DOA tracking method and system based on interactive multiple model auxiliary particle filter

Abstract

The application discloses a DOA tracking method and system based on an interactive multiple model auxiliary particle filter, which comprises the following steps: firstly, receiving the DOA of a single signal by a uniform linear array antenna to obtain observation information, and initializing a particle set; secondly, performing interactive multiple model prediction on the particles in the particle set, and updating the particle set; thirdly, performing spatial filtering on the updated particle state according to the observation information to obtain an auxiliary particle filter particle set; fourthly, calculating a likelihood function based on the auxiliary particle filter particle set, updating the particle set, performing weighted fusion, and obtaining the estimated state value at the current moment; and finally, taking the estimated state value at the current moment as the iterative input at the next moment, and performing the cycle to realize continuous dynamic DOA tracking. The application alleviates the particle degradation problem through the auxiliary particle filter, improves the particle utilization rate and the estimation accuracy, and improves the robustness and continuity of the DOA estimation.

Description

Technical Field

[0001] This invention belongs to the field of array signal processing technology, specifically relating to a Direction of Arrival (DOA) tracking method for maneuvering single targets, and particularly to a DOA tracking method and system based on interactive multi-model assisted particle filtering. Background Technology

[0002] In practical applications such as radar, sonar, wireless communication, passive localization, and vehicle sensing, direction-of-arrival (DOA) estimation is a key technology for target monitoring, localization, and tracking. Traditional DOA estimation methods, such as the Multiple Signal Classification (MUSIC) algorithm, the Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) algorithm, and their improved versions, can achieve relatively ideal spatial spectral resolution under ideal Gaussian noise environments and conditions for stationary or slowly changing targets. However, in real-world engineering environments, targets are usually in motion, and their motion patterns are uncertain, easily switching between constant speed, turning, and acceleration. This makes it difficult for a single filtering model to match the actual motion characteristics, leading to a decrease in estimation accuracy.

[0003] Particle filters (PF) are widely used in dynamic DOA tracking due to their effectiveness in handling state estimation problems of nonlinear and non-Gaussian systems. However, standard particle filters are prone to particle degeneration during iteration, where a large number of particle weights are concentrated on a few particles, reducing the filter's effectiveness and stability. Furthermore, when the target maneuvers, fixed-model particle filters cannot respond promptly to changes in motion, leading to problems such as tracking lag, increased errors, and even tracking interruptions.

[0004] Interactive Multiple Model (IMM) methods construct multiple parallel motion models and achieve state fusion through probabilistic interactive prediction and updates, maintaining high tracking stability even when the target's motion pattern is uncertain. While the IMM-PF method, combining IMM with particle filtering, can handle mode switching, it still has limitations: during model transitions, particle weight calculations rely on prior distributions that do not fully consider the latest observations, leading to a significant loss of particle diversity and requiring further improvement in filtering accuracy. Summary of the Invention

[0005] To overcome the aforementioned shortcomings, this invention integrates an auxiliary particle filter with an interactive multi-mode algorithm, proposing the IMM-APF (Interactive Multiple Model Assisted Particle Filter) method. The auxiliary particle filter effectively mitigates particle degradation and improves particle utilization and filtering accuracy by introducing auxiliary variables and optimizing the selection of the important density function. By incorporating current observation information into the proposal distribution generation and model interaction process through auxiliary variables, it enhances both particle effectiveness and model switching response speed, thereby achieving high-precision and stable tracking of single-target DOA in complex maneuvering scenarios.

[0006] This invention includes the following steps:

[0007] S1: DOA of a single signal received through a uniform linear array antenna at time k. , obtain observation information and initialize the particle set. .

[0008] S2: Perform interactive multi-model predictions on particles in the particle set and update the particle set.

[0009] S2.1: At time k, for the particle set Interactive multi-model prediction and updating are performed on the i-th particle. First, the state of the i-th particle under R different physical motion models is predicted. Then, based on the observation information at time k For each model's predicted state, spatial filtering is performed, the corresponding likelihood function is calculated, and the likelihood weights are obtained by normalization.

[0010] S2.2: Based on the initial model probability With transfer model Calculate the model prediction probability Combined with the normalized likelihood weights obtained in S2.1 Calculate model update probability And normalized to obtain Next, the states predicted by each model are analyzed. Multiply by the probability of the corresponding model Get updated particle state Complete the model interaction.

