Target tracking method based on Gaussian mixture filter under pure orientation positioning

Abstract

The invention discloses a target tracking method based on a Gaussian mixture filter under pure azimuth positioning, which comprises the following steps of: 1) carrying out spatial spectrum estimation on a received array signal through a conventional beam forming method to obtain original angle domain power distribution; 2) constructing a point spread function of an array signal, taking the original spatial spectrum as input, and adopting a Richardson-Lucy deconvolution algorithm to iteratively recover source distribution to obtain an enhanced azimuth spectrum; 3) based on the enhanced spectrum, executing single-station passive target motion analysis TMA, establishing an azimuth angle constraint relation between an observation platform and a target, and constructing a linear equation set to calculate the initial position and speed of the target; 4, in the target tracking process, a Gaussian mixture filter GMF is introduced to be combined with an extended Kalman filter EKF and a multi-interaction model IMM frame, and prediction and measurement updating are conducted on the target state.

Description

Technical Field

[0001] This invention relates to the field of underwater target tracking, specifically to a target tracking method based on Gaussian mixture filters under pure orientation localization, and more particularly to an interactive multi-model Gaussian mixture probability hypothesis density filter localization and tracking method based on deconvolution. Background Technology

[0002] Passive tracking faces challenges such as background clutter, nonlinear filtering tracking modeling, and target maneuvering. Target motion analysis based on pure azimuth information is one of the key technologies for passive tracking, and it is of great significance for long-range, precise, and covert strikes against underwater targets and experimental monitoring of underwater equipment.

[0003] Passive target tracking, also known as bearing-only target tracking (BOT) or bearing-only measurements (BOM) target tracking, is also called target motion analysis (TMA). It uses measured target bearing information to estimate the target's position, velocity, heading, and other motion elements to achieve target localization and trajectory tracking.

[0004] Compared to active tracking, the main advantage of passive tracking is its superior stealth, which enhances the survivability of the tracking system. Therefore, it was first applied in underwater warfare. Passive tracking does not require signal transmission, consumes less energy, and has been widely adopted in underwater monitoring networks. Network nodes can detect enemy aircraft targets and track their trajectories through passive detection. The main disadvantages of passive tracking are that it only provides azimuth measurements, resulting in slow convergence, poor tracking accuracy, filter instability, sensitivity to initial conditions, and unobservability. Furthermore, azimuth measurements in polar coordinates cannot be directly converted to position measurements in rectangular coordinates. Therefore, passive tracking systems are nonlinear systems and cannot use linear Kalman filters; instead, they must be processed using nonlinear filters such as the Extended Kalman Filter (EKF) and the Unscented Kalman Filter (UKF).

[0005] In practical applications, clutter exists due to uncertainties such as system errors, environmental interference, and false alarms. Target tracking is more universally applicable in cluttered environments. Echoes and multiple clutter measurements result in a large amount of effective measurement data entering the tracking sector, and it is impossible to determine whether the measurement data originates from the target or the clutter. These factors all increase the difficulty of target tracking.

[0006] Multi-sensor passive tracking (MST) is a method that integrates multiple sensors into a sensor network and fuses information from the azimuth measurements of each sensor to achieve collaborative tracking. This method offers high accuracy and performance and is primarily used in underwater acoustic sensor networks (UASNs) for multi-node collaborative detection and monitoring of UUVs and other underwater vehicles. With the continuous development of sensor performance, computer processing power, and underwater acoustic networks, the manufacturing cost of MST systems has been decreasing while their functionality has become increasingly powerful, leading to widespread attention and application of MST technology. Common methods for MST information fusion include multi-station direction finding, multi-station direction finding and time difference of measurement, Doppler frequency difference measurement, and phase difference time rate of change measurement. These data fusion methods obtain target position measurements and predict and estimate target states, forming a crucial foundation for MST.

