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

Abstract

The application discloses a multi-target probability hypothesis density DOA tracking method under a wireless sensor network. Firstly, a uniform array is used to receive a non-circular signal under the wireless sensor network to obtain extended measurement information. Secondly, state parameters of signal particles at an initial moment are set as initial distribution of the signal, and signal sampling particles surviving at a current moment are measured. A set of predicted sampling particles is obtained based on an unscented transformation. Then, a covariance matrix of the received signal is calculated by using the extended measurement information at the current moment, and a noise subspace is obtained. A PHD filter is used to update the predicted sampling particles of the signal at the current moment. Finally, more effective particles are found by using resampling, a new signal sampling particle set is composed, a weighted sum of the signal sampling particle states is calculated, and the signal state at the current moment is tracked until the end. The application can more accurately estimate the number of signals and track the state of the signal source.

Description

Technical Field

[0001] This invention belongs to the field of direction of arrival (DOA) tracking and relates to a multi-target probability hypothesis density (WSN-PHD) DOA tracking method for wireless sensor networks. Background Technology

[0002] Currently, moving target tracking in the context of wireless sensor networks has become a hot topic in smart IoT applications, with wide applications in various fields such as illegal vehicle tracking, space exploration, and border security. Moving target tracking in wireless sensor networks can consist of several static or mobile nodes 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. Given a fixed and known number of targets, these two algorithms offer good tracking performance. However, they have certain limitations. For example, in complex wireless sensor networks, when obstacles exist between the target and network nodes (i.e., the number of observed targets changes over time), tracking accuracy is significantly affected. Summary of the Invention

[0004] Objective: To address the problems existing in current technologies, this invention proposes a multi-target probability hypothesis density (DOA) tracking method for wireless sensor networks. This method employs Sequential Monte Carlo (SMC) implementation, using the two-dimensional multiple signal classification (MUSIC) spatial spectrum function as the likelihood function, and exponentially weighting and fusing the likelihood functions of each node. This makes resampling more efficient and achieves accurate signal tracking. It can be applied to fields such as sonar and radar positioning. This invention proposes a random finite set (RFS) to encapsulate the state and number of multiple targets and provides a multi-target probability hypothesis density (DOA) tracking method for wireless sensor networks.

[0005] Technical solution:

[0006] A multi-target probability hypothesis density (DOA) tracking method in wireless sensor networks includes the following steps:

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

[0008] S2: Predict signal state: Set the state parameters of the signal particles at the initial time and use the set state parameters as the initial distribution of the signal; for the signal sampling particles of the previous time, use the state equation to predict and obtain the signal sampling particles that are still alive at the current time, then merge the newly generated signal sampling particles to obtain the merged signal sampling particles; finally, perform a traceless transformation 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 eigenvalue decomposition to obtain the noise subspace N p,k Based on the direction vector corresponding to each predicted signal sampled particle, the corresponding two-dimensional MUSIC spatial spectrum function is calculated and exponentially weighted and fused to serve as the likelihood function of the particle; then, the PHD filter is used to update the predicted sampled particles of the signal at the current time to obtain the updated sampled particles of the signal at the current time.

[0011] S4: State extraction and number estimation: The resampling algorithm is used to find more effective particles and form a new set of signal sampling particles. Then, the weighted sum of the states of the signal sampling particles is calculated as the current signal state being tracked. In addition, the k-means algorithm is used to estimate the updated number of signals for number estimation.

[0012] S5: Determine if all time steps have been processed. If yes, end; otherwise, return to step S3 until end.

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

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

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

[0016] Figure 2 This is a schematic diagram of a multi-target tracking model in a distributed wireless sensor network.

[0017] Figure 3Under the conditions of a single MC experiment, the method of this invention uses a tracking trajectory diagram with 10 nodes;

[0018] Figure 4 This is a graph showing the effect of running 100 MC experiments on estimating the number of signal sources using the method of this invention and other algorithms;

[0019] Figure 5 This is an OSPA error comparison diagram showing the tracking signal position effect of the method of this invention compared with other comparative methods. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of the present invention clearer, 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 in wireless sensor networks, the process is as follows: Figure 1 As shown, the specific implementation process is as follows:

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

[0023] like Figure 2 The diagram illustrates a distributed wireless sensor network (WSN) multi-target tracking model that can utilize this invention. Consider a WSN with P nodes, located on the rooftop 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 Each array element. Assuming the UAV target is flying in a low-altitude environment, both the UAV signal and the sensor array can be considered as point masses. In a two-dimensional plane, at time k, Q... k A number of independent UAVs transmit signals (considered as far-field narrowband sources) and are incident on P WSN nodes at known locations. The locations of the UAV signals are 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 received signal vector of the p-th node at time k can be expressed as:

[0024]

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

[0026]

[0027] in, For real-valued signal vectors, This represents the q-th real signal received by the p-th node. This represents a diagonal matrix containing the non-circular phases of all signals; diag(·) denotes the diagonal operation. This indicates the non-circular phase of the q-th signal.

[0028] Based on the non-circular nature of the signal, an extended received signal vector can be constructed, namely:

[0029]

[0030] in This represents the extended direction matrix, where the q-th vector... Let represent the propagation direction vector of the q-th signal, []. * This indicates a conjugate operation.

[0031] II. Predicted Signal State

[0032] (1) Initialize signal state.

[0033] Based on the signal motion scenario, the state parameters of the signal particles at the initial moment are set, and the set state parameters are used as the initial distribution of the signal.

[0034] Let the initial time k = 0, the initial distribution of the signal is represented by the Gaussian particle parameter set as follows:

[0035]

[0036] in, This represents the state (combination of signal position and velocity) of the j-th sampled particle at the initial moment; N represents the weight corresponding to the state of the i-th signal sampling particle at the initial time; N0 represents the number of signal sampling particles at the initial time.

[0037] (2) Predict the signal state.

[0038] The state of the signal at time k can be represented by a 5-dimensional vector. This indicates that when a signal moves, its motion model changes over time, and the state equation is:

[0039] x k,q =F k x k-1,q +Γ kω k-1

[0040]

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

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

[0043]

[0044] in This represents the particle state at time k-1. N represents the corresponding particle weight. k-1 Indicates the total number of particles;

[0045] The continuously surviving sampled particles are represented as:

[0046]

[0047] in This represents the state prediction of particles that continue to survive from time k-1 to time k. This represents the weight prediction of particles that survive from time k-1 to time k. Indicates signal particles The probability of survival at time k.

[0048] Assume the set of newly sampled particles at time k is Merging surviving particles and newly generated particles using a particle set:

[0049]

[0050] in This represents the merged particle set at time k. N represents the corresponding particle weight. k|k-1 =N k-1 +N B,k This represents the total number of merged particles. This represents the sampled particle of the newborn signal at time k. T represents the weight of the sampled particles of the newly generated signal at time k. B,k N represents the number of newborn signal components. B,k This indicates the number of newly generated particles for each component.

[0051] For the merged particle set, an unscented transformation strategy is used to obtain the predicted sampled particle set:

[0052]

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

[0054] III. Update signal status

[0055] Step 1: Calculate the covariance matrix

[0056] right Sampling is performed, assuming that the number of snapshots at each time step is N. Then the covariance matrix of the array received data of the p-th node at time step k is:

[0057]

[0058] in[] H This indicates the conjugate transpose operation.

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

[0060] For the covariance matrix is Eigenvalue decomposition was performed, and the corresponding signal subspace U was obtained. 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 These represent the velocities of the signal along the x and y axes, respectively. For non-circular phase, define the likelihood function.

[0061]

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

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

[0064] The updated posterior distribution of the sampled signal particles is represented as follows:

[0065]

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

[0067] Using the two-dimensional MUSIC spatial spectrum function of the signal sampling particles at time k as the likelihood function, the signal prediction sampling particles at time k are updated, thus obtaining 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: Based on the measured likelihood function, update and normalize the weights of the signal particles, resulting in:

[0072]

[0073] in Indicates signal particles The detection probability at time k.

[0074] Step 4: State extraction and number estimation

[0075] A resampling algorithm is used to find more effective particles and form a new set of signal sampling particles. Then, a weighted sum of the states of these sampled particles is calculated as the current tracking signal state. Additionally, for particle count estimation, the k-means algorithm is used to estimate the updated number of signal sampling particles. If the k-means algorithm estimates the signal count as follows... The state estimate is as follows:

[0076]

[0077] in, For the estimated j-th signal, the i-th update particle, Indicates the corresponding update weight, x k,j For the state estimation of the j-th signal at the current time, N k Table k shows the number of signal particles after resampling. The number of signals estimated using the k-means algorithm.

