Multi-target probability hypothesis density DOA tracking method under wireless sensor network

Abstract

The invention discloses a multi-target probability hypothesis density DOA tracking method under a wireless sensor network, and the method comprises the steps: receiving a non-circular signal through employing a uniform array under the wireless sensor network, and obtaining extended measurement information; secondly, state parameters of signal particles at the initial moment are set as initial distribution of signals, signal sampling particles continuously surviving at the current moment are measured, and a prediction sampling particle set is obtained based on unscented transformation; and then calculating a covariance matrix of a received signal and obtaining a noise subspace by using extended measurement information at the current moment, and updating signal prediction sampling particles at the current moment by using a PHD filter. Finally, more effective particles are found out through resampling, a new signal sampling particle set is formed, and the weighted sum of the signal sampling particle states is calculated to serve as the signal state tracked at the current moment till the end. According to the invention, the number of signals can be estimated more accurately, and the state of the signal source is tracked.

Description

Technical Field

[0001] The present invention belongs to the field of direction-of-arrival (DOA) tracking, and relates to a method for multi-target probability hypothesis density (WSN-PHD) DOA tracking in a wireless sensor network. Background Art

[0002] Currently, the tracking of moving targets in the context of wireless sensor networks has become a hot topic in intelligent Internet of Things applications and has a wide range of applications in various aspects such as illegal vehicle tracking, space exploration, and border security. The tracking of moving targets in a wireless sensor network can consist of several static or mobile nodes, which are configured with a series of sensors to track moving targets. In recent years, researchers have explored various methods in the field of multi-target tracking, such as time-of-arrival, angle-of-arrival, and received signal strength methods.

[0003] DOA tracking algorithms are divided into subspace-based and particle filter algorithms. Under the premise that the number of targets is fixed and known, the tracking performance of these two algorithms is relatively good. However, they have certain limitations. For example, in a complex wireless sensor network, when there are obstacles between the target and the network nodes (i.e., the observed number of targets changes over time), the tracking accuracy will be significantly affected. Summary of the Invention

[0004] Object of the Invention: To solve the problems existing in the prior art, the present invention proposes a multi-target probability hypothesis density DOA tracking method under a wireless sensor network. This method is implemented using sequential Monte Carlo (SMC), uses the two-dimensional multiple signal classification (MUSIC) spatial spectrum function as the likelihood function, and performs exponential weighted fusion on the likelihood functions of each node, thereby making resampling more effective and achieving precise tracking of signals. It can be applied to fields such as sonar and radar positioning. The method of the present invention proposes a random finite set (RFS) to encapsulate multi-target states and quantities, and provides a multi-target probability hypothesis density DOA tracking method under a wireless sensor network.

[0005] Technical Solution:

[0006] A multi-target probability hypothesis density DOA tracking method under a wireless sensor network includes the following steps:

[0007] S1: At time k, the p-th node under the wireless sensor network uses a uniform array to receive a non-circular signal and obtains non-circular measurement information z p (k), p = 1, …, P; using the non-circular property of the signal, the extended measurement information is obtained

[0008] S2: Predict the signal state: Set the state parameters of the signal particles at the initial moment, and use the set state parameters as the initial distribution of the signal. For the signal sampling particles at the previous moment, use the state equation to predict, obtain the signal sampling particles that continue to survive at the current moment, then merge the newly generated signal sampling particles to obtain the merged signal sampling particles. Finally, perform an unscented transform on the merged signal sampling particles to obtain the predicted sampling particle set.

[0009] S3: Utilize the extended measurement information at the current moment Calculate the covariance matrix of the received signal The calculated covariance matrix

[0010] Perform eigen decomposition to obtain the noise subspace N p,k , calculate the corresponding two-dimensional MUSIC spatial spectrum function according to the direction vector corresponding to each predicted signal sampling particle and perform exponential weighted fusion as the likelihood function of the particle; then use the PHD filter to update the signal predicted sampling particles at the current moment to obtain the updated signal sampling particles at the current moment;

[0011] S4: State extraction and number estimation: Use the resampling algorithm to find more effective particles and form a new set of signal sampling particles, then calculate the weighted sum of the states of the signal sampling particles as the signal state tracked at the current moment; in addition, for number estimation, use the k-mean algorithm to estimate the number of updated signals.