[0007] This invention addresses the challenges of passive target tracking, including clutter backgrounds, nonlinear filtering tracking models, and target maneuvering. It investigates nonlinear filtering tracking technology for passive targets in cluttered environments and verifies the effectiveness and performance of passive target tracking through extensive computer simulations. Summary of the Invention

[0008] The technical problem to be solved by this invention is to provide a target tracking method based on a Gaussian mixture filter with high estimation accuracy under pure azimuth positioning, which utilizes passive target tracking technology and faces problems such as clutter background, nonlinear filtering tracking model, and target maneuvering in passive tracking.

[0009] The technical solution of this invention is as follows:

[0010] A target tracking method based on Gaussian mixture filter under pure orientation localization, the method comprising:

[0011] (1) Spatial spectrum estimation of the received array signal is performed using conventional beamforming methods to obtain the original angular domain power distribution;

[0012] (2) Construct the point spread function of the array signal, and use the original spatial spectrum as input. Use the Richardson-Lucy deconvolution algorithm to iteratively recover the source distribution to obtain the enhanced azimuth spectrum.

[0013] (3) Based on the enhanced spectrum, perform single-station passive target motion analysis (TMA), establish the azimuth constraint relationship between the observation platform and the target, and construct a system of linear equations to calculate the initial position and velocity of the target;

[0014] (4) During the target tracking process, a Gaussian mixture filter (GMF) is introduced in combination with an extended Kalman filter (EKF) and a multi-interaction model (IMM) framework to predict and update the target state, thereby achieving robust tracking under maneuvering conditions.

[0015] Preferably, step (1) specifically includes:

[0016] Assuming the signal originates from a certain direction Under the premise of matching and filtering the received data with the steering vector, a spatial power spectrum is constructed:

[0017]

[0018] in, The data covariance matrix is ​​used in practice, and sampling covariance estimation is employed.

[0019]

[0020] This represents the conjugate transpose of the guiding vector; Indicates direction The output power at that location.

[0021] Preferably, step (2) specifically includes:

[0022] The array-received data is processed using conventional beamforming methods to obtain the angular domain spatial spectrum:

[0023]

[0024] in, For the data covariance matrix, This represents the guide vector of the array. This represents the conjugate transpose of the directional vector. Indicates direction The output power at that location.

[0025] An incident signal of unit amplitude is input into the array from a specific angle, and the corresponding spatial response is calculated using the same beamforming method (such as CBF), denoted as... , as the point extension function of the system.

[0026] The initial estimate is usually set as follows:

[0027]

[0028] Given a maximum number of iterations Alternatively, under convergence conditions, perform the following update iterations:

[0029]

[0030] During the iteration process, strategies such as regularization, constraint window, and minimum value limiting can be added to control stability and convergence speed.

[0031] After the iteration is completed, This refers to the spatial spectrum after deconvolution enhancement, which can be used for target orientation estimation or plotting.

[0032] Preferably, step (3) specifically includes:

[0033] The location of the target can be determined through the observation platform.

[0034] The target angle is:

[0035]

[0036] make for The location of the target at any time The initial position of the target. The velocity of the target along two axes, The location of the observer can be used to determine the location of the target: .

[0037]

[0038] In the formula, for The distance from the target to the observation platform at any given time.

[0039] Multiply the expressions by respectively Subtracting them again, we get:

[0040]

[0041] According to the formula For the quantity obtained by measurement, For known quantities, we also need These four unknowns require four equations to solve, which means four sets of measurement data are needed to solve these equations.

[0042] According to the observability requirement of the TMA algorithm, the order of motion of the observer must be higher than that of the target; only in this way can a unique solution for the target's motion state be obtained. Assuming the target maintains uniform linear motion, the simplest way to satisfy observability is to rotate the observation platform once. Two observation points are taken before and after the rotation, and the four sets of measurement data are substituted into the equations to obtain the following system of equations.

[0043]

[0044] The initial position and velocity of the target can be obtained by using a system of four linear equations in four variables.

[0045] Preferably, step (4) specifically includes:

[0046] 1) Initialization: , , , , , .

[0047] 2) Hybrid Interaction and Particle Prediction: Based on

[0048]

[0049] The GM particles from different models are copied to each model, where the weights are multiplied by the model transition probabilities. Then, each model predicts the GM particles according to its own state transition matrix and process noise covariance.

