias estimation value tends to be stable, iteration is ended, and the final association matrix and bias estimation result are obtained.The application verifies its effectiveness by simulation, and can be used to solve the association and registration problem in multi-sensor detection.

Description

Technical Field

[0001] This invention relates to the field of multi-source data fusion, specifically to a method for correlation and registration of multiple radar cooperative observation systems. Background Technology

[0002] Association and registration are two coupled processes in a multi-sensor fusion system. The core of target association is establishing correspondences between observation data from different sensors, while sensor registration involves estimating and correcting measurement biases to ensure accurate and effective information fusion across multiple platforms and sensors. Due to sensor bias, biased measurements from various sensors are difficult to associate directly, and sensor bias estimation requires prior knowledge of the association results. To address this issue, one approach uses bias-insensitive feature differences as the association cost function, performing association and registration independently. However, this approach is susceptible to false alarms and missed detections. Another approach jointly solves the association and registration problems, achieving mutual optimization through iterative alternation of the association and registration steps. However, in complex scenarios such as densely distributed flocks of birds and other clustered flight targets, radar detection suffers from numerous missed detections and false alarms. In the early stages of the joint association and registration algorithm iteration, erroneous associations are inevitable. When the erroneous associations are large, they will affect the bias estimation results, leading to error accumulation and impacting the final association performance. At the same time, due to the existence of measurement bias, association using only Euclidean distance is prone to association errors, while algorithms that rely solely on local structural features are susceptible to false alarms and missed detections and have difficulty distinguishing targets with similar local structural features. Therefore, it is urgent to combine the two to improve association performance. Summary of the Invention

[0003] To overcome the problems existing in the prior art, this invention provides a topology-assisted robust joint association and registration method, which can achieve accurate association and registration of dense target measurement points by multiple sensors in scenarios with large false alarms.

[0004] Beneficial effects:

[0005] This invention constructs a composite association cost function based on Euclidean distance and topological partial matching similarity within the framework of joint association and registration algorithms to improve association performance in scenarios with large false alarms. Simultaneously, it constructs a nonlinear least squares equation system and combines it with the least median square estimation method to estimate sensor bias, thereby reducing error accumulation during algorithm iteration. This invention can solve the association and registration problem of multiple sensor measurements in scenarios with large false alarms and dense targets.

[0006] In this invention, the specific process of the joint association and registration algorithm is as follows: the association and registration steps are performed alternately and iteratively; in each iteration, firstly, based on the registration result, a composite association cost function based on Euclidean distance and topological partial matching similarity is used to construct a linear assignment problem to solve the association matrix, and an association threshold that gradually decays with iteration is set to reject the influence of false alarms on the target association; then, based on the association result, the Gauss-Seidel iterative method is used to solve the nonlinear least squares problem, and a robust estimate of the sensor bias is obtained by combining the minimum median square estimator, and the measurement is registered based on the bias estimation result; the above association and registration steps are repeated until the bias estimation result tends to stabilize or the maximum number of iterations is reached, that is, the final association matching result and the registered measurement are obtained. Attached Figure Description

[0007] Figure 1 This is a flowchart of the overall process of the joint association and registration method of the present invention.

[0008] Figure 2 This is a schematic diagram of a simulation scenario in a specific implementation example of the present invention.

[0009] Figure 3 This is a diagram showing the association and registration results in a specific implementation example of the present invention. Detailed Implementation

[0010] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0011] This invention is a joint correlation and registration method, which uses two sensors to jointly observe the same batch of targets, with each sensor observing N. s If there are multiple targets, then the sensor measurement is x. s,i =[r s,i ,θ s,i ,η s,i ] T (i = 1, 2, ..., N) s (s = 1, 2), the sensor has distance measurement and angle measurement deviation ξ. s =[Δr s ,Δθ s ,Δη s ] T This invention achieves correlation matching between measurements through alternating iterations of association and registration steps, while simultaneously estimating sensor bias. The method flow is as follows: Figure 1 As shown, the specific steps include the following:

[0012] Step 1: Set the initial sensor bias to 0 and initialize algorithm parameters such as the correlation threshold and maximum number of iterations.

[0013] Step 2: Fix the sensor bias and solve the correlation matrix. First, use the initial value of the sensor bias or the estimated value obtained from the previous iteration to correct the measurement. and The measurements from the two radars after calibration are expressed as follows: and Solve the following related problem:

[0014]

[0015] Where P represents the correlation matrix, consisting of 0-1 binary elements p ij Composition, s ij Indicates y 1,i and y 2,i The association cost function between points is given, where λ represents the threshold for rejecting erroneous associations to prevent excessive mismatches. This problem is a linear assignment problem, solvable using the Jonker-Volgenant algorithm.

