A maritime target tracking algorithm based on Gaussian mixture potential probability hypothesis density filter

Abstract

This invention provides a maritime target tracking algorithm based on a Gaussian mixture potential probability hypothesis density filter (GMDP). The algorithm addresses the performance degradation issues of the GMDP when facing low, slow, and small targets with strong clutter and complex maneuvers at sea, such as false alarms and missed detections. First, a multi-model algorithm is introduced to match various target motion states based on the GMDP. Second, a joint position-Doppler gate is established by utilizing the correlation between the target's Doppler and position measurements to jointly filter the measurement information. Finally, the target is sequentially updated based on the position update. Comparative simulation results show that the proposed algorithm can improve the stability of target number estimation and enhance tracking accuracy.

Description

Technical Field

[0001] This invention relates to a multi-target tracking technology, and more particularly to a maritime “low, slow and small” target tracking algorithm based on a Gaussian mixture potential probability hypothesis density filter. Background Technology

[0002] With the development of technology, traditional multi-target tracking (MTT) algorithms are prone to performance degradation problems such as false alarms and missed detections when dealing with "low, slow, and small" targets that fly at low altitudes, slow speeds, and have complex maneuvers at sea.

[0003] Traditional multi-target tracking algorithms, such as Multiple Hypothesis Tracking (MHT) and Joint Probabilistic Data Association (JPDA), suffer from combinatorial explosion and computational overload when dealing with a large number of targets or measurement points, making them unsuitable for task requirements. In recent years, multi-target tracking algorithms based on Random Finite Sets (RFS) have rapidly emerged. These algorithms avoid complex data association processes and have attracted significant attention from researchers in the field. Probabilistic Hypothesis Density (PHD) filters iteratively update targets by transmitting the first-order statistical moments of multiple targets, i.e., target intensity information. However, PHD filters follow a Poisson distribution, and the variance increases with a large number of targets, leading to significant fluctuations in target estimation. Potential Probabilistic Hypothesis Density (CPHD) filters, building upon PHD filters, simultaneously transmit the second-order statistical moments of multiple targets, i.e., the potential distribution of multiple targets, resulting in higher accuracy. Both algorithms have Gaussian Mixture (GM) implementations for linear conditions and Sequential Monte Carlo (SMC) implementations for nonlinear conditions, denoted as GM-PHD, SMC-PHD, GM-CPHD, and SMC-CPHD, respectively. The two algorithms have different focuses and their performance varies depending on the scenario. In the case of linear Gaussian mixtures, GM-CPHD exhibits relatively optimal performance.

[0004] Considering that "low, slow, and small" targets often perform various high-intensity maneuvers (sudden turns, acceleration, deceleration, etc.) to avoid radar system detection, and given the characteristics of strong background noise and clutter interference at sea, the existing GM-CPHD algorithm under linear conditions is easily interfered with in tracking "low, slow, and small" targets at sea, and cannot achieve effective tracking. Summary of the Invention

[0005] This invention addresses the challenges of strong clutter interference and complex maneuvering patterns of "low, slow, and small" targets in maritime target tracking environments by providing a maritime "low, slow, and small" target tracking algorithm based on a Gaussian mixture potential probability hypothesis density filter.

[0006] The objective of this invention is achieved as follows: The steps are as follows:

[0007] Step 1: Obtain the initialization information of the multiple targets at time K-1, including the potential distribution p of the multiple targets. k-1 (n), target motion model r, multi-objective posterior strength function v of the model k-1 (x,r=q), Model transition probability matrix H pq Parameters, where p and q represent two different models in the set of motion models;

[0008] Step 2: Predict the state information of multiple targets at the next time step. The prediction information includes the potential distribution prediction p of surviving targets and newly formed targets. k / k-1 (n), intensity function prediction v k / k-1 (x,r=q);

[0009] Step 3: Use location-Doppler information combined with gate filtering to select the measurement set Z at time K. k Measurement z in k ;

[0010] Step 4: Update the state information of the multi-objective targets at the next time step. The updated information includes the potential distribution p of the multi-objective targets. k (n) and intensity function v k (x,r=q), where the mean and covariance of the multi-target Gaussian components in the intensity function are obtained by updating the target's position measurement;

[0011] Step 5: Perform sequential updates based on the Doppler measurements of the target to obtain the final state update result. and the corresponding weights

[0012] Step 6: Prune and merge the Gaussian components of the target;

[0013] Step 7: Extract the multi-target state at time K.

