A trajectory phd multi-radiation source adaptive tracking method based on variational bayes

Abstract

The present application belongs to the field of communication technology, especially relates to a kind of trajectory PHD multi-radiation source adaptive tracking method based on variational bayes.The present application uses the multi-radiation source signal measurement information received by multiple sensors, uses Gaussian inverse Wishart (GIW) distribution to model the state of radiation source and noise distribution, uses variational bayes (VB) technology to filter, and the robustness of algorithm is improved.Simulation results show that the algorithm can be adaptive filtering for unknown measurement noise, and compared with the traditional method, it is more suitable for unknown time-varying measurement noise.

Description

Technical Field

[0001] This invention belongs to the field of communication technology, and in particular relates to a PHD (Plan-Do-Check-Act) adaptive tracking method for multiple radiation sources based on variational Bayesian methods. Background Technology

[0002] In recent years, radiation source detection technology has played a crucial role in military and civilian fields such as urban counter-terrorism, drone control, and missile and anti-missile systems. Currently, most radiation source tracking algorithms require prior acquisition of measurement noise parameters; however, in practical applications, accurately estimating noise distribution information is often difficult. Furthermore, the state transition process in multi-radiation source filtering typically only considers the first-order Markov process, neglecting the influence of previous moments, which may lead to poor tracking performance under low signal-to-noise ratio conditions. Therefore, research on multi-frame accumulation adaptive tracking of multi-radiation sources with unknown measurement noise is of greater significance. Under the random finite set of trajectories (RFS), the variational Bayesian (VB) method can be used to perform adaptive tracking of multi-radiation sources under a superposition model based on the trajectory probability hypothesis density (PHD). Summary of the Invention

[0003] To address the aforementioned problems, this invention proposes a variational Bayes-based PHD multi-radiation source adaptive tracking method.

[0004] The technical solution of this invention is as follows:

[0005] A variational Bayes-based adaptive tracking method for PHD trajectories from multiple radiation sources, such as... Figure 1 As shown, it includes the following steps:

[0006] S1. Define M intensity sensors that generate M values ​​at each moment. z =M-1 intensity difference measurements, where the i-th measurement generated by sensor m1 and sensor m2 at time k is

[0007] S2. Define the mixed trajectory state of radiation source state and noise distribution as follows: Where t represents the starting time of the trajectory, x 1:i Represents a time-continuous sequence of radiation source target states. This represents the sum of the noise covariance and the prediction covariance;

[0008] S3. Express the prior distribution of the trajectory PHD at time k-1 as follows:

[0009]

[0010] Suppose the distribution of the newborn trajectory PHD at time k is represented as follows:

[0011]

[0012] in This indicates that x follows a Gaussian distribution with mean m and covariance P. This indicates that R follows an inverse Wissaud distribution with degrees of freedom u and a measure matrix U;

[0013] S4, the trajectory set X of the next moment k k It is the union of the surviving trajectory set and the newborn trajectory set. Applying Mahler's general laws of motion, the predicted trajectory PHD is calculated through set integration.

[0014]

[0015] S5. Applying the Bayesian update criterion, the posterior distribution PHD at time k can be calculated as follows:

[0016]

[0017] Assuming the predicted trajectory is a PhD If it is Poisson, then the above formula can be written as

[0018]

[0019] S6. By introducing the transformation y = r(W) and using the variable transformation formula, the ensemble integral is transformed into an ordinary integral as follows:

[0020]

[0021] Applying a linear version of Campbell's theorem, Q is approximated by a Gaussian distribution. k|k-1 (y) can be obtained as follows:

[0022]

[0023] S7. Truncate the relevant lengths of the trajectory, perform pruning and merging, and extract the state;

[0024] S8. Repeat S3 to S7 to perform iterative filtering and tracking to obtain trajectory information at each time step.