[0050] 3) Measurement update: This includes missed detection correction and measurement update. Missed detection correction uses the missed detection probability. Multiplying by the predicted density, the measurement update uses the measurements to update the particle weights, mean, and covariance; when the measurement set for the current time step is obtained... Then, each of these measurements (Including azimuth and elevation angles) may originate from the target or from a false alarm, and If contamination is missed during detection, the predicted density can be corrected according to the following formula.

[0051]

[0052] The first part of the above formula corrects for missed detections, and the second part updates the measurements. Among them, This measures the probability of a false alarm, while the updated particle weights, mean, and covariance are respectively...

[0053]

[0054]

[0055]

[0056] Wherein, the gain matrix and the approximate measurement matrix are respectively

[0057]

[0058]

[0059] 4) Particle pruning: Remove GM particles with excessively low weights;

[0060] Particles merged in pairs: According to the formula Find the particle mean vector According to the formula Find the particle covariance matrix ;

[0061] Hybrid particles: This involves placing the GM particles from each model together. Alternatively, the model probability can be calculated by summing the particle weights of each model.

[0062] 5) State extraction: Select the GM particle with the largest weight as the state estimate. , ;

[0063] 6) (Transfer to 2).

[0064] A computer product includes computer program instructions that, when executed by a processor, implement the steps of a target tracking method based on a Gaussian mixture filter under pure orientation localization as described in this invention.

[0065] The beneficial effects of this invention are:

[0066] Passive target tracking based on pure azimuth information offers excellent concealment and is a key technology for aircraft command centers to engage subordinate targets at long range, with precision and stealth. Furthermore, in underwater equipment range testing, passive tracking can accurately measure the trajectory of underwater equipment moving over a wide area, making it an important means of monitoring underwater equipment experiments. In underwater monitoring networks, passive tracking does not require signal transmission, consumes little energy, and has strong monitoring capabilities, making it suitable for widespread application. This invention addresses the challenges of passive tracking, such as clutter backgrounds, nonlinear filtering tracking models, and target maneuvering. By introducing a Gaussian mixture filter (GMF) combined with an extended Kalman filter (EKF) and an multiple interaction model (IMM) framework, it predicts and updates the target state, achieving robust tracking under maneuvering conditions. Attached Figure Description

[0067] Figure 1 A schematic diagram showing the positions of the observation platform and the target.

[0068] Figure 2 A flowchart of the method of the present invention.

[0069] Figure 3 A diagram illustrating the correlation of probability data.

[0070] Figure 4 The Markov chain transition diagram of the model.

[0071] Figure 5 Azimuth spectrum estimation of different algorithms under a signal-to-noise ratio of -5dB

[0072] Figure 6 RMSE plots of different algorithms as a function of signal-to-noise ratio

[0073] Figure 7 Initial position error diagram as a function of azimuth measurement error

[0074] Figures 8-12 Simulation diagram of platform tracking of a target moving at a constant speed, wherein:

[0075] Figure 8 The trajectory of the platform and the target;

[0076] Figure 9 Tracking trajectory with a noise standard deviation of 0.1°;

[0077] Figure 10 The root mean square error of position estimation when the noise standard deviation is 0.1°;

[0078] Figure 11 Tracking trajectory with a noise standard deviation of 1°;

[0079] Figure 12 The root mean square error of position estimation when the noise standard deviation is 1°.

[0080] Figures 13-17 Simulation diagram of target tracking with platform moving at constant speed and turning left, where:

[0081] Figure 13 The trajectory of the platform and the target;

[0082] Figure 14 Tracking trajectory with a noise standard deviation of 0.1°;

[0083] Figure 15 The root mean square error of position estimation when the noise standard deviation is 0.1°;

[0084] Figure 16 Tracking trajectory with a noise standard deviation of 1°;

[0085] Figure 17 The root mean square error of position estimation when the noise standard deviation is 1°.

