Fuzzy track association method based on cumulative historical similarity

Abstract

This invention provides a fuzzy track association method based on accumulated historical similarity, comprising: acquiring state estimates of the target track from two radars, and constructing... x , y , z The system calculates the fuzzy factor set and weight set for position, velocity, and acceleration estimation in direction; it obtains the similarity between two tracks based on the membership degree of the fuzzy factors and constructs a similarity matrix; and it obtains the time intervals. k The historical cumulative similarity is used to construct a historical cumulative matrix; the historical cumulative matrix is ​​mapped to the correlation matrix to construct an optimal two-dimensional allocation model; the optimal two-dimensional allocation model is calculated using the Hungarian algorithm to output the associated track pairs.

Description

Technical Field

[0001] This invention relates to a radar target tracking technology, and more particularly to a fuzzy track association method based on accumulated historical similarity. Background Technology

[0002] In multi-radar systems, a distributed radar data fusion architecture is often adopted. Each radar node processes its detected measurement data locally, generates local tracks, and reports this track information to the fusion center. The core task of track association is to determine whether multiple tracks from different nodes originate from the same target. When the tracks received by the fusion center have significant positional differences and there are no complex interactions such as bifurcation, overlap, splitting, or maneuvering, the association problem is relatively simple, and traditional association algorithms can provide correct association results. However, when facing complex dynamic scenarios, traditional methods often struggle to maintain their effectiveness, easily leading to false or missed associations. Existing track association algorithms mainly include those based on statistical mathematics and those based on fuzzy mathematics. Traditional statistical mathematics-based track association methods often classify noise, uncertainty, and complex dynamic scenarios as noise. However, in practical applications, due to radar errors, environmental interference, and the unpredictability of target behavior, the observed data often carries significant uncertainty and fuzziness, making it difficult to obtain suitable prior parameters to build a noise model. Traditional fuzzy track association algorithms only consider the similarity at the current moment, making it difficult to distinguish when targets overlap or intersect. Summary of the Invention

[0003] The purpose of this invention is to provide a fuzzy track association method based on accumulated historical similarity, comprising:

[0004] Step S100: Obtain the state estimates of the target trajectory from the two radars. and Construct a fuzzy factor set {u1(k), u2(k), u3(k)} and a weight set of the fuzzy factors for position estimation, velocity estimation, and acceleration estimation in the x, y, and z directions, respectively. Here, A and B are the radar indices, i and j are the target tracks corresponding to radar A and B, u1(k), u2(k), and u3(k) are the fuzzy factors for position estimation, velocity estimation, and acceleration estimation in the x, y, and z directions, respectively, and k represents time.

[0005] Step S200: Obtain the similarity s between the two tracks based on the membership degree of the fuzzy factors. ij (k), construct the similarity matrix S(k);

[0006] Step S300: Obtain the historical cumulative similarity λ at time k. ij (k), based on historical cumulative similarity λ ij(k) Construct the historical cumulative matrix Γ(k);

[0007] Step S400: Map the historical cumulative matrix Γ(k) to the correlation matrix M(k), construct the optimal two-dimensional allocation model, perform optimal allocation calculation on the optimal two-dimensional allocation model using the Hungarian algorithm, and output the associated track pairs.

[0008] Furthermore, in step S100, the fuzzy factor set consists of the Euclidean distance between the spatial position, velocity, and azimuth heading angle of tracks i and j.

[0009]

[0010] in, and Let i and j represent the spatial positions of the targets at time k, respectively. and Let represent the velocity of the target on trajectory i and j at time k.

[0011] Furthermore, the membership function in step S200 is:

[0012]

[0013] Where l = (1,2,...,n), n is the number of fuzzy factors, the membership function is a normal membership function, u is the expectation, and σ is the expected value. 2 Let Variance be the variance.

[0014] Furthermore, in step S200, each fuzzy factor is substituted into the membership function to obtain the similarity s between track i and track j at time k. ij (k)

[0015]

[0016] Among them, a l (k) represents the l-th fuzzy factor.

[0017] Furthermore, in step S200, the n of radar A at time k is... A Track and radar B's n B By comparing the similarity of each pair of flight paths, we can obtain n. A ×n B There are 10 similarity scores, which are then used to construct a similarity matrix S(k), represented as follows:

[0018]

[0019] Furthermore, in step S300, the historical cumulative similarity λ at time k ij (k) is

[0020] Furthermore, we define the historical cumulative matrix Γ(k).

[0021]

[0022] Right now

[0023] Γ(k)=Γ(k-1)+S(k) (6). Further, the correlation matrix M(k) in step S400 is shown in equation (7).

[0024] The mapping criterion for mapping Γ(k) to the incidence matrix M(k) is:

[0025]

[0026] Where δ s (k) is the similarity threshold.