[0014] Furthermore, the initialization information for the multiple targets at time K-1 in step 1 includes the following parameters: the multi-target potential distribution p k-1 (n), Multi-objective posterior strength function v k-1 (x,r=q), Newborn target intensity function γ k (x, r = q); the set of target motion models M, and the state transition model x of model r in the set. k =f k|k-1 (x k-1 ,r k )+w k-1 (r k Measurement model z k =h k (x k ,rk )+v k (r k Model transition probability matrix H pq Target detection probability P D,k Survival probability P S,k The number of maximum Gaussian components J max Pruning threshold T, merging threshold U;

[0015] Furthermore, the calculation formulas for the potential distribution prediction and intensity function prediction of the multi-objective next time step in step 2 are as follows:

[0016]

[0017]

[0018] In the formula, p Γ,k (n) represents the potential distribution of the target number of newborns. During computation, the transitions between models follow the Markov model transition probability matrix H. pq The probability hypothesis density γ of new targets k (x, r = q) is also in Gaussian form:

[0019]

[0020] The number of Gaussian components of the new target in the formula is J. γ,k Weight mean covariance matrix All of these are derived from prior information.

[0021] Furthermore, the position-Doppler information dual-correlation gate constructed in step 3, the gate center Predicting from the target's location information Doppler velocity prediction Jointly determined:

[0022]

[0023] With the introduction of target Doppler information, the dimension n of the target observation vector is increased. z =3, the volume of the gate is obtained by the following formula:

[0024] V k+1 =(4π / 3)γ 3 / 2 |S k+1 | 1 / 2

[0025] In the formula, γ is the discrimination threshold of the gate, derived from χ 2 The distribution table is based on the probability P of falling into the gate. G Obtain, S k+1The covariance of the target measurement residual (news).

[0026] Then, at time k, the sensor obtains a measurement set Z containing clutter and target information. k The position-Doppler information dual-correlation gate was used to filter the measurements, and the candidate echo measurements that met the criteria were selected. k,i It should meet the following requirements:

[0027] (z k,i -z k / k-1,i ) T S -1 k (z k,i -z k / k-1,i )≤γi=1,2,...m k

[0028] In the formula m k This represents the number of measurements within the gate, i.e., the number of valid measurements.

[0029] Furthermore, in step 4, the potential distribution p of the multiple targets... k (n) and intensity function v k (x, r = q) is derived from the following formula:

[0030]

[0031]

[0032] in,

[0033]

[0034] u = 0, 1

[0035]

[0036]

[0037]

[0038]

[0039] In the formula, p c,k (n) represents the potential distribution of the clutter at time k, P D,k Z represents the detection probability of the target, and <, ·> denote the inner product operation. k Let z be the set of all measurement information of the measurement system at time k, and let z be the set Z. k One of the measurements, g k (z|x,r) is the likelihood function.

[0040] The mean and covariance of the Gaussian component in the intensity function are obtained from the target's position measurement updates. The update process follows the Kalman filtering process, and the calculation formula is as follows:

[0041]

[0042]

[0043] in,

[0044]

[0045]

[0046]

[0047] In the formula and Let be the predicted mean and covariance matrix of the j-th Gaussian component of the target at time k. Let R be the position vector of the m-th polar coordinate system observation z after unbiased transformation to the rectangular coordinate system. c,k This is the corresponding observation noise covariance matrix.

[0048] Furthermore, in step 5, the target-based Doppler measurement... Perform a sequential update to obtain the final state update result of the Gaussian component. The calculation formula is as follows:

[0049]

[0050]

[0051] in,

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[0054]

[0055]

[0056]

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[0059]

[0060]

[0061] In the formula The observation angle is the j-th valid observation.

