Multi-target tracking methods, localization systems, and readable storage media

Abstract

This application relates to target tracking and provides a multi-target tracking method. It acquires measurement data of the target to be tracked using at least two sensors to obtain a first set of measurement data pairs. Then, based on preset constraints, related measurement data pairs in this first set are eliminated to obtain the true target. Next, the starting point of the true target's trajectory is determined using an FCM algorithm and the measurement data pairs of the true target. Then, the true target is correlated using the FCM algorithm and the real-time measurement data of the true target to obtain a stable trajectory. Finally, the true target is tracked based on the starting point and the stable trajectory. This application eliminates false targets using preset constraints and obtains the starting point of the trajectory based on the FCM algorithm in the trajectory initiation part, and uses FCM to determine the stable trajectory of the true target in the trajectory correlation part, thereby achieving the tracking of the true target with short processing time and fast tracking speed.

Description

Technical Field

[0001] This application belongs to the field of target tracking technology, and in particular relates to a multi-target tracking method, a positioning system, and a readable storage medium. Background Technology

[0002] In the field of electronic warfare, due to the development of technologies such as electronic reconnaissance and stealth attacks, traditional active positioning systems such as radar are vulnerable to electronic interference, posing a significant security risk by exposing their location. Compared to active positioning technologies, passive positioning technologies offer advantages such as strong concealment, high anti-interference capabilities, and low cost.

[0003] Whether active or passive, traditional direction-finding methods can only obtain the position information of multiple targets, resulting in poor performance for tracking highly maneuverable multi-target objects. To achieve better target tracking, it is necessary to combine with intelligent algorithms. By using track initiation algorithms, the track initiation problem can be transformed into a binary classification problem using deep learning models. Based on the traditional track initiation algorithm, a binary classification problem can be solved. Such algorithms are suitable for environments with strong clutter, but they require a large amount of training data, have long processing times, and cannot achieve fast tracking. Summary of the Invention

[0004] The technical problem to be solved by this application is to provide a multi-target tracking method, a positioning system and a readable storage medium, which aims to solve the problem that traditional technologies require a lot of training and have long processing time when performing multi-target tracking, and cannot achieve fast tracking.

[0005] This application is implemented as follows: a multi-target tracking method is applied to a positioning system, the positioning system including at least two sensors for tracking and measuring targets, and the multi-target tracking method includes:

[0006] Acquire measurement data of each sensor for the target to be tracked to obtain a first set of measurement data pairs, the first set of measurement data pairs including measurement data pairs of each target to be tracked;

[0007] The true target is determined from the first set of measurement data pairs based on preset constraints.

[0008] The starting point of the real target's trajectory is determined based on the FCM algorithm and the measurement data of the real target;

[0009] Acquire real-time measurement data of the real target from each of the sensors, and associate the real target with the real target according to the FCM algorithm to obtain the stable track of the real target;

[0010] The real target is tracked based on the starting point of the flight path and the stable flight path.

[0011] Preferably, determining the true target from the first set of measurement data pairs according to preset constraints includes:

[0012] The first set of measurement data pairs is subjected to measurement data pair elimination according to preset constraints.

[0013] The true target is determined by using the second measurement data obtained after elimination.

[0014] Preferably, the step of removing measurement data pairs from the first set of measurement data pairs according to preset constraints includes:

[0015] Obtain distance range constraints;

[0016] The first set of measurement data pairs is processed by removing measurement data from the distance range constraint to obtain the second set of measurement data pairs.

[0017] Preferably, the multi-target tracking method further includes:

[0018] Obtain speed range constraints;

[0019] Based on the speed range constraint, the second measurement data set is used to remove measurement data.

[0020] Preferably, the step of associating the real target with the FCM algorithm and the real-time measurement data to obtain the stable trajectory of the real target includes:

[0021] Obtain the stable trajectory of the real target at the previous moment;

[0022] Based on the three-dimensional fuzzy matrix in the FCM algorithm, the real-time measurement data is correlated with the stable trajectory of the previous moment to obtain the stable trajectory of the real target at the current moment.

[0023] Preferably, the step of associating the real-time measurement data with the stable trajectory of the previous moment based on the three-dimensional fuzzy matrix in the FCM algorithm to obtain the stable trajectory of the real target at the current moment includes:

[0024] Obtain the associated gate size and regularization term;

[0025] The three-dimensional fuzzy matrix is ​​determined based on the associated gate size and the regularization term, wherein the three-dimensional fuzzy matrix includes the membership degree between the real-time measurement data pair and the stable track at the previous moment;

[0026] Obtain the target function;

[0027] Based on the three-dimensional fuzzy matrix and the objective function, the stable trajectory of the real target at the current moment is determined.

[0028] Preferably, determining the three-dimensional fuzzy matrix based on the associated gate size and the regularization term includes:

[0029] Let Ω(i,j,t) denote the three-dimensional fuzzy matrix, then:

[0030]

[0031] Where ε represents the associated gate size, and RE(i,j,t) represents the regularization term. Where b represents the intensity coefficient of the regularization term, f t f represents the frequency of the target radiation source. i The measured Doppler frequency is represented by , and i represents the i-th sensor.

[0032] Preferably, determining the stable trajectory of the real target at the current moment based on the three-dimensional fuzzy matrix and the objective function includes:

[0033] With J m (U) represents the objective function.

[0034] By minimizing the objective function using the three-dimensional fuzzy matrix, the target three-dimensional fuzzy matrix is ​​obtained;

[0035] The stable trajectory of the real target at the current moment is determined based on the target fuzzy matrix, the real-time measurement data, and the stable trajectory of the previous moment.