[0011] S3: Update the particle state as described in S2 Based on the observation information at time k Perform spatial filtering and further calculate the likelihood function. Normalization and resampling are performed to obtain the particle set for auxiliary particle filtering. .

[0012] S4: The particle set described in S3 Based once again on the observation information at time k Calculate the likelihood function Normalization and resampling are performed to obtain the updated particle set at time k. Finally, the results are weighted and fused to obtain the estimated state value at the current moment.

[0013] S5: Using the estimated state value at the current moment as the input for the next moment's iteration, the interactive multi-mode algorithm is repeatedly executed for prediction and update, auxiliary particle filtering, and state estimation to achieve continuous dynamic DOA tracking.

[0014] In another aspect, the present invention also provides a DOA tracking system based on interactive multi-model assisted particle filtering, comprising the following modules:

[0015] The particle set initialization module is used to receive the DOA of a single signal through a uniform linear array antenna, obtain observation information, and initialize the particle set.

[0016] The particle multi-model prediction update module is used to perform interactive multi-model predictions on particles in the particle set and update the particle set.

[0017] The particle set module for auxiliary particle filtering is used to perform spatial filtering on the updated particle states based on observation information to obtain the particle set for auxiliary particle filtering.

[0018] The particle state estimation module calculates the likelihood function to update the particle set based on the particle set of the auxiliary particle filter, performs weighted fusion, and obtains the estimated state value at the current time.

[0019] The dynamic DOA tracking module uses the estimated state value at the current moment as the input for the next moment's iteration, and cyclically executes interactive multi-mode algorithm prediction updates, auxiliary particle filtering, and state estimation to achieve continuous dynamic DOA tracking.

[0020] The beneficial effects of this invention are as follows:

[0021] Compared with the prior art, the present invention has the following technical effects: The invention introduces an interactive multi-model framework to adaptively match changes in target maneuvering modes, alleviates particle degradation problems through auxiliary particle filtering, and improves particle utilization and estimation accuracy; at the same time, it uses model probability interactive prediction and updating to achieve state fusion, effectively copes with target motion mode switching, thereby improving the robustness and continuity of DOA estimation. Attached Figure Description

[0022] Figure 1 This is a schematic diagram of the array structure of the present invention;

[0023] Figure 2 This is a flowchart illustrating the overall implementation of the present invention;

[0024] Figure 3 The RMSE comparison curves of the method of this invention with the PF and IMM-PF algorithms are shown.

[0025] Figure 4 A comparison chart showing the estimation performance of the method of the present invention under different particle numbers;

[0026] Figure 5 A magnified view of the DOA estimation of the present invention, PF, and IMM-PF when the target maneuvers. Detailed Implementation

[0027] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0028] This embodiment provides a single-target DOA tracking method based on interactive multi-model assisted particle filtering, as follows: Figure 2 The specific steps are as follows:

[0029] Step 1: Constructing the array receiving model and system equations

[0030] A uniform linear array (ULA) is composed of, for example, Figure 1 of It consists of array elements, with array spacing of [number] elements. , Let be the signal wavelength. At time k, the far-field narrowband single target has an angle of . Incident light. The signal received by the physical antenna is converted into noisy observation data; the observation information is then received and calculated.

[0031]

[0032] in As a direction vector, its complex basis-band representation preserves angular information, facilitating the construction of the likelihood function, where... It is the transpose of the vector. For the signal complex envelope, With a mean of 0 and a variance of The observation noise was reduced, and the particle set from the previous time step was initialized. .

[0033] Step 2: Interactive multi-model prediction and particle set update

[0034] 2.1: A single model cannot capture target maneuvers, while IMM adapts to changes in motion patterns through model fusion, avoiding tracking lag. An IMM framework is constructed, and the filtered output particle set from the previous time step is used... Each particle in the process is performed separately. One physical motion model predicts:

[0035]

[0036] in For the first The state transition matrix of a model (e.g., a uniform velocity model) Steering model , The sampling time interval, (referring to the steering angular velocity) It is the process noise figure matrix. The mean is 0 and the variance is Process noise. Predicted particle angle at the current moment. The signal source was recovered using least-squares spatial filtering. :

[0037]

[0038]

[0039] in The predicted orientation of the i-th particle The corresponding array manifold matrix, matrix From vector composition, It is the conjugate transpose. Invert the matrix. Calculate the observations. The squared norm of the residuals with respect to the reconstructed signal:

[0040]

[0041] matrix From vector The composition is then finalized, and the likelihood weights (unnormalized) are calculated:

[0042]

[0043] in It is the normalization coefficient. It's an exponential function, where L is the number of snapshots. Weight normalization:

[0044]

[0045] Obtain the updated particle weights Each model obtains an independent normalized likelihood, making full use of multi-shot information, suppressing noise, and improving sensitivity to small changes in angle, thus providing a basis for model probability updates in step 3.