[0062] The weights corresponding to the Gaussian components The calculation formula is as follows:

[0063]

[0064]

[0065]

[0066]

[0067] Furthermore, in step 6, when pruning and merging the Gaussian components of the target, Gaussian components with a weight lower than the preset weight T should be pruned, and Gaussian components with a weight lower than the preset merging threshold U should be merged. If the number of Gaussian components after pruning and merging is still greater than the upper limit J of Gaussian components, the pruning and merging process will be terminated. max Then select the J with the largest weight. max Gaussian components.

[0068] Furthermore, in step 7, when extracting the multi-objective state at time K, for the remaining Gaussian components after pruning and merging, only those with weights greater than the decision threshold w are extracted. th The mean of the Gaussian term = 0.5 This serves as the output value of the state at time K.

[0069] Compared with existing technologies, the beneficial effects of this invention are as follows: The algorithm of this invention introduces a multi-model algorithm on the basis of the GM-CPHD filter to match various motion states of the target. It utilizes the correlation between the target's Doppler measurements and position measurements to establish a joint position-Doppler gate, jointly filtering the measurement information, and sequentially updating the target based on the position update. Compared with the traditional GM-CPHD filter that only introduces a multi-model algorithm, the algorithm proposed in this invention can improve the stability of target number estimation and improve tracking accuracy. Attached Figure Description

[0070] Figure 1 A flowchart of an overall algorithm for tracking "low, slow and small" targets at sea based on a Gaussian mixture potential probability hypothesis density filter provided by the present invention;

[0071] Figure 2 This is a real trajectory diagram of multiple targets in an embodiment of the present invention;

[0072] Figure 3 This is a diagram illustrating the multi-target tracking effect in an embodiment of the present invention.

[0073] Figure 4 This is a comparison chart of the tracking errors of the algorithm of the present invention and the traditional GM-CPHD algorithm with multiple models in 50 Monte Carlo experiments in an embodiment of the present invention;

[0074] Figure 5 This is a comparison chart of the standard deviations of the algorithm of the present invention and the traditional GM-CPHD algorithm with multiple models in 50 Monte Carlo experiments in an embodiment of the present invention. Detailed Implementation

[0075] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0076] Figure 1 A flowchart of an overall algorithm for tracking "low, slow, and small" maritime targets based on a Gaussian mixture potential probability hypothesis density filter, provided by this invention, is shown below. Figure 1 The algorithm shown includes:

[0077] Step 1: Obtain the initialization information of the multiple targets at time K-1. The information parameters include the potential distribution p of the multiple targets. k-1 (n), Multi-objective posterior strength function v k-1 (x,r=q), Newborn target intensity function γ k (x, r = q); the set of target motion models M, and the state transition model x of model r in the set. k =f k|k-1 (x k-1 ,r k )+w k-1 (r k Measurement model z k =h k (x k ,r k )+v k (r k Model transition probability matrix H pq Target detection probability P D,k Survival probability P S,k The number of maximum Gaussian components J max Pruning threshold T, merging threshold U;

[0078] Step 2: Predict the state information of multiple targets at the next time step. The prediction information includes the potential distribution prediction p of surviving targets and newly formed targets. k / k-1 (n), intensity function prediction v k / k-1 (x, r = q), the formulas for potential distribution prediction and intensity function prediction are as follows:

[0079]

[0080]

[0081] In the formula, p Γ,k (n) represents the potential distribution of the target number of newborns. During computation, the transitions between models follow the Markov model transition probability matrix H. pq The probability hypothesis density γ of new targets k (x, r = q) is also in Gaussian form:

[0082]

[0083] The number, weight, mean, and covariance of the new target Gaussian components in the formula are all obtained from prior information.

[0084] Step 3: Use location-Doppler information combined with gate filtering to select the measurement set Z at time K. k Measurement z in k First, a dual-correlation gate for the location-Doppler information of multiple targets is constructed, with the gate center... Predicting from the target's location information Doppler velocity prediction Jointly determined:

[0085]

[0086] With the introduction of target Doppler information, the dimension n of the target observation vector is increased. z =3, the volume of the gate is obtained by the following formula:

[0087] V k+1 =(4π / 3)γ 3 / 2 |S k+1 | 1 / 2

[0088] In the formula, γ is the discrimination threshold of the gate, derived from χ 2 The distribution table is based on the probability P of falling into the gate. G Obtain, S k+1 The covariance of the target measurement residual (news).