[0036] This application also provides a positioning system, including at least two sensors, a memory, a processor, and a computer program stored in the memory and running on the processor;

[0037] The sensor is used to track and measure the target;

[0038] When the processor executes the computer program, it implements the various steps in the multi-target tracking method described above.

[0039] This application also provides a readable storage medium storing a computer program thereon, characterized in that, when the computer program is executed by a processor, it implements the various steps of the multi-target tracking method described above.

[0040] Compared with the prior art, the beneficial effects of this application are as follows: The multi-target tracking method provided in this application acquires measurement data of the target to be tracked through at least two sensors to obtain a first measurement data pair set. The first measurement data pair set includes measurement data pairs of each target to be tracked. Then, relevant measurement data pairs in the first measurement data pair set are eliminated according to preset constraints to obtain the real target. Then, the starting point of the real target's trajectory is determined according to the FCM algorithm and the measurement data pairs of the real target. Next, the real target's real-time measurement data is acquired from each sensor. The real target is correlated according to the FCM algorithm and the real-time measurement data to obtain the stable trajectory of the real target. Finally, the real target is tracked according to the starting point of the trajectory and the stable trajectory. This application acquires measurement data pairs of the target to be tracked through sensors, eliminates false targets in the initial part of the track using preset constraints, and obtains the track start point based on the FCM algorithm. In the track association part, FCM is used to determine the stable track of the real target, thereby realizing the tracking of the real target. The embodiments of this application do not require a lot of training and can track the real target in real time based on the sensor measurement data. The processing time is short and the tracking speed is fast. Attached Figure Description

[0041] Figure 1 This is a flowchart of a multi-target tracking method provided in an embodiment of this application;

[0042] Figure 2 This is a schematic diagram of three unknown targets under distance range constraints provided in another embodiment of this application;

[0043] Figure 3 This is a schematic diagram of a dual-station motion track provided in another embodiment of this application;

[0044] Figure 4 This is a diagram illustrating the effect of parallel target correlation tracking provided in another embodiment of this application;

[0045] Figure 5 This is a parallel target correlation tracking position error map provided in another embodiment of this application;

[0046] Figure 6 This is a diagram illustrating the effect of cross-target correlation tracking provided in another embodiment of this application;

[0047] Figure 7 This is a cross-target correlation tracking position error diagram provided in another embodiment of this application;

[0048] Figure 8 This is a schematic diagram of the flight paths of five targets provided in another embodiment of this application;

[0049] Figure 9This is a diagram illustrating the multi-maneuvering target NNDA tracking effect provided in another embodiment of this application;

[0050] Figure 10 This is a multi-maneuvering target NNDA tracking position error map provided in another embodiment of this application;

[0051] Figure 11 This is a GNNDA tracking effect diagram for multiple maneuvering targets provided in another embodiment of this application;

[0052] Figure 12 This is a multi-maneuvering target GNNDA tracking position error map provided in another embodiment of this application;

[0053] Figure 13 This is a multi-maneuvering target GFCMDA tracking effect diagram provided in another embodiment of this application;

[0054] Figure 14 This is a multi-maneuvering target GFCMDA tracking position error diagram provided in another embodiment of this application. Detailed Implementation

[0055] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0056] In the field of electronic warfare, due to the development of technologies such as electronic reconnaissance and stealth attacks, traditional active positioning systems such as radar are vulnerable to electronic interference, posing a significant security risk by exposing their own position. Compared to active positioning technologies, passive positioning technologies have advantages such as strong concealment, strong anti-interference capabilities, and low cost. Common passive positioning and tracking methods include frequency difference of arrival (FDOA), time difference of arrival (TDOA), and direction of arrival (DOA). Among them, FDOA locates the target by acquiring the frequency difference information generated by the relative motion between the observation station and the target. Since the frequency difference information is a nonlinear function of the target source's position and velocity, it requires four observation stations in two-dimensional space, making it difficult to apply in dual-station conditions. TDOA (Time Difference of Arrival) calculates the arrival time difference of the same signal received by different observation stations, constructing a hyperbolic model for positioning. This method offers high positioning accuracy but suffers from positioning ambiguity. Furthermore, when using multiple observation stations, it requires transmitting large amounts of data, and the data transmission cost between observation stations increases under long-distance, low-precision conditions. DOA (Directional Aspect-Oriented Positioning) works by measuring the azimuth angle of the same target at two or more observation stations. Accurate azimuth angle measurements are crucial for precise positioning. This method is simple to implement and highly feasible, but it places high demands on the hardware of the direction-finding equipment. Motion-based single-station pure azimuth positioning and tracking only meets observability conditions when the moving station undergoes significant maneuvering. Under long-distance, low-precision conditions, its observability is limited by maneuverability. Compared to motion-based single-station methods, motion-based dual-station methods can directly perform positioning through direction-finding crossover, satisfying observability requirements without complex maneuvers. Traditional direction-finding positioning methods only obtain the target's position information, resulting in poor tracking performance for highly maneuverable targets. To address these issues, direction-finding Doppler positioning has been proposed in related technologies.