[0025] The beneficial effects of this invention are as follows: This invention is a PHD (Positioning, Hierarchical, and Dynamic) adaptive tracking method for multiple radiation sources based on variational Bayesian methods. It utilizes multi-sensor signal measurement information from multiple radiation sources, models the radiation source state and noise distribution using the Gaussian Inverse Wissaud (GIW) distribution, and employs VB (Wissaud) filtering techniques to improve the algorithm's robustness. Simulation results show that this algorithm can adaptively filter for unknown measurement noise and is better suited to unknown time-varying measurement noise. Attached Figure Description

[0026] Figure 1This is a flowchart illustrating the specific process of the trajectory PHD multi-radiation source adaptive tracking method proposed in this invention.

[0027] Figure 2 This is a schematic diagram of a scene where the sensor and radiation source are moving.

[0028] Figure 3 It is the curve of the variation of the measured noise parameter in the simulation over time.

[0029] Figure 4 This is a schematic diagram illustrating the tracking effect of the VB trajectory PHD adaptive tracking algorithm.

[0030] Figure 5 This is a diagram showing the number of radiation sources estimated by the PHD tracking algorithm and the VB PHD tracking algorithm.

[0031] Figure 6 It is the OSPA distance between the PHD tracking algorithm and the VB PHD tracking algorithm. Detailed Implementation

[0032] The present invention will now be described in detail with reference to the accompanying drawings.

[0033] The specific method of this invention is as follows:

[0034] Define the i-th measurement generated by sensors m1 and m2 at time k as

[0035]

[0036] Where i is the path attenuation coefficient. v represents the distance from the m-th sensor to all historical locations of the l-th radiation source. k It is the additive noise in the measurement model at time k;

[0037] Suppose the prior distribution of the trajectory probability hypothesis density (PHD) at time k-1 is expressed as: The distribution of the newborn trajectory PHD at time k is as follows

[0038] The PHD that survives part of the trajectory at time k is

[0039]

[0040] The parameters are calculated as follows:

[0041] α j,k|k-1 =p s ·α j,k-1

[0042]

[0043] in This represents the Kronecker product.

[0044] In the update step, to maintain the consistency of the trajectory state, its posterior distribution needs to be approximated using the VB method for the next iteration. Based on the linearization assumption, the likelihood function can be expressed as...

[0045]

[0046] Assume the updated trajectory PHD is

[0047]

[0048] The VB method is used to find the parameters of the posterior approximate distribution, and the KL divergence is minimized for approximate approximation. The parameters in the above formula are calculated by performing the VB approximation at the fixed point in the nth iteration, where the formula for the nth iteration is:

[0049]

[0050] in

[0051]

[0052] make Likelihood form can be represented as

[0053]

[0054] The parameters updated after iteration are calculated as follows:

[0055] u j,k =u j,k|k-1 +1

[0056]

[0057] m j,k|k =m j,k|k-1 +K k,j (Z k -h k (m j,k|k-1 )-s k )

[0058]

[0059] in

[0060]

[0061] Before performing multi-source state extraction and noise covariance estimation, pruning and merging are necessary. Pruning involves removing terms with weights less than a pruning threshold, and then merging the pruned posterior PHD parameters. The merging principle prioritizes absorbing terms with larger weights; for example, assuming the e-th term in the formula has the largest weight, ... The process involves comparing the result with the merging threshold to determine whether to absorb the j-th item. After traversing all items, the first absorption is completed. Then, the item with the second largest weight is absorbed. This process is repeated to complete the pruning and merging steps.

[0062] As time progresses, the length of the trajectory gradually increases. Here, the L-scan approximation method is used, which only propagates the joint state density of the last L time steps and the independent density of the earlier time steps.

[0063] Simulation Examples

[0064] This example uses MATLAB to simulate and demonstrate the above-mentioned adaptive tracking method for PHD multiple radiation sources based on superposition variational Bayes.