[0046] 2.2: Apply the normalized likelihood weights obtained in 2.1 The core coefficients are used to update the posterior probabilities of each motion model. The predicted probabilities are calculated. :

[0047]

[0048] The initial model Transfer model ,in This represents the probability of switching from model i to model j. It is combined with the likelihood weights. Calculate and normalize the model update probability:

[0049]

[0050]

[0051] Obtain the normalized posterior probability As the next moment .

[0052] Updating the model probability effectively suppresses noise interference, improves sampling efficiency and likelihood assessment accuracy, and makes the fused particle set more concentrated near the true state. Calculate the updated particle state:

[0053]

[0054] Step 3: Auxiliary Particle Filtering

[0055] Based on the observation information at time k Update the particle state obtained in the previous step Perform spatial filtering and further calculate the likelihood function. Normalization And resampling: Calculate Cumulative weight at time step Generate resampling particle sampling points Using particle indexing Select new particles and reset their weights. The particle set for auxiliary particle filtering is obtained. This completes one full iteration of the auxiliary particle filter.

[0056] Step 4: Weight Update and State Fusion

[0057] Particle set based on APF output Once again, based on the observation information at time k... Calculate the likelihood function Normalization and resampling are performed to obtain the updated particle set at time k. Finally, the results are weighted and fused to obtain the estimated state value at the current time:

[0058]

[0059] Finally, a resampling is performed and the particle weights are reset to a uniform distribution before proceeding to the next iteration.

[0060] Step 5: Iterative Loop and Continuous Tracking

[0061] The current particle state Normalized weights And the model probability is used as the input for the next time step. Let Repeat steps 1 to 5 to achieve continuous dynamic DOA tracking.

[0062] In another aspect, the present invention also provides a DOA tracking system based on interactive multi-model assisted particle filtering, for implementing the aforementioned DOA tracking method, including a particle set initialization module, a particle multi-model prediction update module, a particle set module for assisted particle filtering, a particle state estimation module, and a dynamic DOA tracking module:

[0063] The initialization particle set module is used to receive the DOA of a single signal through a uniform linear array antenna, obtain observation information, and initialize the particle set.

[0064] The particle multi-model prediction update module is used to perform interactive multi-model prediction on particles in the particle set and update the particle set.

[0065] The particle set module for auxiliary particle filtering is used to perform spatial filtering on the updated particle state based on the observation information to obtain the particle set for auxiliary particle filtering.

[0066] The particle state estimation module calculates the likelihood function to update the particle set based on the particle set of the auxiliary particle filter, performs weighted fusion, and obtains the estimated state value at the current time.

[0067] The dynamic DOA tracking module is used to take the estimated state value at the current moment as the iterative input for the next moment, and cyclically execute interactive multi-mode algorithm prediction update, auxiliary particle filtering and state estimation to achieve continuous dynamic DOA tracking.

[0068] Performance analysis and experimental analysis:

[0069] 1. Complexity Analysis

[0070] The computational complexity is evaluated using the number of floating-point operations. The complexity of the method in this invention mainly includes the computational complexity required to calculate multi-model predictions. ,in Represents the number of particles; the complexity of likelihood calculation is O(n). ,in For the number of array elements, The number of snapshots; the complexity of weight normalization and resampling is O(n). Combining all these components, the overall computational complexity of the proposed algorithm is:

[0071]

[0072] 2. Experimental Analysis

[0073] To verify the effectiveness of the above method, multiple simulation experiments were conducted in this embodiment, and the experimental performance was analyzed, as follows:

[0074] (1) Experimental performance evaluation indicators

[0075] To verify the effectiveness of the proposed method, Monte Carlo simulation experiments were conducted, and the performance of the proposed method was compared with that of the PF and IMM-PF algorithms. The performance evaluation metric is the root mean square error (RMSE), defined as follows:

[0076]

[0077] in For the first The first Monte Carlo simulation process Signal Azimuth estimation, It is the number of information sources. This indicates the number of Monte Carlo simulations. Among the experimental parameters in this section are: number of array elements. Quick shot number Signal-to-noise ratio Sampling interval Process noise variance Number of IMM models Particle filter particle number .