[0057] Multi-target tracking technology is a key technology in electronic warfare, consisting of three parts: track initiation, track association, and track termination. Track association is the prerequisite and foundation for information fusion and target tracking, directly affecting the accuracy and rationality of subsequent information processing. The Nearest Neighbor Data Association (NNDA) algorithm sequentially associates the observations with the smallest distance falling within the association gate with the target. This algorithm has low computational complexity and is suitable for sparse target scenarios and scenarios with little clutter, but it can get stuck in local optima. To address this issue, the Global Nearest Neighbor Data Association (GNNDA) algorithm has been proposed, which can achieve global distance optimization, but the time required increases dramatically with the amount of data. The Probabilistic Data Association (PDA) algorithm is suitable for single-target tracking in cluttered environments. This algorithm considers all valid echoes within the association gate, but ignores the relationship between valid measurements and measurement predictions, increasing the randomness of measurement noise distribution and leading to false tracking and loss of tracking. The Joint Probabilistic Data Association (DPDA) algorithm... Association (JPDA) is suitable for multi-target tracking in cluttered environments. The JPDA algorithm introduces the possibility of observations from adjacent tracks, effectively overcoming tracking errors in dense target scenarios. However, as data and clutter increase, a combinatorial explosion occurs, leading to a surge in computational load. Furthermore, correct track initiation is crucial for subsequent association and tracking. Research on track initiation is limited, and most studies are based on active localization systems. Passive localization systems, unable to directly acquire target location information, face increased difficulty in track initiation. Traditional track initiation algorithms can be categorized into sequential processing techniques, batch processing techniques, and track initiation combined with intelligent algorithms. Initialization algorithms. Sequential processing techniques include intuitive methods, logical methods, and their improvements. The basic idea is to process the echo data obtained from each scan one by one, and determine whether to establish an initial track based on the point correlation results within a certain time. These algorithms require point correlation results from multiple scans to determine whether to establish a target track, and are suitable for initiating tracks in environments with weak clutter, but have poor real-time performance. Batch processing techniques include Hough transform and its improvements. These algorithms mainly process the echo data obtained from multiple scans together, using Hough transform to achieve incoherent accumulation of echo data, improving track initiation performance. They are used for track initiation in environments with strong clutter, but are difficult to apply to track initiation in passive positioning.The track initiation algorithm combined with intelligent algorithms transforms the track initiation problem into a binary classification problem using a deep learning model. Based on the traditional track initiation algorithm, it performs a binary classification problem. This type of algorithm is suitable for environments with strong clutter, but it requires a large amount of training data and has a long processing time.

[0058] The technical solution provided in this application proposes a multi-target tracking method suitable for dual-station motion tracking under long-distance and low-precision conditions. This multi-target tracking method consists of two parts: track initiation and track association. In the track initiation part, false targets are eliminated using distance and velocity range constraints, and the track starting point is obtained based on the Fuzzy C-Means (FCM) algorithm. In the track association part, the distance matrix between the target and the measurement data pair is given using an association gate and a regularization term. The fuzzy matrix of the FCM is used as the distance matrix of the NNDA, utilizing global information to avoid getting trapped in local optima.

[0059] See Figure 1 The multi-target tracking method provided in this application embodiment is applied to a positioning system, the positioning system including at least two sensors for tracking and measuring targets, and the multi-target tracking method includes:

[0060] S101, acquire the measurement data of each sensor for the target to be tracked, and obtain a first set of measurement data pairs, the first set of measurement data pairs including the measurement data pairs of each target to be tracked.

[0061] In this embodiment, the positioning system includes at least two sensors. Therefore, when measuring a target to be tracked, the target includes measurement data from at least two sensors. In this application, the measurement data of the same target to be tracked is referred to as the measurement data pair of the target to be tracked. For example, assuming the positioning system includes sensor 1 and sensor 2, sensor 1 measures the target to be tracked (Target1) to obtain measurement data data1, and sensor 2 measures the target to be tracked (Target1) to obtain measurement data data2. Then, the measurement data pair of the target to be tracked (Target1) is data1 and data2. By storing multiple measurement data pairs of the target to be tracked in a set, the first measurement data pair set is obtained.

[0062] S102, determine the real target from the first set of measurement data pairs according to preset constraints.

[0063] In this embodiment, determining the true target from the first set of measurement data pairs according to preset constraints includes: removing measurement data pairs from the first set of measurement data pairs according to preset constraints, and determining the true target based on the second set of measurement data pairs obtained after removal. The preset constraints include distance range constraints and velocity range constraints. By removing relevant measurement data pairs from the first set of measurement data pairs according to these constraints, the true target can be determined based on the second set of measurement data pairs obtained after removal. For example, if the first set of measurement data pairs originally contained 12 measurement data pairs (representing 12 targets to be tracked), after removing false targets using the distance range constraints and velocity range constraints, the second set of measurement data pairs obtained only contains 5 measurement data pairs. The target to be tracked corresponding to these 5 measurement data pairs is the true target.

[0064] S103, determine the starting point of the real target's trajectory based on the FCM algorithm and the measurement data of the real target.

[0065] In this step, the starting point of the real target's trajectory is obtained based on the FCM algorithm and the measurement data of the real target. The starting point of the trajectory is then filtered to obtain the final starting point of the real target's trajectory.

[0066] S104, acquire real-time measurement data of the real target from each of the sensors, and associate the real target with the real target according to the FCM algorithm and the real-time measurement data to obtain the stable track of the real target.

[0067] S105, Track the real target based on the starting point of the trajectory and the stable trajectory.

[0068] This application acquires measurement data pairs of the target to be tracked through sensors, eliminates false targets in the initial part of the track using preset constraints, and obtains the track start point based on the FCM algorithm. In the track association part, FCM is used to determine the stable track of the real target, thereby realizing the tracking of the real target. The embodiments of this application do not require a lot of training and can track the real target in real time based on the sensor measurement data. The processing time is short and the tracking speed is fast.