[0027] Furthermore, the optimal two-dimensional allocation model in step S400 is:

[0028]

[0029] This invention, based on the fuzzy track association algorithm, proposes a historical cumulative matrix. This matrix accumulates similarity information from all past moments, forming a comprehensive evaluation mechanism along the time series dimension. A similarity threshold is set for the historical cumulative matrix, which is then mapped to an association matrix. Ambiguity is assessed within the association matrix. When ambiguity arises, the historical cumulative matrix is ​​combined with the Hungarian algorithm for resolution, ultimately outputting the decision track association pair. Even when targets overlap or intersect, and data from individual moments may not provide sufficient distinguishing information, the historical cumulative similarity matrix can still provide a reliable basis for association decisions. This method improves the correct association rate and stability.

[0030] The present invention will now be further described with reference to the accompanying drawings. Attached Figure Description

[0031] Figure 1 This is a schematic diagram of the method flow of the present invention.

[0032] Figure 2 This is a schematic diagram of a radar detection track intersection scenario.

[0033] Figure 3 This diagram illustrates the correct correlation rates of various algorithms in cross-scenarios.

[0034] Figure 4 This diagram illustrates the error correlation rates of various algorithms in cross-cutting scenarios.

[0035] Figure 5This diagram illustrates the missing correlation rates of various algorithms in cross-scenarios.

[0036] Figure 6 This is a schematic diagram illustrating a radar detection scenario involving a formation of moving targets.

[0037] Figure 7 This diagram illustrates the correct correlation rate of various algorithms in a formation maneuver scenario.

[0038] Figure 8 This diagram illustrates the error correlation rates of various algorithms in a formation maneuver scenario.

[0039] Figure 9 This diagram illustrates the missing correlation rates of various algorithms in a formation maneuver scenario.

[0040] Figure 10 This is a schematic diagram of a radar detection scenario involving multiple targets.

[0041] Figure 11 This diagram illustrates the correct correlation rates of various algorithms in a multi-objective scenario.

[0042] Figure 12 This diagram illustrates the error correlation rates of various algorithms in a multi-objective scenario.

[0043] Figure 13 This diagram illustrates the error correlation rates of various algorithms in a multi-objective scenario. Detailed Implementation

[0044] Step S100: Obtain the state estimates of the target trajectory from the two radars. and Construct a fuzzy factor set {u1(k), u2(k), u3(k)} and a weight set of the fuzzy factors for position estimation, velocity estimation, and acceleration estimation in the x, y, and z directions, respectively. Here, A and B are the radar indices, i and j are the target tracks corresponding to radar A and B, u1(k), u2(k), and u3(k) are the fuzzy factors for position estimation, velocity estimation, and acceleration estimation in the x, y, and z directions, respectively, and k represents time.

[0045] Step S200: Obtain the similarity s between the two tracks based on the membership degree of the fuzzy factors. ij (k), construct the similarity matrix S(k);

[0046] Step S300: Obtain the historical cumulative similarity λ at time k. ij (k), based on historical cumulative similarity λ ij (k) Construct the historical cumulative matrix Γ(k);

[0047] Step S400: Map the historical cumulative matrix Γ(k) to the correlation matrix M(k), construct the optimal two-dimensional allocation model, perform optimal allocation calculation on the optimal two-dimensional allocation model using the Hungarian algorithm, and output the associated track pairs.

[0048] In step S100, the fuzzy factor set is the Euclidean distance between the spatial position, velocity, and azimuth heading angle of tracks i and j.

[0049]

[0050] in, and Let i and j represent the spatial positions of the targets at time k, respectively. and Let $\frac{i}{j}$ represent the velocity of the target at time $k$. In this embodiment, the weight set of the fuzzy factor is set to ${0.55, 0.35, 0.1}$.

[0051] The membership function in step S200 is

[0052]

[0053] Where l = (1,2,...,n), n is the number of fuzzy factors, the membership function is a normal membership function, u is the expectation, and σ is the expected value. 2 Let be the variance. Substituting each fuzzy factor into the membership function yields the similarity s between track i and track j at time k. ij (k)

[0054]

[0055] Among them, a l (k) represents the l-th fuzzy factor.

[0056] In step S200, the n of radar A at time k is... A Track and radar B's n B By comparing the similarity of each pair of flight paths, we can obtain n. A ×n B There are 10 similarity scores, which are then used to construct a similarity matrix S(k), represented as follows:

[0057]

[0058] In step S300, the historical cumulative similarity λ at time k is... ij (k) is

[0059]

[0060] Define the historical cumulative matrix Γ(k).

[0061]

[0062] Right now

[0063] Γ(k)=Γ(k-1)+S(k) (6)

[0064] The correlation matrix M(k) in step S400 is shown in equation (7).