[0086] Figures 18-22 Simulation diagram of target tracking with platform at constant speed and S-shaped trajectory, wherein:

[0087] Figure 18 The trajectory of the platform and the target;

[0088] Figure 19 Tracking trajectory with a noise standard deviation of 0.1°;

[0089] Figure 20 The root mean square error of position estimation when the noise standard deviation is 0.1°;

[0090] Figure 21 Tracking trajectory with a noise standard deviation of 1°;

[0091] Figure 22 The root mean square error of position estimation when the noise standard deviation is 1°. Detailed Implementation

[0092] I. Direction Estimation Methods

[0093] Conventional beamforming (CBF) is a traditional and widely used spatial filtering technique, often used to estimate the location of sound or electromagnetic sources. Its core idea is to achieve spatial filtering in a specific direction by weighting and summing array signals, thereby enhancing the target signal and suppressing interference noise. This method is simple in structure, computationally inexpensive, and suitable for real-time processing scenarios, thus finding widespread application in engineering practice.

[0094] 1. Signal Model

[0095] Consider a An array composed of 1000 array elements receives signals from the direction. The narrowband signal received by the array can be represented as:

[0096]

[0097] in, The data vector received by the array; For direction The array guide vector; As an additive noise term, it is usually modeled as zero-mean white noise.

[0098] 2. Spatial Spectrum Estimation

[0099] The core idea of ​​conventional beamforming is: assuming the signal comes from the direction... Under the premise of matching and filtering the received data with the steering vector, a spatial power spectrum is constructed:

[0100]

[0101] in, The data covariance matrix is ​​used in practice, and sampling covariance estimation is employed.

[0102]

[0103] This represents the conjugate transpose of the guiding vector; Indicates direction The output power at that location.

[0104] 3. Azimuth scanning and estimation

[0105] To estimate the direction of the signal source, the CBF method typically uses an angular range. Perform a scan to find the output power spectrum. Peak value:

[0106]

[0107] The direction corresponding to this angle is the estimated direction of the signal source.

[0108] Deconvolution Beamforming Method Based on Richardson–Lucy Algorithm

[0109] In the field of array signal processing, conventional beamforming (CBF), while simple to implement, suffers from main lobe broadening and high side lobes in its spatial spectrum, resulting in low angular resolution and difficulty in meeting the requirements for accurate multi-target resolution. To improve the clarity of the spatial spectrum and direction estimation performance, deconvolution beamforming technology is introduced. By borrowing methods from image restoration, it effectively compresses the main lobe, suppresses side lobes, and improves angular resolution. Among these methods, the Richardson–Lucy (RL) algorithm is a classic iterative deconvolution method that has been widely used in astronomical image restoration and medical image processing, and is gradually being introduced into beamforming problems, demonstrating superior performance.

[0110] II. Deconvolution Beamforming

[0111] 1. Point extension function

[0112] In the beamforming problem, the received spatial spectrum can be regarded as the result of convolving the "true source distribution" with the "point spread function" (PSF) of the array system. The model is expressed as follows:

[0113]

[0114] in, This represents the spatial spectrum obtained through CBF or other beamforming methods; This represents the true source angular distribution function; is the point spread function, representing the array's response to a signal in a unit direction; This is for measuring the noise term.

[0115] 2. Richardson–Lucy Algorithm Principle

[0116] The Richardson–Lucy algorithm is a deconvolution method based on maximum likelihood estimation, and its iterative formula is as follows:

[0117]

[0118] in, For the first The estimation of the source distribution at the next iteration; It is a mirror image of PSF; This represents angular domain convolution; all operations are performed point-by-point and guarantee... It possesses non-negativity.

[0119] The basic logic of the algorithm is as follows: in each iteration, the deviation between the current estimate and the actual observation is used for weighted correction, continuously approaching the optimal estimate. Since this method does not require prior target estimation and has good recovery capabilities for low signal-to-noise ratio and adjacent targets, it is suitable for orientation estimation problems in complex environments.