[0069] The following description further illustrates this application by using a positioning system comprising two sensors (also known as a motion bistation) to track multiple targets within the positioning system.

[0070] 1.1 Method for determining the start of a flight path based on FCM:

[0071] Track initiation and track association algorithms are based on active localization systems for multi-target tracking. Multi-target tracking methods applicable to passive localization systems are mostly specific to those systems. Passive localization systems require multiple sensors to locate the target; therefore, in multi-target tracking scenarios, pairing the measurement data from each sensor is a critical issue.

[0072] Assuming there are n unknown targets at time k, and neglecting clutter interference, the measurement sets of these unknown targets from the two motion observation stations (i.e., a motion bistation) are as follows:

[0073] {Z i (k,1)|1≤i≤n} (1)

[0074] Z j (k,2)|1≤j≤n} (2)

[0075] A single motion observation station (i.e., one station with a single sensor) cannot perform maneuvers that meet observability requirements under long-range, low-precision conditions; therefore, a single motion observation station cannot achieve independent localization. Two motion observation stations do not have sufficient measurement information for the same target to directly pair them; therefore, for n unknown targets, there will be n... 2 Possible pairs of measurement data:

[0076] {Y ij (k)=(Z i (k,1),Z j (k,2))|1≤i≤n,1≤j≤n} (3)

[0077] Since one possible measurement data point corresponds to one possible target, n real targets correspond to n 2 There are several possible targets. In a bistationary motion tracking scenario without constraints, existing measurement data cannot initiate multi-target tracking. If the distance range for associated tracking is limited to a certain interval [rmax], ... min Therefore, by using distance range constraints, some incorrectly matched measurement data can be used to eliminate false targets, leaving only the true targets. For example... Figure 2 As shown, after removing the relevant false targets, the remaining real targets are A1, A2, and A3.

[0078] A measurement data for Y ij (k) can directly obtain the target's position and velocity estimate, and determine its velocity range based on the target type, limiting the velocity to a certain interval [vmax]. min Within a certain range, false targets are eliminated by constraining the speed range. In this embodiment, the long-distance condition is generally set to r. min r max vmin ,v max .

[0079] 1.2 Track Association Method Based on FCM Fuzzy Matrix

[0080] NNDA is the simplest and most direct track association algorithm, boasting advantages such as low computational cost and strong robustness. In tracking problems, NNDA can be used to match the target at the current moment with the target at the previous moment, thereby achieving target tracking. In clutter-free environments, NNDA has lower computational cost compared to other complex data association algorithms, and its performance in associated tracking is not inferior to other complex data association algorithms. However, it cannot consider the global situation, i.e., it cannot achieve the minimum global distance. GNNDA effectively solves this problem by selecting the measurement that minimizes the global distance as the candidate measurement for the target, thus addressing the issue of poor association performance of simple NNDA in dense target scenarios. The biggest problem with NNDA is its inability to handle data association of intersecting tracks, leading to situations where the observation and target cannot be correctly matched, resulting in estimated tracks being unrelated to the actual tracks.

[0081] In some embodiments, track association algorithms are mostly designed for single-station independent positioning applications. In this application, a single motion observation station only has two measurements: azimuth and Doppler frequency. This makes it impossible to directly decouple the target's position and velocity information. Furthermore, under long-distance, low-precision conditions, the maneuvers required to meet single-station observability are impractical in some embodiments. Unlike typical track association scenarios where the measurement data of a single motion observation station can be independently associated, track association between two motion observation stations requires consideration of measurement pairing. To simplify this problem, embodiments of this application provide a multi-target tracking method for environments without clutter interference.

[0082] This application proposes a track association method based on the FCM fuzzy matrix (Global FCM Data Association, GFCMDA). Assuming that at time k, both motion observation stations obtain n measurement data points, then n 2 One possible pair of measurement data, namely:

[0083] {Y ij (k)=(Z i (k,1),Z j (k,2))|1≤i≤n,1≤j≤n} (4)

[0084] At time k-1, there are c stable tracks, and the state of the t-th stable track is... The estimated covariance is P t (k|k), then the predicted measurement at time k The corresponding residual covariance matrix is ​​S t (k), defining the measurement data for Y ij (k) and the predicted measurement at time k If the distance between them is D(i,j,y), then D(i,j,t) is:

[0085]

[0086] The measurement data for Y is represented by a three-dimensional matrix Ω. ij (k) is the distance matrix between the stable track and the target track. The elements Ω(i,j,t) of the three-dimensional matrix represent the measurement data relative to Y. ij The distance (k) to the t-th stable track is calculated as follows, with the associated gate size ε set:

[0087]

[0088] Where a >> 1 represents Y ij (k) is definitely not related to the t-th stable track, and the regularization term RE(i,j,t) is calculated as follows:

[0089]

[0090] Where b represents the intensity coefficient of the regularization term, f t f represents the frequency of the target radiation source. t =10GHz; f i This represents the Doppler frequency measured by the motion observation station, where i = 1, 2 refers to two motion observation stations, i representing the i-th sensor. In this embodiment, the regularization term is added to account for the difference between azimuth noise and Doppler frequency noise, meaning that Doppler frequency is more accurate than azimuth. Doppler frequency corresponds to the target's velocity information, and different targets often have different velocities in magnitude and direction. Using velocity information allows for better correlation between measurement data and the target; therefore, the regularization term RE(i,j,t) is added to achieve this purpose.