[0089] Then, at time k, the sensor obtains a measurement set Z containing clutter and target information. k The position-Doppler information dual-correlation gate was used to filter the measurements, and the candidate echo measurements that met the criteria were selected. k,i It should meet the following requirements:

[0090] (z k,i -z k / k-1,i ) T S -1 k (z k,i -z k / k-1,i )≤γi=1,2,...m k

[0091] In the formula m k This represents the number of measurements within the gate, i.e., the number of valid measurements.

[0092] Step 4: Potential distribution p of multiple objectives k (n) and intensity function v k (x, r = q) is derived from the following formula:

[0093]

[0094]

[0095] in,

[0096]

[0097] u = 0, 1

[0098]

[0099]

[0100]

[0101]

[0102] In the formula, p c,k (n) represents the potential distribution of the clutter at time k, P D,k Z represents the detection probability of the target, and <, ·> denote the inner product operation. k Let z be the set of all measurement information of the measurement system at time k, and let z be the set Z. k One of the measurements, g k (z|x,r) is the likelihood function.

[0103] The mean and covariance of the Gaussian component in the intensity function are obtained from the target's position measurement updates. The update process follows the Kalman filtering process, and the calculation formula is as follows:

[0104]

[0105]

[0106] in,

[0107]

[0108]

[0109]

[0110] In the formula and Let be the predicted mean and covariance matrix of the j-th Gaussian component of the target at time k. Let R be the position vector of the m-th polar coordinate system observation z after unbiased transformation to the rectangular coordinate system. c,k This is the corresponding observation noise covariance matrix.

[0111] Step 5: Target-based Doppler measurement Perform a sequential update to obtain the final state update result. The calculation formula is as follows:

[0112]

[0113]

[0114] in,

[0115]

[0116]

[0117]

[0118]

[0119]

[0120]

[0121]

[0122]

[0123]

[0124] The weights corresponding to the Gaussian components The calculation formula is as follows:

[0125]

[0126]

[0127]

[0128]

[0129] Step 6: Prune and merge the Gaussian components of the target. Prune Gaussian components with a weight lower than the preset weight T, and merge Gaussian components with a weight lower than the preset merging threshold U. If the number of Gaussian components after pruning and merging is still greater than the upper limit J of Gaussian components, the pruning and merging process will be terminated. maxThen select the J with the largest weight. max One Gaussian component;

[0130] Step 7: Extract the multi-objective state at time K. For the remaining Gaussian components after pruning and merging, only extract the components with weights greater than the decision threshold w. th The mean of the Gaussian term = 0.5 This serves as the output value of the state at time K.

[0131] The effects of this invention can be further illustrated by the following simulation experiments:

[0132] Simulation experiment parameter settings:

[0133] The sensor monitoring area is defined as a two-dimensional plane of [-1000, 1000] x [-1000, 1000]. The sensor simultaneously tracks 9 targets within the area. The targets move in uniform linear motion (CV) or uniform turning motion (CT) within the monitoring area. The target motion state is described by a four-dimensional vector: In the vector x k y k Let the target be located in the coordinate system. Let be the velocity of the target in both directions of the coordinate system. Table 1 shows the birth and death times of each target, as well as its motion during its survival period.

[0134] The clutter is assumed to be uniformly distributed within the monitoring area, with a clutter intensity of λ = 1.2 × 10⁻⁶. -5 m -2 The standard deviation of process noise is σ v =0.5m / s, the standard deviation of the measured noise is σ c =10m. Because the target is "low, slow, and small," its Doppler velocity range is set to [-30m / s, 30m / s]. Target detection probability P D,k =0.98, survival probability P S,k =0.99, sampling period is 1s, target motion model set includes uniform velocity model, left turn and right turn model, the angular velocity of the target left turn / right turn is ω=(2π / 100) / s, the initial model probability of uniform velocity and turning is [0.5,0.25,0.25]. Maximum Gaussian component number J max =100, pruning threshold T = 1 × 10 -5 The merging threshold U = 5. The number of newly generated targets at any given time is 4. The initial states of newly generated targets 1 through 4 are: [0; 0; 0; 0], [400; 0; -600; 0], [-800; 0; -200; 0], [-200; 0; 800; 0], respectively. The weight w of the newly generated targets... γ,k =0.03. The OSPA cutoff parameter and order parameter are set to c=100 and p=2, respectively.