[0012] S5: Determine whether all time steps have been processed. If so, end. Otherwise, return to step S3 until the end.

[0013] The beneficial effects of the present invention are as follows:

[0014] In the present invention, the two-dimensional MUSIC spatial spectrum function is used to replace the likelihood function of the particle, and it is observed that the main lobe of the likelihood function is diffused in a low signal-to-noise ratio environment. Therefore, further exponential weighted fusion is performed on the likelihood function to generate a sharper peak, improving the particles sampled in the high likelihood region. Therefore, the present invention can more accurately estimate the number of signals and track the state of the signal source. Compared with the existing methods, the method of the present invention has higher tracking accuracy and lower OSPA error. Description of the Drawings

[0015] Figure 1 is the flowchart of the present invention;

[0016] Figure 2 is the schematic diagram of the multi-target tracking model of the distributed wireless sensor network;

[0017] Figure 3Under the conditions of a single MC experiment, the tracking trajectory diagram of 10 nodes is adopted by the method of the present invention;

[0018] Figure 4 It is the effect diagram of the estimation of the number of signal sources by the method of the present invention and other algorithms when running 100 MC experiments;

[0019] Figure 5 It is the OSPA error effect diagram of the method of the present invention and other comparison methods for tracking the signal position. Detailed implementation manners

[0020] To make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the technical solutions of the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0021] A multi-target probability hypothesis density DOA tracking method under a wireless sensor network has a process as Figure 1 shown, and the specific implementation process is as follows:

[0022] I. Uniform array receives non-circular signals

[0023] As Figure 2 shown is a schematic diagram of a multi-target tracking model of a distributed wireless sensor network that can use the present invention. Considering a distributed sensor network WSN with P nodes, whose positions are located on the roof of a low-altitude building. In this WSN, each node is configured with a uniform linear array, and the p-th node has M p array elements. Assume that during the flight of the UAV target in the low-altitude environment, both the UAV signal and the sensor array can be regarded as point masses. In the two-dimensional plane, at the k-th moment, there are Q k uncorrelated UAV transmitted signals (regarded as far-field narrowband signal sources) incident on P WSN nodes with known positions. The UAV signal positions are p q = [p q,x , p q,y T , q = 1, …, Q k , and the nodes are located at u p = [u p,x , u p,y T Then the array received signal vector of the p-th node at the k-th moment can be expressed as:

[0024]

[0025] where represents the direction matrix received by the p-th node, represents the direction vector of the q-th signal received by the p-th node, where d = λ / 2 represents the element spacing, and λ is the signal carrier wavelength. n p(k) represents the measurement noise, θ p,q is the DOA when the q-th signal arrives at the p-th node, satisfying:

[0026]

[0027] where is a real-valued signal vector, represents the q-th real signal received by the p-th node, represents a diagonal matrix containing all the non-circular phases of the signals, and diag(·) represents the diagonal operation, represents the non-circular phase of the q-th signal.

[0028] According to the non-circular characteristics of the signals, an extended received signal vector can be constructed, i.e.:

[0029]

[0030] where represents the extended direction matrix, and its q-th vector represents the extended direction vector of the q-th signal, * represents the conjugate operation.

[0031] II. Predicting the Signal State

[0032] (1) Initializing the signal state.

[0033] According to the signal motion scenario, set the state parameters of the signal particles at the initial moment, and use the set state parameters as the initial distribution of the signals.

[0034] Let the initial moment k = 0, and the initial distribution of the signals is represented in the form of a Gaussian particle parameter set as follows:

[0035]

[0036] where represents the state (a combination of signal position and velocity) of the j-th signal sampling particle at the initial moment; represents the weight corresponding to the state of the i-th signal sampling particle at the initial moment; N 0 represents the number of signal sampling particles at the initial moment.

[0037] (2) Predicting the signal state.

[0038] The state of the signal at time k can be represented by a 5-dimensional vector When the signal is in motion, its motion model changes with time, and the state equation is:

[0039] x k,q = F k x k-1,q + Γk ω k-1

[0040]

[0041] Among them, F k represents the state transition equation at time k, and x k-1,q represents the state at time k - 1, ω k-1 represents the state noise, and Σ k-1 = diag(3, 3, 0.01), Γ k is the coefficient matrix, and ΔT = 1s represents the time step.