[0091] Directly using nearest neighbor data association on the three-dimensional matrix Ω can achieve the goal of associating measurement data pairs with the target. However, as mentioned earlier, nearest neighbor data association is only a locally optimal association algorithm and cannot optimize global information. This application's embodiment uses an FCM fuzzy matrix to achieve global association.

[0092] The FCM algorithm uses a three-dimensional fuzzy matrix U, where U(i,j,t) represents Y. ij The membership degree between (k) and the t-th stable track is defined by considering the predicted measure for each stable track. It is known that the cluster center matrix V of the FCM algorithm deviates slightly from the predicted measurement. The weighted sum of squared errors objective function J is defined. m (U):

[0093]

[0094] Then the objective function J m The calculation of the minimized three-dimensional fuzzy matrix U is as follows:

[0095]

[0096] Based on the FCM-based Track Association and Initiation (FCMTAI) algorithm proposed in the application embodiments, the pseudocode of the multi-target tracking method provided in this application embodiment is shown in Table 1 below:

[0097]

[0098] In this embodiment of the application, the acquired data needs to be preprocessed, including:

[0099] (1) Pair the measurements from the two motion observation stations;

[0100] (2) Use the cross-positioning method to calculate the target position and velocity information corresponding to the paired measurements;

[0101] (3) Use distance constraints and velocity constraints to eliminate false targets generated by incorrect matching measurements;

[0102] (4) Use FCM to obtain the cluster center, i.e. the starting point of the track, from the constrained measurement set.

[0103] This application's embodiments select azimuth Doppler information cross-location. Based on the different locations of the two observation stations, a cross-location method is used to measure the azimuth of the target. Simultaneously, the received Doppler information is used to measure the target's velocity in space. Combining the azimuth and Doppler information, the estimated values ​​of the target's spatial position and velocity can be determined. Furthermore, in multi-target tracking experiments, targets may suddenly disappear or appear. Therefore, using range constraints is more reasonable. This is mainly because the elliptical neighborhood constraint defined by Mahalanobis distance is derived from historical data, while suddenly appearing or disappearing targets do not have historical trajectory data. Range constraints can directly restrict the target's position without relying on historical data, making them more suitable for handling sudden events.

[0104] In this embodiment, the FCM clustering algorithm is selected. Although both DNSCAN and FCM clustering can be used for false target detection, the DCBSCAN clustering algorithm is suitable for false targets and non-false targets that have significant differences. However, if false targets and non-false targets have a certain similarity, the FCM clustering algorithm is more effective.

[0105] This application embodiment is a multi-target tracking method capable of tracking targets that appear and disappear suddenly. The method principle utilizes pairing association and distance / velocity constraints to eliminate incorrect matches for tracking. In object processing, it primarily handles the set of bistationary motion measurement azimuth and Doppler information for the localization and tracking of moving targets. The implementation of this application embodiment requires steps such as pairing association, constraint calculation, cluster center calculation, and UKF prediction.

[0106] To address the problem of false targets arising from insufficient motion bistation measurement information under long-distance, low-precision conditions, this application proposes a multi-target tracking method using motion bistations. This method consists of two parts: track initiation and track association. In the track initiation part, false targets are eliminated using distance and velocity range constraints, and the track starting point is obtained based on the Fuzzy C-Means (FCM) algorithm. In the track association part, the distance matrix between the target and the measurement pair is derived using an association gate and a regularization term. The fuzzy matrix of FCM is used as the distance matrix for the nearest neighbor algorithm, and global information is introduced to avoid getting trapped in local optima. Simulation experiments show that, in various tracking scenarios, compared with the NNDA and GNNDA algorithms, the proposed association tracking algorithm improves accuracy by 1.38%–6.97% and 0.64%–3.28%, respectively. Specific simulation experiments are as follows.

[0107] 2. Simulation Experiment Analysis:

[0108] To verify the correctness and feasibility of the bistatic multi-target tracking method provided in this application, simulations were performed on different multi-target combinations, and the tracking performance under different observation noise combinations was presented. The sampling interval Δt = 1 s, the total sampling duration T = 300 s, and the target radiation source frequency was f. t =10GHz, the mobility of the two mobile base stations is as follows:

[0109] (1) Motion observation station 1: The initial position is (-20km, 0km), and it moves in a uniform circular motion with a radius of 15km and an angular velocity of 20.9mrad / s counterclockwise with (-35km, 0km) as the center.

[0110] (2) Motion observation station 2: The initial position is (50km, 0km), and it moves in a uniform circular motion counterclockwise with a radius of 15km and an angular velocity of 20.9mrad / s with (35km, 0km) as the center.

[0111] A schematic diagram of the trajectory of the two motion stations is shown below. Figure 3 As shown. In Figure 3 In the diagram, the horizontal and vertical axes represent the positions of the observation station in the x and y directions at corresponding moments during its movement from 1 to 300 seconds.

[0112] Different combinations of observation noise are set, and the observation noise of the two observation stations remains consistent. The range of azimuth noise is σ. β The range of Doppler frequency noise is σ ∈{17.5mrad,35.0mrad,52.4mrad}. f The range of the target distance from the observation station is [300km, 600km], ∈1Hz,10Hz,100Hz.