[0135] Table 1

[0136]

[0137]

[0138] Figure 2 This represents the actual movement trajectories of the nine targets in this experiment within the monitoring area.

[0139] Figure 3 The figure shows the tracking effect of the algorithm of the present invention on 9 targets. As can be seen from the figure, the algorithm of the present invention can achieve effective tracking of the targets as a whole.

[0140] Figure 4 The figure shows a comparison of the tracking errors of the algorithm of this invention and the traditional GM-CPHD algorithm with multiple models in 50 Monte Carlo experiments. As can be seen from the figure, the average OSPA distance error of the algorithm of this invention is lower than that of the traditional GM-CPHD algorithm with multiple models, that is, the algorithm of this invention has higher tracking accuracy.

[0141] Figure 5 The figure shows a comparison of the stability of the algorithm of the present invention and the traditional GM-CPHD algorithm with multiple models in 50 Monte Carlo experiments in the embodiments of the present invention. As can be seen from the figure, the average standard deviation of the algorithm of the present invention is lower than that of the traditional GM-CPHD algorithm with multiple models, that is, the number estimation accuracy and stability of the algorithm of the present invention are higher.

[0142] This invention provides a tracking algorithm for low, slow, and small targets at sea based on a Gaussian mixture potential probability hypothesis density filter. Addressing the issue that current GM-CPHD algorithms often suffer from performance degradation when facing multiple low, slow, and small targets with strong clutter and complex maneuvers at sea, this invention first introduces a multi-model algorithm to match various target motion states based on the Gaussian mixture potential probability hypothesis density filter. Second, it utilizes the correlation between the target's Doppler and position measurements to establish a joint position-Doppler gate for joint filtering of measurement information. Finally, it sequentially updates the target based on position updates, significantly improving the tracking accuracy for multiple targets. The algorithm is applicable to, but not limited to, the tracking scenarios described in this embodiment, and has high application value.

[0143] In summary, this invention relates to a tracking algorithm for low, slow, and small maritime targets based on a Gaussian mixture potential probability hypothesis density filter (GMDP). The algorithm addresses the performance degradation issues, such as false alarms and missed detections, that arise with GMDP when facing low, slow, and small targets with strong clutter and complex maneuvers at sea. A solution is provided. First, a multi-model algorithm is introduced based on the GMDP to match various target motion states. Second, a joint position-Doppler gate is established using the correlation between the target's Doppler and position measurements to jointly filter the measurement information. Finally, the target is sequentially updated based on the position update. Comparative simulation results show that the proposed algorithm can improve the stability of target number estimation and enhance tracking accuracy.

Claims

1. A maritime target tracking algorithm based on a Gaussian mixture potential probability hypothesis density filter, characterized in that, The steps are as follows: Step 1: Obtain the initialization information of multiple targets at time k-1; Step 2: Predict the state information of multiple targets at the next time step. The prediction information includes the potential distribution prediction p of surviving targets and newly formed targets. k / k-1 (n), intensity function prediction v k / k-1 (x,r=q); Step 3: Use location-Doppler information combined with gate filtering to select the measurement set Z at time k. k Measurement z in k ; Constructing a location-Doppler information joint gate, gate center Predict based on target location information Doppler velocity prediction Jointly determined: With the introduction of target Doppler information, the dimension n of the target observation vector is increased. z =3, the volume of the gate is obtained by the following formula: V k+1 =(4π / 3)γ 3 / 2 |S k+1 | 1 / 2 Where γ is the discrimination threshold of the gate, derived from χ 2 The distribution table is based on the probability P of falling into the gate. G Obtain; S k+1 The covariance of the target measurement residual; At time k, a measurement set Z containing clutter and target information is obtained through the sensor. k The position-Doppler information combined with the gate was used to screen the measurements, and the candidate echo measurements that met the criteria were selected. k,i satisfy: (z k,i -z k / k-1,i ) T S -1 k (z k,i -z k / k-1,i )≤γi=1,2,...m k Where, m k This refers to the number of measurements within the gate, i.e., the number of valid measurements. Step 4: Update the state information of the multi-objective targets at the next time step. The updated information includes the potential distribution p of the multi-objective targets. k (n) and intensity function v k (x,r=q), where the mean and covariance of the multi-target Gaussian components in the intensity function are obtained by updating the target's position measurement; Step 5: Perform sequential updates based on the Doppler measurements of the target to obtain the final state update result. and the corresponding weights Step 6: Prune and merge the Gaussian components of the target; Step 7: Extract the multi-target state at time k.