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

[0079] III. Experimental Performance Analysis

[0080] 1. Experimental performance evaluation indicators

[0081] The performance estimation standard is the commonly used Optimal Submode Allocation (OSPA), and the signal-to-noise ratio is defined as follows:

[0082]

[0083] Where the signal energy σ 2 =2, other experimental parameters: number of array elements M p =10, signal-to-noise ratio (SNR) = 10dB, number of snapshots N = 200, 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 Newly generated particles are produced around the initial position of the signal, and the number of newly generated particles for each component is N. B,k =1000, the number of particles N is updated every time after resampling. k =1000.

[0084] 2. Experimental results diagram

[0085] Consider a scenario with four signals. Figure 3 This figure shows the trajectory tracked in a single MC experiment using the method of the present invention. As can be seen from the figure, the method of the present invention can effectively track the trajectories of multiple signals.

[0086] Consider a scenario with four signals. Figure 4 This image shows the results of running 100 McLeod experiments comparing the proposed method and the unscented transform probabilistic hypothesis density tracking method for estimating the number of signal sources. Clearly, the unscented transform probabilistic hypothesis density tracking method overestimates the number of signal sources, leading to increased estimation error. In contrast, the proposed method accurately estimates the number of signal sources, solving the problem of time-varying signal numbers.

[0087] Consider a scenario with two signals. Figure 5 This diagram illustrates the OSPA error of the proposed method compared to the particle filtering method and the direct positioning and tracking method after 100 MC experiments. As can be seen from the diagram, the OSPA of the proposed method is lower than that of the other algorithms.

[0088] In summary, the analysis of the simulation results shows that the multi-target probability hypothesis density tracking algorithm for distributed wireless sensor networks proposed in this invention achieves state tracking and number estimation of multiple signals, with good tracking performance, which is superior to other comparative methods.

[0089] It should be noted that although the embodiments described above are illustrative, they are not intended to limit the invention. Therefore, the invention is not limited to the specific embodiments described above. Any other embodiments obtained by those skilled in the art under the guidance of this invention without departing from its principles are considered to be within the protection scope of this invention.

Claims

1. A multi-target probability hypothesis density (DOA) tracking method in wireless sensor networks, characterized in that, Includes the following steps: S1: In a wireless sensor network, a uniform array is used to receive non-circular signals to obtain extended measurement information. Among them, z p (k) represents the array received signal vector of the p-th node at time k. Represents the extended direction matrix. Let n be a real-valued signal vector. p (k) represents measurement noise, and * indicates conjugate operation; 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 are continuously alive at the current moment, and obtain the predicted sampling particle set based on the unscented transformation; S3: Using the extended measurement information at the current moment, calculate the covariance matrix of the received signal and obtain the noise subspace. Then, update the predicted sampled particles of the signal at the current moment, as follows: Based on the direction vector corresponding to each predicted signal sampled particle, the corresponding two-dimensional MUSIC spatial spectrum function is calculated and exponentially weighted and fused to serve as the likelihood function of the particle; then, the PHD filter is used to update the predicted sampled particles of the signal at the current time to obtain the updated signal sampled particles at the current time. S4: Use the resampling algorithm to find more particles, form a new set of signal sampling particles, and calculate the weighted sum of the states of the signal sampling particles as the current tracking signal state. S5: Determine if the time step has been completed. If yes, end the process; otherwise, return to step S3 until the process ends.

2. The multi-target probability hypothesis density (DOA) tracking method in wireless sensor networks according to claim 1, characterized in that, The specific implementation process of step S1 is as follows: A distributed sensor network (WSN) with P nodes, each node configured with a uniform linear array, has M nodes. p There are array elements; in the two-dimensional plane, at time k, Q has k Several independent drones transmit signals, which are incident on P WSN nodes whose positions are known. The drone signal positions are 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 received signal vector of the p-th node at time k is represented as: in This represents the direction matrix received by the p-th node. This represents the direction vector of the p-th node receiving the q-th signal, d = λ / 2 represents the element spacing, and λ is the signal carrier wavelength; n p (k) represents the measurement noise, θ p,q Let the DOA be the distance to the p-th node when the q-th signal arrives, satisfying: For real-valued signal vectors, This represents the q-th real signal received by the p-th node. This represents a diagonal matrix containing the non-circular phases of all signals; diag(·) denotes the diagonal operation. This indicates the non-circular phase of the q-th signal; Based on the non-circular nature of the signal, an extended received signal vector is constructed, namely: in This represents the extended direction matrix, where the q-th vector... This represents the propagation direction vector of the q-th signal, and * indicates the conjugate operation.