[0042] Assume that the posterior distribution of the signal sampling particles at time k - 1 is:

[0043]

[0044] Among them represents the particle state at time k - 1, represents the corresponding particle weight, and N k-1 represents the total number of particles;

[0045] Then the continuously surviving sampling particles are expressed as:

[0046]

[0047] Among them represents the state prediction of the continuously surviving particles from time k - 1 to time k, represents the weight prediction of the continuously surviving particles from time k - 1 to time k; represents the signal particle at the survival probability at time k.

[0048] Suppose the set of newly generated sampling particles at time k is Merge the continuously surviving particles and the newly generated sampling particle set:

[0049]

[0050] Among them represents the merged particle set at time k, represents the corresponding particle weight, and N k|k-1 = N k-1 + N B,k represents the total number of merged particles, represents the sampling particles of the newly generated signal at time k, represents the weight of the sampling particles of the newly generated signal at time k, T B,k represents the number of components of the newly generated signal, and N B,k represents the number of newly generated particles for each component.

[0051] For the combined particle set, an unscented transformation strategy is adopted to obtain the predicted sampling particle set:

[0052]

[0053] where represents the predicted state of the i-th signal sampling particle from time k-1 to time k, the particle weight and the total number of particles N k|k-1 remain unchanged, and UT(·) represents the unscented transformation operation.

[0054] III. Update the signal state

[0055] Step 1: Calculate the covariance matrix

[0056] Sample . Assume that the number of snapshots at each moment is N. Then, the covariance matrix of the array received data at the p-th node at time k is:

[0057]

[0058] where[] H represents the conjugate transpose operation.

[0059] Step 2: Construct the measurement likelihood function.

[0060] Perform eigenvalue decomposition on the covariance matrix to obtain the corresponding signal subspace U p,k and noise subspace N p,k . For the q-th signal state where [p q,x , p q,y represents the two-dimensional coordinates of the signal, v q,x , v q,y represent the velocities of the signal along the x and y axes respectively, is the non-circular phase. Define the likelihood function

[0061]

[0062] where represents the p-th measurement to obtain the likelihood function of the i-th particle using the non-circular phase of the q-th signal, represents the direction vector, r is the exponential weighting factor, and its magnitude can affect the number of effective particles in the resampling step. P 2D-MUSIC (·) represents the two-dimensional spectral peak search function.

[0063] Step 3: Update the signal source state.

[0064] The updated posterior distribution of the signal sampling particles is expressed as:

[0065]

[0066] where represents the i-th updated sampling particle at time k, represents the updated weight of the i-th signal sampling particle at time k; N k|k-1 represents the number of predicted signal sampling particles at time k, N k represents the number of signal particles after resampling at time k.

[0067] Using the two-dimensional MUSIC spatial spectrum function of the signal sampling particles at time k as the likelihood function, update the signal prediction sampling particles at time k to obtain the updated signal sampling particles at time k.

[0068] The specific update method can be completed by the following steps.

[0069] Step 3.1, construct the measurement likelihood function from Step 2:

[0070]

[0071] Step 3.2, according to the measurement likelihood function, update the weights of the signal particles and normalize them to get:

[0072]

[0073] where represents the signal particle at the detection probability at time k.

[0074] Step 4, state extraction and number estimation

[0075] Use the resampling algorithm to find more effective particles and form a new signal sampling particle set, then calculate the weighted sum of the signal sampling particle states as the signal state tracked at the current moment; in addition, in terms of number estimation, we use the k-mean algorithm to estimate the number of updated signal sampling particles. If the number of signals estimated by the k-mean algorithm at this time is then the state estimation is as follows:

[0076]

[0077] where is the i-th updated particle corresponding to the j-th estimated signal, represents the corresponding updated weight, x k,j is the state estimation of the j-th signal at the current moment, N k represents the number of signal particles after resampling at time k, is the number of signals estimated using the k-mean algorithm.

[0078] Step 5: Determine whether all time steps have been processed. If so, end; otherwise, return to Step 2 until the end.