2. The maritime target tracking algorithm based on a Gaussian mixture potential probability hypothesis density filter according to claim 1, characterized in that: The initialization information for the multi-target at time k-1 in step 1 includes the following parameters: multi-target potential distribution p k-1 (n), Multi-objective posterior strength function v k-1 (x,r=q), Newborn target intensity function γ k (x, r = q); the set of target motion models M, and the state transition model x of model r in the set. k =f k|k-1 (x k-1 ,r k )+w k-1 (r k Measurement model z k =h k (x k ,r k )+v k (r k Model transition probability matrix H pq Target detection probability P D,k Survival probability P S,k The number of maximum Gaussian components J max , pruning threshold T, merging threshold U, where p and q represent two different models in the motion model set.

3. The maritime target tracking algorithm based on a Gaussian mixture potential probability hypothesis density filter according to claim 2, characterized in that: The calculation formulas for the potential distribution prediction and intensity function prediction of the multi-objective next time step in step 2 are as follows: In the formula, p Γ,k (n) represents the potential distribution of the target number of newborns. During computation, the transitions between models follow the Markov model transition probability matrix H. pq The probability hypothesis density γ of new targets k (x, r = q) is also in Gaussian form: The number of Gaussian components of the new target in the formula is J. γ,k Weight mean covariance matrix All of these are derived from prior information.

4. The maritime target tracking algorithm based on a Gaussian mixture potential probability hypothesis density filter according to claim 3, characterized in that: The potential distribution p of the multiple targets in step 4 k (n) and intensity function v k (x, r = q) is derived from the following formula: in, In the formula, p c,k (n) represents the potential distribution of the clutter at time k, P D,k Z represents the detection probability of the target, where <, ·> denotes the inner product operation. k Let z be the set of all measurement information of the measurement system at time k, and let z be the set Z. k One of the measurements, g k (z|x,r) is the likelihood function. The mean and covariance of the Gaussian component in the intensity function are obtained from the target's position measurement updates. The update process follows the Kalman filtering process, and the calculation formula is as follows: in, In the formula and Let be the predicted mean and covariance matrix of the j-th Gaussian component of the target at time k. Let R be the position vector of the m-th polar coordinate system observation z after unbiased transformation to the rectangular coordinate system. c,k This is the corresponding observation noise covariance matrix.

5. The maritime target tracking algorithm based on a Gaussian mixture potential probability hypothesis density filter according to claim 4, characterized in that: Step 5 involves target-based Doppler measurement. Perform a sequential update to obtain the final state update result of the Gaussian component. The calculation formula is as follows: in, In the formula The observation angle for the j-th valid observation. The weights corresponding to the Gaussian components The calculation formula is as follows:

6. The maritime target tracking algorithm based on a Gaussian mixture potential probability hypothesis density filter according to claim 5, characterized in that: In step 6, when pruning and merging the Gaussian components of the target, Gaussian components with a weight lower than a preset weight T are pruned, and Gaussian components with a weight lower than a preset merging threshold U are merged. If the number of pruned and merged Gaussian components is greater than the upper limit J of the Gaussian components, the merging process is considered complete. max Then select the J with the largest weight. max Gaussian components.

7. The maritime target tracking algorithm based on a Gaussian mixture potential probability hypothesis density filter according to claim 6, characterized in that: When extracting the multi-objective state at time k in step 7, for the remaining Gaussian components after pruning and merging, the extracted weights are greater than the decision threshold w. th The mean of the Gaussian term = 0.5 This serves as the output value of the state at time k.

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