3. The multi-target probability hypothesis density (DOA) tracking method in wireless sensor networks according to claim 2, characterized in that, The specific implementation process of step S2 is as follows: S2.

1. Let the initial time k = 0, and the initial distribution of the signal be represented by the Gaussian particle parameter set: in This represents the state of the j-th signal sampled particle at the initial time; Ni represents the weight corresponding to the state of the i-th signal sampling particle at the initial time; N0 represents the number of signal sampling particles at the initial time. S2.2, The state of the signal at time k is represented by the vector x. k,q This indicates that when a signal moves, its motion model changes over time, and the state equation is: x k,q =F k x k-1,q +C k oh k-1 ; Among them, F k Let x represent the state transition equation at time k. k-1,q ω represents the state at time k-1. k-1 Indicates state noise, and Γ k Here is the coefficient matrix, and ΔT represents the time step; Assume the posterior distribution of the sampled particles at time k-1 is: in This represents the particle state at time k-1. N represents the corresponding particle weight. k-1 Indicates the total number of particles; The continuously surviving sampled particles are represented as: in This represents the state prediction of particles that continue to survive from time k-1 to time k. This represents the weight prediction of particles that survive from time k-1 to time k. Indicates signal particles The survival probability at time k; assuming the set of newly sampled particles at time k is... By merging the continuously surviving particles and the newly generated particle set, we obtain: in This represents the merged particle set at time k. N represents the corresponding particle weight. k|k-1 =N k-1 +N B,k This represents the total number of merged particles. This represents the sampled particle of the newborn signal at time k. T represents the weight of the sampled particles of the newly generated signal at time k. B,k N represents the number of newborn signal components. B,k This indicates the number of newly generated particles for each component; For the merged particle set, an unscented transformation strategy is used to obtain the predicted sampled particle set: in The particle weight represents the predicted state of the i-th signal sampled particle from time k-1 to time k. and the total number of particles N k|k-1 constant.

4. The multi-target probability hypothesis density (DOA) tracking method in wireless sensor networks according to claim 3, characterized in that, The specific implementation process of step 3 is as follows: S3.1, To Sampling is performed, assuming that the number of snapshots at each time step is N. Then the covariance matrix of the array received data of the p-th node at time step k is: in[] H This represents the conjugate transpose operation; S3.2, for the covariance matrix is Perform eigenvalue decomposition 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 The two-dimensional coordinates of the signal, v q,x ,v q,y These represent the velocities of the signal along the x and y axes, respectively. For non-circular phase, define the measurement likelihood function: in Indicates the p-th measurement The likelihood function of the i-th particle is obtained by using the non-circular phase of the q-th signal. This represents the direction vector, r is the exponential weighting factor, and P... 2D-MUSIC (·) represents a two-dimensional spectral peak search function; S3.3, The updated posterior distribution of the signal sampled particles is represented as follows: in, This represents the i-th updated sampling particle at time k. N represents the update weight of the i-th signal sampling particle at time k; k|k-1 N represents the number of particles sampled in the predicted signal at time k. k This represents the number of signal particles after resampling at time k; Using the two-dimensional MUSIC spatial spectrum function of the signal sampling particles at time k as the likelihood function, the signal prediction sampling particles at time k are updated, thus obtaining the updated signal sampling particles at time k.

5. The multi-target probability hypothesis density (DOA) tracking method in wireless sensor networks according to claim 4, characterized in that, The update process in step S3.3 is as follows: Construct the measurement likelihood function; based on the measurement likelihood function, update and normalize the weights of the signal particles, resulting in: in Indicates signal particles The detection probability at time k.

6. The multi-target probability hypothesis density (DOA) tracking method in wireless sensor networks according to claim 5, characterized in that, In step S4, the k-means algorithm is used to estimate the updated signal count; if the estimated signal count is at this point... The state estimate is as follows: in, For the estimated j-th signal, the i-th update particle, For the corresponding update weight, x k,j For the state estimation of the j-th signal at the current time, N k The number of signal particles after resampling at time k.

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