[0113] Due to the characteristics of the bistatic positioning system, the FCM-based track initiation method proposed in this application uses distance and velocity constraints to eliminate false targets, and then uses the FCM algorithm to initiate tracks for the remaining targets, thus improving the accuracy of track initiation. No comparable methods are provided for the track initiation part; however, comparisons are made with NNDA and GNNDA for the track association part. Three multi-target scenarios are set: parallel targets, intersecting targets, and multiple maneuvering targets of different types. Each scenario undergoes 100 Monte Carlo simulations under different combinations of observation noise standard deviations, and the target tracking position RMSE is given.

[0114] To compare the performance of correlation methods, this application uses the root mean square error (RMSE) as the standard:

[0115]

[0116] 2.1 Parallel target tracking:

[0117] The maneuvering patterns of the two parallel targets are as follows:

[0118] (1) Target 1: The initial position is (-50km, 400km), the appearance time is t1 = 1s, the termination time is t2 = 300s, and it moves in uniform linear motion along the positive x-axis at a speed of 0.3km / s.

[0119] (2) Target 2: The initial position is (-50km, 450km), the appearance time is t1 = 1s, the termination time is t2 = 300s, and it moves in uniform linear motion along the positive x-axis at a speed of 0.3km / s.

[0120] The observation noise combination (σ) β =17.5mrad,σ f Taking 1Hz as an example, the correlation tracking effect and correlation tracking position error of parallel targets are as follows: Figure 4 , Figure 5 As shown. In Figure 4 In the diagram, the horizontal and vertical axes represent the x-axis and y-axis positions of the parallel target during its motion, respectively. Figure 5 In the figure, the horizontal axis t represents the current time, and the vertical axis RMSE represents the root mean square error of target tracking at time t.

[0121] Table 2 shows the RMSE of the tracking position corresponding to different combinations of observation noise after 100 Monte Carlo simulation experiments.

[0122] Table 2: Tracking Position RMSE of Parallel Targets

[0123]

[0124] Table 2 shows that for parallel targets, the correlation tracking performance of GFCMDA and the comparison method is not significantly different. Table 2 presents the tracking RMSE of the three correlation methods under different combinations of observation noise. Under different noise levels, the tracking performance of the three correlation methods for the same target is not significantly different, but the tracking RMSE of target 2 is larger than that of target 1 because the distance between target 2 and the observation station is greater than that between target 1 and the observation station. When the azimuth noise increases linearly and the Doppler frequency noise increases exponentially, the azimuth angle has a greater impact on the tracking RMSE than the Doppler frequency, because the azimuth angle affects the position and velocity positioning accuracy.

[0125] Parallel targets are a common form of multi-target interaction. Simulation results of parallel targets show that the proposed bi-stationary multi-target tracking method can effectively track parallel targets.

[0126] 2.2 Cross-target tracking:

[0127] The maneuverability of the two intersecting targets is as follows:

[0128] (1) Target 1: The initial position is (-45km, 420km), the time of appearance is t1 = 1s, the time of termination is t2 = 300s, the velocity along the positive x-axis is 0.3km / s, the velocity along the positive y-axis is 0.1km / s, and it moves in uniform linear motion.

[0129] (2) Target 2: The initial position is (45km, 420km), the appearance time is t1 = 1s, the termination time is t2 = 300s, the velocity along the negative x-axis is 0.3km / s, the velocity along the positive y-axis is 0.1km / s, and it moves in uniform linear motion.

[0130] Two intersecting targets meet at point (0km, 435km) at t3 = 150s to observe the noise combination (σ). β =17.5mrad,σ f Taking 1Hz as an example, the correlation tracking effect and correlation tracking position error of the cross-target are as follows: Figure 6 and Figure 7 As shown. In Figure 6 In the diagram, the horizontal and vertical axes represent the target's position in the x-direction and y-direction, respectively, during its movement. Figure 7 In the figure, the horizontal axis t represents the current time, and the vertical axis RMSE represents the root mean square error of target tracking at time t.

[0131] Table 3 shows the RMSE of the tracking position corresponding to different combinations of observation noise after 100 Monte Carlo simulation experiments.

[0132] Table 3: Average Tracking Position (RMSE) of Crossing Targets

[0133]

[0134] Figure 3 The results show that for intersecting targets, NNDA performs well in correlated tracking before and after the two targets intersect, but its performance deteriorates during the intersection. GNNDA has the largest correlation error at the beginning of the two targets' intersection, and the error increases during the intersection, decreasing after the intersection. GFCMDA handles correlated tracking well during target intersection. Table 3 shows the tracking RMSE of the three correlation methods under different combinations of observation noise. Under different noise levels, NNDA's tracking performance for the same target is weaker than GFCMDA, while GNNDA is stronger than GFCMDA under low noise conditions, but GFCMDA is the best under high noise conditions. When azimuth noise increases linearly and Doppler frequency noise increases exponentially, the azimuth angle has a greater impact on the tracking RMSE than the Doppler frequency, because the azimuth angle affects the accuracy of position and velocity positioning.

[0135] Cross-target interaction is a common form of multi-target interaction. Simulation results of cross-target interaction show that the proposed bi-stationary multi-target tracking method can perform associated tracking of cross-target interaction.

[0136] 2.3 Multi-maneuvering target tracking:

[0137] The maneuvering patterns of the five different types of maneuvering targets are as follows:

[0138] (1) Target 1: The initial position is (-45km, 420km), the time of appearance is t1 = 1s, the time of termination is t2 = 300s, the velocity along the positive x-axis is 0.3km / s, the velocity along the positive y-axis is 0.1km / s, and it moves in uniform linear motion.

[0139] (2) Target 2: The initial position is (45km, 420km), the appearance time is t1 = 1s, the termination time is t2 = 250s, the velocity along the negative x-axis is 0.3km / s, the velocity along the positive y-axis is 0.1km / s, and it moves in uniform linear motion.