[0120] 3. Algorithm Implementation Steps

[0121] Considering the beamforming requirements in array signal processing, the complete process of Richardson–Lucy deconvolution beamforming is as follows:

[0122] Step 1: Constructing the original spatial spectrum

[0123] The array-received data is processed using conventional beamforming methods (such as CBF or MVDR) to obtain the angular domain spatial spectrum:

[0124]

[0125] in, For the data covariance matrix, This represents the guide vector of the array. This represents the conjugate transpose of the directional vector. Indicates direction The output power at that location.

[0126] Step 2: Generate the Point Extension Function (PSF)

[0127] An incident signal of unit amplitude is input into the array from a specific angle, and the corresponding spatial response is calculated using the same beamforming method (such as CBF), denoted as... , as the point extension function of the system.

[0128] Step 3: Initialize the estimation

[0129] The initial estimate is usually set as follows:

[0130]

[0131] Step 4: Perform RL iteration

[0132] Given a maximum number of iterations Alternatively, under convergence conditions, perform the following update iterations:

[0133]

[0134] During the iteration process, strategies such as regularization, constraint window, and minimum value limiting can be added to control stability and convergence speed.

[0135] Step 5: Output Enhanced Spectrum

[0136] After the iteration is completed, This refers to the spatial spectrum after deconvolution enhancement, which can be used for target orientation estimation or plotting.

[0137] III. Positioning Principle

[0138] For an underwater target moving at a constant velocity in a straight line, when the observation platform measures the target's orientation, the relative position is as follows: Figure 1 As shown in the figure. The target location point... for Location of the observation platform for The location of the target can be determined through the observation platform.

[0139] The target angle is:

[0140]

[0141] make for The location of the target at any time The initial position of the target. The velocity of the target along two axes, The location of the observer can be used to determine the location of the target: .

[0142]

[0143] In the formula, for The distance from the target to the observation platform at any given time.

[0144] Multiply the expressions by respectively Subtracting them again, we get:

[0145] According to the formula For the quantity obtained by measurement, For known quantities, we also need These four unknowns require four equations to solve, which means four sets of measurement data are needed to solve these equations.

[0146] According to the observability requirement of the TMA algorithm, the order of motion of the observer must be higher than that of the target; only in this way can a unique solution for the target's motion state be obtained. Assuming the target maintains uniform linear motion, the simplest way to satisfy observability is to rotate the observation platform once. Two observation points are taken before and after the rotation, and the four sets of measurement data are substituted into the equations to obtain the following set of equations.

[0147]

[0148] The initial position and velocity of the target can be obtained by using a system of four linear equations in four variables.

[0149] IV. Maneuvering Target Tracking Method Based on Gaussian Mixture Filter and Extended Kalman Filter

[0150] Probabilistic Data Association (PDA) primarily addresses target tracking in cluttered environments. Its basic idea is that every measurement could originate from a target or a false alarm, only with varying probabilities of originating from the target. For any given measurement, the smaller the distance to a predicted state of a target, the higher the probability of it originating from that target, and vice versa. Typically, a Gaussian likelihood function is used to represent the correct probability of originating from the target. Updating the predicted state of the target with different measurements yields a state estimate, each with a different probability of correctness; this probability of correctness is the measurement's probability of correctness. By weighting and summing the correct probabilities of the measurements across the various state estimates, the final state estimate of the target is obtained.

[0151] A diagram illustrating the correlation of probability data is shown below. Figure 3 As shown in the diagram. White circles represent state estimates, red circles represent predicted states, and blue squares represent measurements. Measurements Predicted state of distance to target Recently, therefore The correct probability Maximum, measurement Predicted state of distance to target The farthest, therefore The correct probability Minimum. Correct for every measurement. Update, then use probability By performing a weighted summation of the updated results, the state estimate of the target can be obtained. .

[0152] Interactive multiple models (IMMs) are a set of models that use Markov processes to describe the transformations between them, and can be applied to many practical problems. It has been proven that, in generalized pseudo-Bayesian (GPB) maneuvering target tracking algorithms, IMM algorithms offer the best performance under comparable computational requirements, making them a mainstream research direction in this field.

[0153] The IMM model set has the following assumptions:

[0154] (1) The number of models in the model set is finite, and the parameters of each model are known. The model is represented as follows: , This represents the total number of models.