[0079] III. Experimental Performance Analysis

[0080] 1. Experimental Performance Evaluation Metrics

[0081] The performance estimation criterion is the commonly used Optimal Sub-Pattern Assignment (OSPA), and the signal-to-noise ratio is defined as follows:

[0082]

[0083] where the signal energy σ 2 = 2, and other experimental parameters: the number of array elements M p = 10, the signal-to-noise ratio SNR = 10 dB, the number of snapshots N = 200, and the particle survival probability and detection probability are both constant p S,k (x) = 0.99, p D,k (x) = 0.98. The set of newborn particles is Newborn particles are all generated around the initial positions of the signals, and the number of newborn particles for each component N B,k = 1000, and the number of particles updated at each moment after resampling N k = 1000.

[0084] 2. Experimental Effect Diagrams

[0085] Consider a scenario with 4 signals. Figure 3 is the single MC experiment tracking trajectory of the method of the present invention. It can be seen from the figure that the method of the present invention can effectively track the trajectories of multiple signals.

[0086] Consider a scenario with 4 signals. Figure 4 is the effect diagram of the signal number estimation of the method of the present invention and the Unscented Transform Probability Hypothesis Density Tracking method in running 100 MC experiments. Obviously, the Unscented Transform Probability Hypothesis Density Tracking method overestimates the number of signals, resulting in an increase in the estimation error. While the method of the present invention can accurately estimate the number of signal sources and solve the problem of time-varying signal numbers.

[0087] Consider a scenario with 2 signals. Figure 5 is the OSPA error schematic diagram of the method of the present invention and the Particle Filter method and the Direct Positioning Tracking method in running 100 MC experiments. It can be seen from the figure that the OSPA of the method of the present invention is less than that of other algorithms.

[0088] In summary, from the analysis of the simulation results, it can be seen that the multi-target probability hypothesis density tracking algorithm proposed by the present invention for distributed wireless sensor networks realizes the state tracking and number estimation of multiple signals, has good tracking performance, and its performance is relatively superior to other comparison methods.

[0089] It should be noted that although the embodiments described above of the present invention are illustrative, they are not limitations of the present invention. Therefore, the present invention is not limited to the above specific embodiments. Without departing from the principle of the present invention, any other embodiments obtained by those skilled in the art under the inspiration of the present invention are regarded as within the protection scope of the present invention.

Claims

1. A multi-target probability hypothesis density DOA tracking method in wireless sensor networks, characterized in that: The steps include: S1: Using uniform array to receive non-circular signals in wireless sensor networks to obtain extended measurement information; S2: Set the state parameters of the signal particles at the initial moment as the initial distribution of the signal, measure the signal sampling particles that survive continuously at the current moment, and obtain the predicted sampling particle set based on the traceless transformation; S3: Using the extended measurement information at the current moment, the covariance matrix of the received signal is calculated and the noise subspace is obtained, and then the signal prediction sampling particles at the current moment are updated; S4: Use the resampling algorithm to find more particles to form a new signal sampling particle set, and calculate the weighted sum of the signal sampling particle states as the signal state being tracked at the current moment; S5: Determine whether the time step has been processed. If so, end. Otherwise, return to step S3 until it ends.

2. The multi-target probability hypothesis density DOA tracking method in a wireless sensor network according to claim 1 is characterized in that: The specific implementation process of step S1 is as follows: There are P nodes in the distributed sensor network WSN. Each node is configured with a uniform linear array. The pth node has M p array elements; in the two-dimensional plane, at the kth moment, there are Q k The signals transmitted by unrelated drones are incident on P WSN nodes with known positions. The position of the drone signal is p q =[p q,x ,p q,y ] T ,q=1,…,Q k , the node is located at u p =[u p,x ,u p,y ] T , then the array receiving signal vector of the pth node at time k is expressed as: in represents the direction matrix received by the pth node, represents the direction vector of the qth signal received by the pth node, d = λ2 represents the array element spacing, λ is the signal carrier wavelength; n p (k) is the measurement noise, θ p,q is the DOA when the qth signal arrives at the pth node, satisfying: is a real-valued signal vector, represents the qth real signal received by the pth node, represents the diagonal matrix containing all non-circular phases of the signal, diag(·) represents the diagonal operation, represents the non-circular phase of the qth signal; According to the non-circular characteristics of the signal, the extended received signal vector is constructed, namely: in Represents the expansion direction matrix, whose qth vector represents the extended direction vector of the qth signal, and * represents the conjugate operation.