[0140] (3) Target 3: The initial position is (-70km, 400km), the appearance time is t1 = 150s, the termination time is t2 = 300s, the velocity along the positive x-axis is 0.4km / s, and it moves in uniform linear motion.

[0141] (4) Target 4: Initial position is (50km, 390km), appearance time is t1 = 30s, termination time is t2 = 270s, initial velocity along the positive x-axis is 0.2km / s, and acceleration is 1.7m / s². 2 Uniformly accelerated linear motion.

[0142] (5) Target 5: The initial position is (155km, 440km), the appearance time is t1=1s, the termination time is t2=300s, and it moves in a counterclockwise uniform circular motion with a radius of 15km and an angular velocity of 20.9mrad / s.

[0143] The appearance and termination times of the five different types of maneuvering targets are not consistent. Targets 3 and 4 appear at t=150s and t=30s respectively, which verifies the feasibility of the multi-target tracking method in the initial part of the track. Targets 2 and 4 terminate at t=250s and t=270s respectively, which verifies the feasibility of the multi-target tracking method in the termination part of the track. The five targets form parallel and intersecting interactive situations, and targets 4 and 5 perform uniformly accelerated linear motion and uniform circular motion respectively. The complex target maneuvering situation can test the proposed multi-target tracking method.

[0144] The flight path diagram of the 5 targets is as follows: Figure 8 As shown. In Figure 8 In the diagram, the horizontal and vertical axes represent the target's position in the x-direction and y-direction, respectively, during its movement.

[0145] The observation noise combination (σ) β =17.5mrad,σ f Taking 1Hz as an example, the multi-target correlation tracking effect is as follows: Figure 9 , Figure 11 and Figure 13 As shown, the position error of multi-target correlation tracking is as follows: Figure 10 , Figure 12 and Figure 14 As shown. In Figure 9 , Figure 11 and Figure 13 In the diagram, the horizontal and vertical axes represent the target's position in the x-direction and y-direction, respectively, during its movement. Figure 10 , Figure 12 and Figure 14 In the figure, the horizontal axis t represents the current time, and the vertical axis RMSE represents the root mean square error of target tracking at time t.

[0146] Table 4 shows the RMSE of the tracking position corresponding to different combinations of observation noise after 100 Monte Carlo simulation experiments.

[0147] Table 4: Average Tracking RMSE for 5 Targets

[0148] <![CDATA[Observation noise combination (σ β , σ f )]]> NNDA(km) GNNDA(km) GFCMDA(km) (17.5 mrad, 1 Hz) 7.91 6.87 6.23 (17.5 mrad, 10 Hz) 8.58 6.88 7.20 (17.5 mrad, 100 Hz) 10.38 7.20 8.45 (35.0 mrad, 1 Hz) 15.42 13.59 11.30 (35.0 mrad, 10 Hz) 16.17 13.63 12.22 (35.0 mrad, 100 Hz) 17.84 14.44 12.86 (52.4 mrad, 1 Hz) 22.31 18.74 15.95 (52.4 mrad, 10 Hz) 23.79 18.87 16.82 (52.4 mrad, 100 Hz) 24.72 21.49 18.21

[0149] Figures 9 to 14 The comparison charts show that in multi-target scenarios, GFCMDA's overall correlation tracking performance is better than the compared correlation methods, and its initial convergence effect is significant. Table 4 shows the tracking RMSE of the three correlation methods under different combinations of observation noise. Under different noise levels, the average tracking performance of NNDA and GNNDA is weaker than that of GFCMDA. When azimuth noise increases linearly and Doppler frequency noise increases exponentially, the azimuth angle has a greater impact on the tracking RMSE than the Doppler frequency, because the azimuth angle affects the position and velocity positioning accuracy. Simulation results on multi-target scenarios verify the feasibility of the method proposed in this application in complex scenarios.

[0150] Figure 10 , Figure 12 and Figure 14 The start and end times of the track tracking error curve are consistent with the appearance and disappearance times of the target, indicating that targets appearing and disappearing at different times can initiate and terminate tracks, verifying the correctness of the track initiation method in this application. Simulation results from three experiments show that azimuth noise has a more significant impact on multi-target tracking performance than Doppler frequency noise. Therefore, in a moving bistatic scenario, azimuth noise is crucial for overall correlated tracking.

[0151] Based on the results and analysis of three simulation experiments, the motion bistation multi-target tracking method proposed in this application has been verified and can basically meet the requirements of multi-target tracking under long-distance and low-precision conditions.

[0152] This application proposes a bistatic multi-target tracking method based on FCM, taking into account the characteristics of bistatic multi-target tracking. In the initial stage of the track, distance and velocity range constraints are used to eliminate false targets, and the track starting point is obtained using FCM. In the track association stage, the FCM fuzzy matrix is ​​used as the distance matrix for the nearest neighbor association algorithm. To address the problem of excessive deviation between the real target state and the measurement data pair under long-range and low-precision conditions, this application directly uses the predicted measurement and actual measurement data pairs for association, and adds a Doppler frequency correlation regularization term to the association gate. Simulation results in various scenarios show that, compared with NNDA and GNNDA, the proposed association algorithm improves the tracking accuracy by 1.38%–6.97% and 0.64%–3.28%, respectively, demonstrating better association tracking performance. The bistatic multi-target tracking method proposed in this application is studied in a clutter-free environment; further in-depth research on multi-target tracking methods in cluttered environments is possible in the future.