[0065] Simulation conditions and parameters: In a two-dimensional planar scene, there are 8 intensity detection sensors distributed around the measurement area, and the dimension of the measurement vector at each time step is M. z =7; The measurement area is a square area with a side length of 1000 meters. There are 6 moving radiation sources in the tracking scene, and their trajectories are as follows... Figure 2 As shown. The path loss parameter is set to i = 3, and the reference radiation source signal strength is set to [A]. 1 ,…,A 1 [10, 12, 14, 16, 16, 14, 12, 10], in dBM. The covariance matrix of the measurement noise is set to... in It is M z An identity matrix of dimension η. The true measurement noise covariance is set to have a time-varying parameter, η. k The values ​​are as follows Figure 3 As shown. It is assumed that the motion of the radiation source target within the monitoring area follows a constant velocity model, and the sampling time T is set to 0.25 s; noise covariance... and Set the threshold to 10; set the number of iterations to 50. Use the OSPA distance (truncation value c = 40 and order p = 30) and the estimated number of radiation source targets as metrics to evaluate the algorithm's performance.

[0066] Figure 4 This is based on the multi-radiation source adaptive tracking results of the VB trajectory PHD. Figure 5 The results show the estimation of the number of radiation sources for the VB trajectory PHD adaptive tracking algorithm and the ordinary trajectory PHD tracking algorithm. Figure 6The optimal sub-pattern allocation (OSPA) distance between the VB trajectory PHD adaptive tracking algorithm and the ordinary trajectory PHD tracking algorithm.

[0067] from Figure 5 It can be seen that the VB trajectory PHD algorithm of this invention has better performance in estimating the number of radiation sources than the trajectory PHD filter with a fixed noise covariance matrix. However, when the noise covariance used by the trajectory PHD algorithm does not match the true value, it will produce a large number estimation error. Figure 6 It can be seen that when the trajectory PHD algorithm uses a fixed noise covariance, its OSPA distance is large, and the performance of the VB trajectory PHD adaptive filtering algorithm is better than that of the trajectory PHD filtering algorithm under different parameter settings. Therefore, the VB trajectory PHD algorithm proposed in this invention can perform adaptive filtering for unknown measurement noise, and is more adaptable to time-varying noise than the traditional trajectory PHD algorithm.

Claims

1. A PHD (Parametric Hierarchical Hierarchy Process) trajectory adaptive tracking method based on variational Bayesian methods, utilizing multiple sensors to measure the radiation sources, characterized in that... Includes the following steps: S1, Definition Each intensity sensor generates [data / intensity] every moment. One strength difference measurement, among which Constant by sensors and sensors The first Individual measurement ; S2. Define the mixed trajectory state of radiation source state and noise distribution as follows: ,in Indicates the starting time of the trajectory. Represents a time-continuous sequence of radiation source target states. This represents the sum of the noise covariance and the prediction covariance; S3, will The prior distribution of the probability hypothesis density of the time trajectory (PHD) is expressed as: ， definition The distribution of the newly generated trajectory PHD at time step is represented as follows: ， in express Follow the mean Covariance is Gaussian distribution, express Obeying the degree of freedom The measure matrix is The reverse distribution of Saudi Arabia; exist The PhD who survives part of the trajectory at any given time is: ， in, ， in Represents the Kronecker product; S4, Next Moment trajectory set It is the union of the surviving trajectory set and the newborn trajectory set. Applying Mahler's general laws of motion, the predicted trajectory PHD is calculated through set integration as follows: ； S5. Apply the Bayesian update criterion. The posterior distribution PHD at time t is calculated as follows: ， Setting the predicted trajectory for PhD If it is Poisson, then the above equation can be rewritten as follows: ； S6, Introduction of Transformation Using the formula for transformation of variables, the ensemble integral can be transformed into an ordinary integral as follows: ， Applying a linear version of Campbell's theorem, approximated by a Gaussian distribution. get: ； S7. Truncate the relevant lengths of the trajectory, perform pruning and merging, and extract the state; S8. Repeat S3~S7 to perform iterative filtering and tracking to obtain trajectory information at each time step.

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