[0016] In multi-sensor association problems, the choice of association cost function is particularly important. Considering the influence of measurement bias, topological features are introduced into the traditional Euclidean distance cost function to assist in association. The target reference topology is defined as follows: for a certain target measurement point x... s,i Select its neighboring targets to form a reference measurement set, and then compare all elements in the reference measurement set with x. s,i The set of difference vectors is called x. s,i The reference topology. Given an upper bound Nt for the number of elements in the constraint set, construct x. s,i Nt-nearest neighbor reference topology in Let represent the k-th element in the reference topology of the i-th target of radar s. Calculate the topological partial matching similarity D(T) between the measurements of the two sensors. 1,i ,T 2,j The composite cost function is constructed as follows:

[0017] s ij (x 1,i ,x 2,j )=α||x 1,i -x 2,j || 2 +(1-α)f(D(T 1,i ,T 2,j (2)

[0018] Where, ||x 1,i -x 2,j || 2 Let α be the Euclidean distance between the measurements, α be the feature weighting coefficient, and f(g) be the scaling function that transforms the second and first terms to the same range of values.

[0019] Since false alarms and missed detections can interfere with the reference topology and thus affect the correlation matching performance, in D(T) 1,i ,T 2,j In the calculation of topological partial matching similarity, the topological similarity is calculated using the K most similar elements among the Nt elements of the reference topology. In the following text, K is taken as 3 and Nt as 5. The mathematical expression for topological partial matching similarity is:

[0020]

[0021] Where h is the allocation matrix of the reference topology elements, n 1,i and n 2,j These represent the number of elements (n) in the two reference topologies, respectively. 1,i ,n 2,j ≤Nt), q h Represents the number of pairs in h (q) h <K); 2K-q h 2K-2q represents the sum of the number of isolated points and the number of paired points in two sets. h This represents the sum of isolated points in two sets; Let c be the Euclidean distance between elements in two reference topologies, c represent the penalty distance for isolated points, and p represent the order parameter, typically p = 2; set the association threshold g, if ||x 1,i -x 2,j || 2 If > g, then directly let D(T) 1,i ,T 2,j ) = c.

[0022] The allocation matrix h needs to satisfy:

[0023]

[0024] The allocation matrix can be solved using a greedy algorithm, as follows:

[0025] 1) The Euclidean distance matrix between two reference topological elements is calculated using the following formula:

[0026]

[0027] 2) Select the smallest value d in the matrix. ij If d ij If <c, then determine that track i is related to track j, and let h ij =1, and simultaneously, delete all elements in the i-th row and j-th column of d to obtain a new matrix d. Repeat this step K times, stopping when matrix d is empty or all its elements are greater than a threshold, finally obtaining matrix h = {h ij}

[0028] Step 3: Fix the correlation coefficients and solve for the sensor bias. After obtaining the correlation matrix P, the n correlation pairs x of the sensor measurements are determined. 1,i and x 2,i (i = 1, 2, ..., n), the bias estimation problem can be described as:

[0029]

[0030] in, f1(g) and f2(g) are functions that transform local coordinates to the global coordinate system, and UB and LB are upper and lower bound constraints on the parameters to be estimated. This is a convex optimization problem, and the objective function is differentiable. Therefore, the gradient of the cost function at the optimal solution is 0.

[0031]

[0032] Expanding, we get the system of equations:

[0033]

[0034]

[0035]

[0036]

[0037]

[0038]

[0039] in,

[0040]

[0041]

[0042]

[0043]

[0044] The Gauss-Seidel iterative method is used to solve the above system of equations.

[0045] Considering that erroneous associations inevitably occur during the alternating iteration of joint association and registration algorithms, thus affecting the bias estimation results, and that large bias estimation errors can lead to association errors, resulting in error accumulation and deterioration of association performance, a minimum median squared estimator is introduced. Two sub-equations (6) are extracted from n association pairs, and equations (8)-(11) are solved to obtain a set of estimation results. By traversing all combinations, a total of [number missing] estimation results are obtained. Solution set, calculate each solution set. and estimated median of residuals Where med is the median operation, and the squared residual is:

[0046]

[0047] Finally, by taking the smallest median of squared residuals among the M groups, we can obtain the minimum median squared estimate:

[0048]

[0049] Step 4: Determine if the convergence condition has been met, i.e., the bias estimation result tends to stabilize after multiple iterations. If the condition is met, end the iteration; otherwise, return to Step 2. Furthermore, as the iteration progresses, the sensor bias gradually decreases. To better reject false alarms, the correlation threshold is multiplied by a decay factor γ in each iteration, where k represents the iteration number.