[0078] 3. Experimental results diagram

[0079] Figure 3 This is a comparison curve of the RMSE of the proposed method with the PF and IMM-PF algorithms in a target maneuver scenario. In the experiment, the signal-to-noise ratio... , the number of array elements , number of particles It is evident that during the target maneuver (times 16 and 27), the traditional PF algorithm exhibits a drastic jump in RMSE due to its lack of multi-model adaptation capability; while the IMM-PF algorithm can respond to mode changes, it still suffers from significant tracking delay; the proposed IMM-APF method has a significantly lower RMSE than the comparative algorithms, better tracking smoothness, and faster fluctuation decay, demonstrating stronger maneuver adaptability and tracking robustness.

[0080] Figure 4 These are RMSE comparison images of the method of this invention under different particle numbers, with the particle number taken as... =500, 1000, 1500, other simulation parameters are the same as... Figure 3 Consistent results. Experimental results show that the state estimation accuracy of the algorithm steadily improves with the increase of the number of particles: when the number of particles is 500, the low particle utilization rate leads to a high mean RMSE; when the number of particles is increased to 1000, the pre-sampling advantage of the auxiliary particle filter begins to emerge, and the estimation error decreases significantly; when the number of particles is increased to 1500, the RMSE further converges, and the error fluctuation range is significantly narrowed, verifying that the method can effectively improve tracking performance by increasing particle diversity under a reasonable particle number configuration, and the performance gain shows a marginal decrease law with the increase of the number of particles, providing a reference for the selection of the number of particles in engineering applications.

[0081] Figure 5 This is a magnified view of the DOA estimation using the method of this invention, the PF algorithm, and the IMM-PF algorithm when the target maneuvers. Target initial azimuth angle. When the target motion mode changes, the DOA estimation value of the PF algorithm shows obvious lag and oscillation, and the tracking error is significantly amplified. Although the IMM-PF algorithm can quickly identify the mode change, the estimated trajectory still has a slight overshoot. However, the IMM-APF method of this invention can smoothly transition the DOA estimation curve, with smaller tracking lag and weaker fluctuation amplitude, clearly demonstrating the fast response capability and stable tracking performance of this method when the motion mode changes.

[0082] In summary, analysis of the simulation results shows that the single-target DOA tracking method based on interactive multi-model assisted particle filtering proposed in this invention achieves high-precision and high-stability tracking of maneuvering single targets in the direction of arrival. This method not only adaptively matches changes in target motion patterns through an interactive multi-model framework but also effectively mitigates particle degradation by utilizing assisted particle filtering, thereby improving particle utilization and estimation accuracy. Compared with conventional particle filtering and the IMM-PF algorithm, the proposed method exhibits higher tracking continuity and robustness in target maneuvering scenarios and demonstrates superior estimation performance, showing promising application prospects in dynamic target monitoring scenarios such as radar and passive positioning.

[0083] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

Claims

1. A DOA tracking method based on interactive multi-model-assisted particle filtering, characterized in that, Includes the following steps: S1: Obtain observation information by receiving the DOA of a single signal through a uniform linear array antenna, and initialize the particle set; S2: Perform interactive multi-model prediction on particles in the particle set and update the particle set; S3: For the updated particle state, perform spatial filtering based on the observation information to obtain the particle set for auxiliary particle filtering. The specific implementation process is as follows: Based on the observation information at time k Update the particle state obtained in the previous step Perform spatial filtering and calculate the likelihood function. Normalization and resampling: Based on the normalized likelihood weights ,calculate Cumulative weight at time step , Indicates the number of particles, generating resampled particle sampling points. Using particle indexing Select new particles and reset their weights. The particle set for auxiliary particle filtering is obtained. This completes one full iteration of the auxiliary particle filter; S4: Based on the particle set of auxiliary particle filtering, calculate the likelihood function to update the particle set, perform weighted fusion, and obtain the estimated state value at the current time. S5: Using the estimated state value at the current moment as the input for the next moment's iteration, the interactive multi-mode algorithm is repeatedly executed for prediction and update, auxiliary particle filtering, and state estimation to achieve continuous dynamic DOA tracking.