[0153] This application also provides a positioning system, including at least two sensors, a memory, a processor, and a computer program stored in the memory and running on the processor;

[0154] The sensor is used to track and measure the target;

[0155] When the processor executes the computer program, it implements the various steps in the multi-target tracking method described above.

[0156] This application also provides a readable storage medium storing a computer program thereon, characterized in that, when the computer program is executed by a processor, it implements the various steps of the multi-target tracking method described above.

[0157] In the several embodiments provided in this application, it should be understood that the disclosed methods and systems can be implemented in other ways. For example, the system embodiments described above are merely illustrative; for instance, the division of modules is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple modules or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between systems or modules may be electrical, mechanical, or other forms.

[0158] The modules described as separate components may or may not be physically separate. The components shown as modules may or may not be physical modules; that is, they may be located in one place or distributed across multiple network modules. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs.

[0159] Furthermore, the functional modules in the various embodiments of this application can be integrated into one processing module, or each module can exist physically separately, or two or more modules can be integrated into one module. The integrated modules described above can be implemented in hardware or as software functional modules.

[0160] If the integrated module is implemented as a software functional module and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0161] It should be noted that, for the sake of simplicity, the foregoing method embodiments are all described as a series of actions. However, those skilled in the art should understand that this application is not limited to the described order of actions, as some steps may be performed in other orders or simultaneously according to this application. Furthermore, those skilled in the art should also understand that the embodiments described in the specification are preferred embodiments, and the actions and modules involved are not necessarily essential to this application.

[0162] In the above embodiments, the descriptions of each embodiment have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0163] The above is a description of a multi-target tracking method and system provided in this application. For those skilled in the art, based on the ideas of the embodiments of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A multi-target tracking method, characterized in that, The multi-target tracking method is applied to a positioning system, which includes at least two sensors for tracking and measuring targets. The multi-target tracking method includes: Acquire measurement data of each sensor for the target to be tracked to obtain a first set of measurement data pairs, the first set of measurement data pairs including measurement data pairs of each target to be tracked; The true target is determined from the first set of measurement data pairs based on preset constraints. The starting point of the real target's trajectory is determined based on the FCM algorithm and the measurement data of the real target; Acquire real-time measurement data of the real target from each of the sensors, and associate the real target with the real target according to the FCM algorithm to obtain the stable track of the real target; The real target is tracked based on the starting point of the flight path and the stable flight path; The step of associating the real target with the FCM algorithm and the real-time measurement data to obtain the stable track of the real target includes: Obtain the stable trajectory of the real target at the previous moment; Based on the three-dimensional fuzzy matrix in the FCM algorithm, the real-time measurement data is correlated with the stable trajectory of the previous moment to obtain the stable trajectory of the real target at the current moment. The step of associating the real-time measurement data with the stable trajectory of the previous moment based on the three-dimensional fuzzy matrix in the FCM algorithm to obtain the stable trajectory of the real target at the current moment includes: Obtain the associated gate size and regularization term; The three-dimensional fuzzy matrix is ​​determined based on the associated gate size and the regularization term, wherein the three-dimensional fuzzy matrix includes the membership degree between the real-time measurement data pair and the stable track at the previous moment; Obtain the target function; Based on the three-dimensional fuzzy matrix and the objective function, the stable trajectory of the real target at the current moment is determined.

2. The multi-target tracking method as described in claim 1, characterized in that, The step of determining the true target from the first set of measurement data pairs according to preset constraints includes: The first set of measurement data pairs is subjected to measurement data pair elimination according to preset constraints. The true target is determined by using the second measurement data obtained after elimination.

3. The multi-target tracking method as described in claim 2, characterized in that, The step of removing measurement data pairs from the first set of measurement data pairs according to preset constraints includes: Obtain distance range constraints; The first set of measurement data pairs is processed by removing measurement data from the distance range constraint to obtain the second set of measurement data pairs.

4. The multi-target tracking method as described in claim 3, characterized in that, The multi-target tracking method also includes: Obtain speed range constraints; Based on the speed range constraint, the second measurement data set is used to remove measurement data.

5. The multi-target tracking method as described in claim 4, characterized in that, Determining the three-dimensional fuzzy matrix based on the associated gate size and the regularization term includes: by Let the three-dimensional fuzzy matrix be represented by: ； in, Indicates the size of the associated gate. This represents the regular expression term. ,in This represents the intensity coefficient of the regularization term. Indicates the frequency of the target radiation source. This indicates the measured Doppler frequency. Indicates the first One sensor, Indicates a pair of measurement data. Indicates measurement data pair and Predictive measurement of time The distance between them.

6. The multi-target tracking method as described in claim 5, characterized in that, Determining the stable trajectory of the real target at the current moment based on the three-dimensional fuzzy matrix and the objective function includes: by Denotes the objective function, ; The objective function is minimized using the three-dimensional fuzzy matrix to obtain the target three-dimensional fuzzy matrix; The stable trajectory of the real target at the current moment is determined based on the target's three-dimensional fuzzy matrix, the real-time measurement data, and the stable trajectory of the previous moment. express and the The degree of membership between stable tracks.

7. A positioning system, characterized in that, The positioning system includes at least two sensors, a memory, a processor, and a computer program stored in the memory and running on the processor; The sensor is used for tracking and measuring the target; When the processor executes the computer program, it implements each step of the multi-target tracking method as described in any one of claims 1 to 6.

8. A readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements each step of the multi-target tracking method as described in any one of claims 1 to 6.

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