[0155] (2) The transition between models is a transition probability of The Markov process. The Markov transition probability is... It represents the transition probability of model i at time k to model j at time (k+1) when there is no external measurement information, or the probability of model j appearing at time (k+1).

[0156] The Markov chain transition graph when the model set M contains only two models is shown below. Figure 4 As shown in the figure, and These are models and The probability of no transfer. and These are models and The probability of mutual transition. The transition probability between models after obtaining measurement information is the same as the transition probability without external measurement information. and measurement set The maximum posterior probability.

[0157] The Gaussian Mixture Filter (GMF) uses a Gaussian mixture model to represent the Markov transition density and likelihood function in a Bayesian recursive filter, and is a generalization of the Kalman filter. A Gaussian mixture model is a form of probability distribution that uses a linear combination of multiple Gaussian distributions to express a more complex non-Gaussian probability distribution. The GMF expresses the target state density as a weighted sum of multiple Gaussian functions; the weights, mean, and covariance of a set of Gaussian functions are collectively referred to as a GM particle.

[0158] GMF assumes that the Markov transition density and likelihood function are non-Gaussian, but this non-Gaussian density can be approximated by a weighted sum of the following Gaussian densities (also known as the Gaussian mixture density):

[0159]

[0160]

[0161] In the formula, and It is a weight, and satisfies ; . , It is the number of Gaussian components.

[0162] If known The posterior distribution of the target state at time t is

[0163]

[0164] In the formula, It's weight. and These are the mean and covariance of the Gaussian distribution, respectively. Therefore, according to the Bayesian prediction equation, the one-step state prediction can be expressed as...

[0165]

[0166] According to Gauss's identity:

[0167]

[0168] in, , They are respectively and A positive definite matrix, for The matrix; and , . We can obtain

[0169]

[0170] in, This is the prediction formula for the covariance matrix. The remaining parameters are... , .therefore, It also follows a Gaussian mixture distribution, which is denoted as...

[0171]

[0172] in, , , , , , .

[0173] Obtain measurement Afterwards, the posterior PDF of the target state is

[0174]

[0175] Then, by Gauss's identity, we can obtain

[0176]

[0177] In the formula, , It is the update formula for the covariance matrix. This is the formula for updating the mean.

[0178] Obviously, It also follows a Gaussian mixture distribution, which is denoted as...

[0179]

[0180] In the formula, , , And the weight update formula is

[0181]

[0182] Clearly, the posterior distribution The number of Gaussian terms increases combinatorially over time. To facilitate calculation, various techniques must be used to remove low-weight terms and merge similar terms.

[0183] In practice, observation models It is fixed, and at this point, the measurement spontaneous function can be written as: .

[0184] The steps of the IMM-EKF-GMF algorithm are given below.

[0185] Suppose that the target posterior density at the previous time step n can be expressed as:

[0186]

[0187] In the formula, , and Let be the weight, mean, and covariance of the i-th GM particle, respectively; It represents the total number of GM particles under model assumption n.

[0188] If the model space consists of N models, according to the first-order Markov process, the prediction density under each model assumption is:

[0189]

[0190] In the formula, It is the transition probability of the model from m to n; and These are the state transition matrix and the associated process noise covariance under model assumption m, respectively.

[0191] The predicted density is uniformly rewritten as

[0192]

[0193] Among them, the number of GM particles , .

[0194] When the measurement set at the current moment is obtained Then, each of these measurements (Including azimuth and elevation angles) may originate from the target or from a false alarm, and If contamination is missed during detection, the predicted density can be corrected according to the following formula.

[0195]

[0196] The first part of the above formula corrects for missed detections, and the second part updates the measurements. Among them, This measures the probability of a false alarm, while the updated particle weights, mean, and covariance are respectively...

[0197]

[0198]

[0199]

[0200] Wherein, the gain matrix and the approximate measurement matrix are respectively

[0201]

[0202]

[0203] Rewrite the updated target state density as follows:

[0204]

[0205] Due to random false alarms and missed detections, the updated density contains GM particles with excessively low weights and GM particles that are close together. To reduce computational cost, particles with weights below a preset threshold should be removed. Particles that satisfy the following formula...