2. The DOA tracking method based on interactive multi-model assisted particle filtering according to claim 1, characterized in that, The specific implementation process of step S1 is as follows: Uniform linear array ULA is composed of It consists of array elements, with array spacing of [number] elements. , Let be the signal wavelength. At time k, the far-field narrowband single target has an angle of . Incident; converting the signal received by the physical antenna into noisy observation data, receiving and calculating the observation information. The observation information consists of the direction vector. With signal complex envelope The product of these is summed with the observation noise to obtain the result; And initialize the particle set from the previous time step. , For the i-th particle Predicted particle angle at time of moment For the i-th particle Particle weights at time step.

3. The DOA tracking method based on interactive multi-model assisted particle filtering according to claim 2, characterized in that, The specific implementation process of step S2 is as follows: S2.1: First, predict the state of the i-th particle under R different physical motion models. Then, based on the observation information at time k For each model's predicted state, spatial filtering is performed, the corresponding likelihood function is calculated, and the likelihood weights are normalized. S2.2: Based on the initial model probability With transfer model Calculate the model prediction probability The model update probability is calculated by combining the normalized likelihood weights. And normalized to obtain Next, the states predicted by each model are analyzed. Multiply by the probability of the corresponding model Get updated particle state Complete the model interaction.

4. The DOA tracking method based on interactive multi-model assisted particle filtering according to claim 3, characterized in that, The specific implementation process of step S2.1 is as follows: Construct the IMM framework to filter the particle set of the previous time step. Each particle in the set is predicted using multiple models to obtain the particle set at the current time. ; For the current moment, the Particle prediction angle in a physical motion model ; Particle prediction angle The predicted orientation of particles is obtained by extracting the angle matrix. Calculate the predicted orientation of the i-th particle. The corresponding array manifold matrix ,Depend on vectors in pass Calculated ,in This is the conjugate transpose. To find the inverse of a matrix, all Combining to obtain ; Calculation observation With reconstructed signal The square of the residual norm between ; Finally, likelihood weights are calculated. Calculation, expressed as ,in It is the normalization coefficient. It is an exponential function, where L is the number of snapshots, and likelihood weights are applied. Normalization yields the normalized likelihood weights. .

5. The DOA tracking method based on interactive multi-model assisted particle filtering according to claim 4, characterized in that, The specific implementation process of step S2.2 is as follows: Based on the initial model probability and transfer model The product of these factors is used to calculate the predicted probability. ; Where the initial model probability Transfer model ,in It is the probability of switching from model i to model j; Predicted probability Likelihood weights after dot product normalization Calculate the model update probability and normalize it to obtain The normalized posterior probability is obtained. As the next moment Calculate all particles The sum of these values ​​yields the updated particle state. .

6. The DOA tracking method based on interactive multi-model assisted particle filtering according to claim 5, characterized in that, The specific implementation process of step S4 is as follows: The particle set based on the auxiliary particle filter is then used again based on the observation information at time k. Calculate the likelihood function Normalization and resampling are performed to obtain the updated particle set at time k. Finally, the results are weighted and fused to obtain the estimated state value at the current time. ; Finally, a resampling is performed and the particle weights are reset to a uniform distribution before proceeding to the next iteration.

7. A DOA tracking system based on interactive multi-model-assisted particle filtering, used to implement the DOA tracking method according to any one of claims 1 to 6, characterized in that, Includes the following modules: The particle set initialization module is used to receive the DOA of a single signal through a uniform linear array antenna, obtain observation information, and initialize the particle set. The particle multi-model prediction update module is used to perform interactive multi-model predictions on particles in the particle set and update the particle set. The particle set module for auxiliary particle filtering is used to perform spatial filtering on the updated particle state based on the observation information to obtain the particle set for auxiliary particle filtering. The particle state estimation module calculates the likelihood function to update the particle set based on the particle set of the auxiliary particle filter, performs weighted fusion, and obtains the estimated state value at the current time. The dynamic DOA tracking module uses the estimated state value at the current moment as the input for the next moment's iteration, and cyclically executes interactive multi-mode algorithm prediction updates, auxiliary particle filtering, and state estimation to achieve continuous dynamic DOA tracking.

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