[0050] λ (k+1) =λ (k) ×γ,λ (k+1) >λ0 (20)

[0051] The following example, using a scenario with two radars detecting multiple targets, illustrates and analyzes the algorithm. Let the position coordinates of the two radars be (0,0,0)m and (400,0,0)m, respectively. Twenty targets are randomly generated within the spatial range X∈[100,200], Y∈[-100,100], X∈[200,400]. Simultaneously, each radar detects 10 false alarms within the target area. The random errors in radar angle and distance measurements both follow a zero-mean Gaussian distribution, with standard deviations of 0.1° and 0.2m, respectively. Sensor biases are set as Δr1=Δr2=10m, Δθ1=Δθ2=1°, and Δη1=Δη2=2°. The radar positions, real targets, measurements of the real targets by the two radars, and false alarms are analyzed. Figure 2 As shown in the figure. Joint association and registration experiments were conducted using this invention, with the following algorithm parameters set: initial association threshold of 150 meters, threshold decay factor of 0.75, maximum number of iterations of 30, and topological similarity penalty distance of 50 meters. The results after association and registration are shown in the figure. Figure 3 As shown, the present invention can achieve accurate association and registration of real target measurements, while false alarms are not associated.

[0052] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A topology-aided robust joint association and registration method, characterized in that, The method comprises the following steps: The joint association and registration method is realized by alternating iteration of the two steps of association and registration; in each iteration, firstly, based on the registration result of the measurement track of the two radars in the last iteration, a composite association cost function based on Euclidean distance and topological partial matching similarity is used to construct a linear assignment problem to solve the association matrix, obtain the associated measurement pairs, and set an association threshold that gradually decays with iteration to reject the influence of false alarm on target association; Then, based on all the associated measurement pairs, a nonlinear least square equation set is constructed, the sensor bias estimation is performed by combining the least median square estimation method, and the measurements are registered based on the bias estimation result; The above association and registration steps are repeatedly executed until the bias estimation result tends to be stable or the maximum number of iterations is reached, that is, the final association matching result and the registered measurements are obtained; In the solving process of the association matrix, a composite association cost function based on Euclidean distance and topological partial matching is used: ； wherein, respectively represent the measurements of the two sensors, is the Euclidean distance between the measurements, is the topological partial matching similarity between the measurements, is the feature weighting coefficient, is a scaling function transforming the second term to the same value interval as the first term; The linear assignment problem is constructed to solve the association matrix, which specifically includes: First, the measurements of the two radars are corrected using the initial value of the sensor bias or the estimated value from the last iteration and The corrected measurements of the two radars are denoted as and The following association problem is solved ； wherein, represents a correlation matrix composed of 0-1 binary elements , represents and a correlation cost function between and, λ represents a threshold for rejecting false correlations, preventing too many point mismatches.

2. The method of claim 1, wherein, In the sensor bias estimation process, based on any two associated measurement pairs, a nonlinear least square problem is constructed to solve the bias estimation result, and then the least median square estimation method is used to select a group of bias estimation results as the final estimation value, so as to reduce the influence of false association on bias estimation; the specific calculation method is as follows: Take any two of the n pairs of associated measurements and b = 1,2, construct the following estimation problem: ； where, , are sensor biases, and are functions that convert local coordinates to global coordinate system, UB and LB are upper and lower bound constraints of the parameters to be estimated; to solve this convex optimization problem, the derivative of the objective function is obtained ； After the above formula is expanded, the Gauss-Seidel iteration method is used to solve; For n pairs of associations, a total of Group solutions, compute each group solution and the estimated median of the residuals , m = 1, 2, …, M, where med is the median operation, and the residual square is: ； Finally, the minimum residual square median of the M groups is taken, that is, the least median square estimation is obtained: 。 3. The method of claim 1, wherein, The calculation method of the topological partial matching similarity is that, first, the neighbor target set of the measurement and the corresponding reference topological set are constructed , and then the calculation formula of the topological partial matching similarity is as follows: ； where, and represent the number of elements in two reference topologies respectively, is the assignment matrix of elements in the reference topology set, represents the number of pairs in, and requires ; represents the sum of the number of isolated points and the number of pairs in two sets, represents the total sum of isolated points in two sets; is the Euclidean distance between the elements and in two reference topologies, c represents the penalty distance of isolated points, and p is the order parameter, generally p=2; set the association threshold g, if , then directly let .

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