[0206]

[0207] They should be merged into one, and the merging formula is:

[0208]

[0209]

[0210]

[0211] After pruning and merging, the posterior density under model assumption n is still denoted as... .

[0212] When tracking a maneuvering target whose state model changes, the GM particle with the highest weight is selected as the state estimate. When tracking a maneuvering target with a complex combined state model, the GM particle weights of each model are used as the state estimate. Calculate the proportion of each model Target state estimation for each model and target state estimation The calculation formula is:

[0213]

[0214] The effects of the present invention will be further described below with reference to simulation examples:

[0215] 1) Target initial position estimation

[0216] The initial target position is (2746m, 3394m), and the initial platform position is (0m, 0m). The signal model is set as a linear frequency modulated signal with a start frequency of 20kHz, an end frequency of 30kHz, a pulse width of 50ms, 17 array elements, 500 snapshots, and an element spacing of half a wavelength. Azimuth angle estimation is performed using CBF, MVDR, and deconvolution beamforming. The simulation results are shown in the figure, including azimuth spectrum estimation of different algorithms under a signal-to-noise ratio of -5dB, RMSE plots of different algorithms as a function of signal-to-noise ratio, and initial position error plots as a function of azimuth measurement error.

[0217] 2) Tracking of targets moving at a constant speed on the platform

[0218] The initial target position is (2746m, 3394m), and the initial platform position is (0m, 0m). Both the target and platform move at a constant velocity in a straight line. Considering standard deviations of 0.1° and 1° for angle measurements, and with a signal-to-noise ratio of -5dB, after obtaining the initial state through pure azimuth target analysis, the moving platform uses PDA-EKF, PDA-UKF, IMM-UKF-GMF, and IMM-EKF-GMF to track the target for 600 seconds. Simulation results are as follows. Figures 5-9 As shown, this includes the target tracking trajectory and position estimation error.

[0219] 3) Target tracking with platform moving at a constant speed and turning left

[0220] The initial target position is (2746m, 3394m), and the initial platform position is (0m, 0m). The target moves at a constant velocity in a straight line, and the platform then performs a left turn maneuver. Considering the standard deviations of angle measurements are 0.1° and 1°, and under a signal-to-noise ratio of -5dB, after obtaining the initial state of the target through pure azimuth target analysis, the motion platform's PDA-EKF, PDA-UKF, IMM-UKF-GMF, and IMM-EKF-GMF are used to track the target for 600 seconds. The simulation results are as follows. Figures 10-14 As shown, this includes the target tracking trajectory and position estimation error.

[0221] 4) Target tracking with platform at constant speed and S-shaped trajectory

[0222] The initial target position is (2746m, 3394m), and the initial platform position is (0m, 0m). The target moves in uniform linear motion, and the platform performs a right turn followed by a left turn after the uniform linear motion. Considering the standard deviations of angle measurements are 0.1° and 1° respectively, and under a signal-to-noise ratio of -5dB, after obtaining the initial state of the target through pure azimuth target analysis, the motion platform's PDA-EKF, PDA-UKF, IMM-UKF-GMF, and IMM-EKF-GMF are used to track the target for 600 seconds. The simulation results are as follows. Figures 15-19 As shown, this includes the target tracking trajectory and position estimation error.

[0223] 5) Simulation results show that in cluttered scenarios, the PDA-EKF, PDA-UKF, IMM-UKF-GMF, and IMM-EKF-GMF passive tracking algorithms can correctly track targets using only angle measurements and provide target motion analysis results. These target motion analysis results will provide a basis for target identification and threat assessment.