[0065]

[0066] The mapping criterion for mapping Γ(k) to the incidence matrix M(k) is:

[0067]

[0068] Where δ s (k) is the similarity threshold, a value that changes over time. It is typically a recursive formula and can be expressed as δ. s (k)=δ s (k)+ε.

[0069] In this embodiment, the historical cumulative matrix can effectively solve the ambiguity problem. When ambiguity occurs, it can be transformed into an optimal two-dimensional allocation problem for processing. The mathematical model is as follows:

[0070]

[0071] The Hungarian algorithm is used to calculate the optimal allocation, resolve the ambiguity problem, and finally output the associated track pairs.

[0072] Comparative Example

[0073] Compared to traditional weighted trajectory association algorithms and sequential trajectory association algorithms, this patented traditional fuzzy trajectory association algorithm has the highest correct association rate and the best stability in complex scenarios such as target intersection, dense flight, and maneuvering formation flight.

[0074] Since the true probability of association cannot be obtained in practice, frequency is used to approximate the probability, let E c For the correct correlation rate, E e E represents the error association rate. s N represents the missing association rate. l Let N be the total number of associations. c To determine the correct number of associations, N e N represents the number of erroneous associations. s Let N be the number of missed associations. l =N c +N e +N s So there is

[0075]

[0076] E c +E e +E s =1. To measure the correlation performance at each step, the instantaneous correlation rate at time k is...

[0077]

[0078] Average association rate

[0079]

[0080] Use the metrics mentioned above to measure the quality of the algorithm.

[0081] Table 1. Average association rate of 100 Monte Carlo trials in the target cross scenario.

[0082]

[0083] Table 2. Average correlation rate of 100 Monte Carlo trials in formation maneuver scenario.

[0084]

[0085] Table 3. Average association rates of 100 Monte Carlo trials in multi-objective scenarios.

[0086]

[0087] pass Figures 2-13 The simulation comparison results show that the algorithm proposed in this patent is suitable for complex scenarios such as target intersection, maneuver formation, and multiple targets, and its correct correlation rate and stability are better than the comparison algorithm.

Claims

1. A fuzzy track association method based on cumulative historical similarity, characterized in that, include: Step S100: Obtain the state estimates of the target trajectory from the two radars. and Construct a fuzzy factor set {u1(k), u2(k), u3(k)} and a weight set of the fuzzy factors for position estimation, velocity estimation, and acceleration estimation in the x, y, and z directions, respectively. Here, A and B are the radar indices, i and j are the target tracks corresponding to radar A and B, u1(k), u2(k), and u3(k) are the fuzzy factors for position estimation, velocity estimation, and acceleration estimation in the x, y, and z directions, respectively, and k represents time. Step S200: Obtain the similarity s between the two tracks based on the membership degree of the fuzzy factors. ij (k), construct the similarity matrix S(k); Step S300: Obtain the historical cumulative similarity λ at time k. ij (k), based on historical cumulative similarity λ ij (k) Construct the historical cumulative matrix Γ(k); Step S400: Map the historical cumulative matrix Γ(k) to the correlation matrix M(k), construct the optimal two-dimensional allocation model, perform optimal allocation calculation on the optimal two-dimensional allocation model using the Hungarian algorithm, and output the associated track pairs.

2. The method according to claim 1, characterized in that, In step S100, the fuzzy factor set consists of the Euclidean distance between the spatial position, velocity, and azimuth / heading angle of tracks i and j. in, and Let i and j represent the spatial positions of the targets at time k, respectively. and Let represent the velocity of the target on trajectory i and j at time k.

3. The method according to claim 2, characterized in that, The membership function in step S200 is Where l = (1,2,...,n), n is the number of fuzzy factors, the membership function is a normal membership function, u is the expectation, and σ is the expected value. 2 Let Variance be the variance.

4. The method according to claim 3, characterized in that, In step S200, each fuzzy factor is substituted into the membership function to obtain the similarity s between track i and track j at time k. ij (k) Among them, a l (k) represents the l-th fuzzy factor.

5. The method according to claim 4, characterized in that, In step S200, the n of radar A at time k is... A track and radar B's n B By comparing the similarity of each pair of flight paths, we can obtain n. A ×n B There are 10 similarity scores, which are then used to construct a similarity matrix S(k), represented as follows: （6）。 6. The method according to claim 5, characterized in that, In step S300, the historical cumulative similarity λ at time k is... ij (k) is （5）。 7. The method according to claim 6, characterized in that, Define the historical cumulative matrix Γ(k). Right now Γ(k)=Γ(k-1)+S(k) (6).

8. The method according to claim 7, characterized in that, The correlation matrix M(k) in step S400 is shown in equation (7). The mapping criterion for mapping Γ(k) to the incidence matrix M(k) is: Where δ s (k) is the similarity threshold.

9. The method according to claim 8, characterized in that, The optimal two-dimensional allocation model in step S400 is

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