3. The multi-target probability hypothesis density DOA tracking method in a wireless sensor network according to claim 2 is characterized in that: The specific implementation process of step S2 is as follows: S2.1, let the initial time k = 0, the initial distribution of the signal is represented by the Gaussian particle parameter set: in Represents the state of the jth signal sampling particle at the initial moment; represents the weight corresponding to the state of the i-th signal sampling particle at the initial moment; N0 represents the number of signal sampling particles at the initial moment; S2.2, the state of the signal at time k is represented by the vector x k,q It means that when the signal moves, its motion model changes with time, and the state equation is: x k,q =F k x k-1,q +C k oh k-1 ; Among them, F k represents the state transition equation at time k, x k-1,q represents the state at time k-1, ω k-1 represents the state noise, and Γ k is the coefficient matrix, ΔT represents the time step; Assume that the posterior distribution of the signal sampling particle at time k-1 is: in represents the particle state at time k-1, Represents the corresponding particle weight, N k-1 represents the total number of particles; Then the continuously surviving sampling particles are expressed as: in represents the state prediction of the particles that survive continuously from time k-1 to time k, represents the weight prediction of the particles that survive from time k-1 to time k; Signal Particle The survival probability at time k; assuming that the set of newly sampled particles at time k is Combining the set of continuously surviving particles and newly adopted particles, we get: in represents the merged particle set at time k, Represents the corresponding particle weight, N k|k-1 =N k-1 +N B,k represents the total number of merged particles, represents the sampling particle of the new signal at time k, represents the weight of the new signal sampling particle at time k, T B,k Represents the number of new signal components, N B,k represents the number of newly generated particles of each component; For the merged particle set, the unscented transformation strategy is used to obtain the predicted sampling particle set: in represents the predicted state of the i-th signal sampling particle from time k-1 to time k, and the particle weight and the total number of particles N k|k-1 constant.

4. The multi-target probability hypothesis density DOA tracking method in a wireless sensor network according to claim 3 is characterized in that: The specific implementation process of step 3 is as follows: S3.

1. Yes Sampling is performed, assuming that the number of snapshots at each moment is N, then the covariance matrix of the array receiving data of the p-th node at moment k is: in[] H represents the conjugate transpose operation; S3.2, the covariance matrix is Perform eigendecomposition and obtain the corresponding signal subspace U p,k and the noise subspace N p,k , for the qth signal state where p q,x ,p q,y Represents the two-dimensional coordinates of the signal, v q,x ,v q,y represent the speed of the signal along the x and y axes respectively, For the non-circular phase, define the measurement likelihood function: in Indicates the pth measurement The non-circular phase of the qth signal is used to obtain the likelihood function of the ith particle, represents the direction vector, r is the exponential weighting factor, P 2D-MUSIC (·) represents the two-dimensional spectrum peak search function; S3.3, the updated signal sampling particle posterior distribution is expressed as: in, represents the i-th updated sampling particle at time k, represents the update weight of the i-th signal sampling particle at time k; N k|k-1 represents the number of particles sampling the predicted signal at time k, N k Table k time after resampling signal particles number; The two-dimensional MUSIC space spectrum function of the signal sampling particle at time k is used as the likelihood function to update the signal prediction sampling particle at time k and obtain the updated signal sampling particle at time k.

5. The multi-target probability hypothesis density DOA tracking method in a wireless sensor network according to claim 4, characterized in that: The updating process in step S3.3 is as follows: Construct the measurement likelihood function; according to the measurement likelihood function, update the weight of the signal particle and normalize it to get: in Signal Particle The detection probability at time k.

6. The multi-target probability hypothesis density DOA tracking method in a wireless sensor network according to claim 5, characterized in that: In step S4, the k-mean algorithm is used to estimate the number of updated signals. If the estimated number of signals is The state estimation is as follows: in, is the i-th updated particle corresponding to the estimated j-th signal, is the corresponding update weight, x k,j is the state estimate of the jth signal at the current moment, N k is the number of signal particles after resampling at time k.

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