Claims

1. A target tracking method based on a Gaussian mixture filter under pure orientation localization, characterized in that, The method includes: (1) Spatial spectrum estimation of the received array signal is performed using conventional beamforming methods to obtain the original angular domain power distribution; (2) Construct the point spread function of the array signal, and use the original spatial spectrum as input. Use the Richardson-Lucy deconvolution algorithm to iteratively recover the source distribution to obtain the enhanced azimuth spectrum. (3) Based on the enhanced spectrum, perform single-station passive target motion analysis (TMA), establish the azimuth constraint relationship between the observation platform and the target, and construct a linear equation system to calculate the initial position and velocity of the target; (4) During the target tracking process, a Gaussian mixture filter (GMF) is introduced in combination with an extended Kalman filter (EKF) and a multi-interaction model (IMM) framework to predict and update the target state, thereby achieving robust tracking under maneuvering conditions.

2. The method according to claim 1, characterized in that, The specific steps (1) are as follows: Assuming the signal originates from a certain direction Under the premise of matching and filtering the received data with the steering vector, a spatial power spectrum is constructed: ； in, For the data covariance matrix, This represents the conjugate transpose of the directional vector. Indicates direction The output power at that location.

3. The method according to claim 1, characterized in that, Step (2) specifically involves: (2.1) The array received data is processed using conventional beamforming methods to obtain the angular domain spatial spectrum: ； in, For the data covariance matrix, This represents the guide vector of the array. This represents the conjugate transpose of the directional vector. Indicates direction Output power at the location; (2.2) Using a unit amplitude incident signal input to the array from a specific angle, the corresponding spatial response is calculated using the same beamforming method. As a point spread function of the system: Set initial estimate ; Given a maximum number of iterations Alternatively, under convergence conditions, perform the following update iterations: ； After the iteration is completed, This refers to the spatial spectrum after deconvolution enhancement, which is used for target orientation estimation or plotting.

4. The method according to claim 1, characterized in that, Step (3) specifically involves: (3.1) The target's azimuth was measured by the observation platform, and the target's angle was: ； make for The location of the target at any time The initial position of the target. The velocity of the target along two axes, The position of the observer is used to obtain the target position expression: ； ； In the formula, for The distance from the target to the observation platform at any given time; (3.2) Multiply the target position expression by... Subtracting them again, we get: ； In the formula For the quantity obtained by measurement, Given the initial position and velocity of the target. It was obtained through calculation.

5. The method according to claim 1, characterized in that, Step (4) specifically involves: (4.1) Initialization: , , , , , ; (4.2) Hybrid Interactions and Particle Prediction: Based on ； The GM particles under different models are copied to each model, where the weights are multiplied by the model transition probabilities, and then each model predicts the GM particles according to its own state transition matrix and process noise covariance. (4.3) Measurement update: This includes missed detection correction and measurement update. Missed detection correction uses the missed detection probability. Multiplying by the predicted density, the measurement update uses the measurements to update the particle weights, mean, and covariance; when the measurement set for the current time step is obtained... Then, each of these measurements The predicted density is corrected according to the following formula: ； in, This measures the probability of a false alarm, and the updated particle weights, mean, and covariance are as follows: ； ； ； The gain matrix and the approximate measurement matrix are as follows: ； ； (4.4) Particle pruning: Remove GM particles with too small a weight, including merging particles and mixed particles; (4.5) State extraction: Select the GM particle with the largest weight as the state estimate. , ; (4.6) Proceed to step (4.2).

6. The method according to claim 2, characterized in that, The data covariance matrix is ​​estimated using the sampling covariance: 。 7. The method according to claim 3, characterized in that, In step (2.2), regularization, constraint window, or minimum value limit are added during the iteration process to control stability and convergence speed.

8. The method according to claim 4, characterized in that, In step (3.2), assuming the target maintains uniform linear motion, two observation points are taken before and after the observation platform turns. The four sets of measurement data are substituted into the following system of equations: ； The initial position and velocity of the target are obtained through calculation. .

9. The method according to claim 5, characterized in that, In step (4.4): The pairwise merging particles include: According to the formula Find the particle mean vector According to the formula Find the particle covariance matrix .

10. The method according to claim 5, characterized in that, In step (4.4): The hybrid particles include placing the GM particles of each model together or calculating the model probability by summing the particle weights of each model.

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