A tracking method based on distributed likelihood consensus

Abstract

The application belongs to the technical field of target tracking, and particularly relates to a tracking method based on distributed likelihood consensus. The application is particularly suitable for multi-sensor cooperative positioning, target tracking and the like. The application linearizes a local likelihood function through first-order Taylor expansion, diffuses information in the whole network through a consensus protocol, and thus cooperatively approaches a global optimal estimation without a central processor. The method of the application guarantees the boundedness of estimation error, and effectively improves the overall estimation precision and stability of the distributed system under nonlinear observation conditions.

Description

Technical Field

[0001] This invention belongs to the field of target tracking technology, specifically relating to a tracking method based on distributed likelihood consensus. Background Technology

[0002] Traditional distributed filtering methods, such as distributed Kalman filtering (DKF), are mostly based on linear observation assumptions and Gaussian noise models, making it difficult to handle nonlinear systems and bounded non-Gaussian noise. Especially in practical applications, such as wireless positioning, robot cooperative navigation, and environmental monitoring, system dynamics and observation functions often exhibit strong nonlinear characteristics. Traditional linearization methods, such as extended Kalman filtering (EKF), are prone to estimation bias or even divergence when the nonlinearity is large.

[0003] Moving Level Estimation (MHE), a rolling optimization-based estimation method, is suitable for handling constrained nonlinear systems. MHE constructs a cost function using historical data within a sliding window, combining system dynamics and observation models to achieve an optimal estimate of the current state. Compared to Kalman filtering, MHE is more suitable for scenarios with bounded noise and state constraints, and exhibits better robustness in nonlinear systems.

[0004] However, extending MHE to distributed environments faces numerous challenges. The core issue lies in how to effectively integrate local information from various nodes in a distributed network to improve overall estimation accuracy. Existing distributed MHE methods mainly fall into two categories: one is methods based on state or information consensus, such as DMHE based on predictive state consensus proposed by Farina et al.; the other is methods based on cost function decomposition and coordination, such as Arrival Cost Consensus (AC-DMHE) proposed by Battistelli. These methods have improved distributed estimation performance to some extent, but certain problems still exist in nonlinear observation systems.

[0005] Furthermore, in practical scenarios such as passive localization and multi-target tracking, the location of the launch station is often unknown or time-varying, further increasing the complexity of distributed estimation. The traditional two-step method (first estimating the launch station location, then estimating the target location) ignores the correlation between parameters, leading to the accumulation of estimation bias. Although joint estimation methods can improve accuracy, their implementation in a distributed architecture still requires an efficient consensus mechanism. Summary of the Invention

[0006] This invention proposes a distributed mobility level estimation method based on likelihood consensus (LC-DMHE). By using local linearization and consensus iteration, it achieves efficient distributed state estimation under nonlinear observations to obtain more robust tracking performance.

[0007] The technical solution adopted in this invention is:

[0008] A tracking method based on distributed likelihood consensus is used to track all targets within the sensor range in a nonlinear sensor network, comprising the following steps:

[0009] S1. System modeling, considering a nonlinear dynamic system as follows:

[0010] ,

[0011] ,

[0012] in, This represents the state of the system at time t; For the observation of the i-th sensor; and Let represent the nonlinear dynamic function and the measurement function of sensor i at time t, respectively; and It is bounded noise;

[0013] S2, Local MHE Construction: For each sensor, a local cost function is constructed based on a sliding window of length T.

[0014] ,

[0015] in, This represents the predicted state of node i at time t. It is a positive definite weight matrix used for quantization state estimation. Compared with the predicted value The differences between them; This is the weight matrix, used to measure the importance of dynamic noise; N represents the set of sensor nodes. This represents the state estimate of node i at time t. With measured value The relevant likelihood function;

[0016] The likelihood function is the weighted Euclidean distance:

[0017] ,

[0018] in, Here is the positive definite weight matrix to be designed;

[0019] S3, Likelihood Consensus:

[0020] Measurement function of the sensor Perform a first-order Taylor expansion:

[0021] ,

[0022] in, To predict the state, Given the Jacobian matrix, the likelihood function after linearization becomes:

[0023] ,

[0024] in, For equivalent observation;

[0025] Initialize consensus parameters:

[0026] ,

[0027] ,

[0028] The sensor exchanges and updates local likelihood parameters with its neighbors:

[0029] ,

[0030] ,

[0031] Among them, consensus weight All are positive numbers and satisfy Define N i Let l be the set of in-neighbor nodes of node i, and l be the current consensus count. , This represents the total number of consensuses.

[0032] Reconstruct the global likelihood function after reaching a consensus:

[0033] ;

[0034] S4. Introducing the consensus likelihood into the cost function, we obtain the cost function required for the final estimate as follows:

[0035] ,

[0036] in, As a compensation factor, to ensure that the likelihood function after consensus remains consistent with its original form, it is usually taken as... ;

[0037] S5. By minimizing the cost function to obtain the state estimation sequence, the predicted state and weight matrix for the next time step are updated to achieve recursive estimation:

[0038] ,

[0039] ,

[0040] Where α is any scalar satisfying 0 < α < 1. Let represent any chosen positive definite scaling matrix, and we have:

[0041] ,

[0042] ,

[0043] ,

[0044] ,

[0045] ,

[0046] ,

[0047] .

[0048] The beneficial effects of this invention are:

[0049] This invention is designed for nonlinear dynamic systems and bounded non-Gaussian noise scenarios. Compared with traditional distributed target estimation methods, it reduces the communication overhead in the distributed network while ensuring estimation accuracy. It is suitable for practical applications such as multi-sensor cooperative localization and target tracking, improving the robustness and adaptability of distributed state estimation in real-world environments. Attached Figure Description

[0050] Figure 1 This is a simulation scenario diagram for multi-sensor single-target tracking.

[0051] Figure 2 A comparison chart of tracking position performance for different algorithms with the same number of consensus steps;

[0052] Figure 3 A comparison chart of tracking speed performance for different algorithms with the same number of consensus steps;

[0053] Figure 4 This diagram illustrates the impact of consensus steps on performance. Detailed Implementation

[0054] The present invention will now be described in detail with reference to embodiments:

[0055] Example:

[0056] This example considers a wireless sensor network consisting of N=25 sensor nodes, randomly deployed within a 600m × 600m two-dimensional monitoring area. The maximum communication distance between nodes is 120m. The sensors observe the target as follows: .

[0057] The target dynamic model is a linear Gaussian model. ,in

[0058] ,

[0059] in This represents the sampling interval. It is compared to the DMHE algorithm based on arrival cost consensus (denoted as the AC-DMHE algorithm). Both algorithms use the same parameter settings: sliding window T=4; initial prediction values... It follows a Gaussian distribution. ( ; ); any node weight matrix ; Matrix S is set as a 4-dimensional identity matrix.

[0060] Single-target tracking simulation experiments were conducted on the two algorithms. Through 100 Monte Carlo experiments, the RMSE of the two algorithms were compared under the condition of increasing the number of consensus steps with the number of samples and under the condition of increasing the total number of samples with the number of consensus steps.

[0061] Tracking effect:

[0062] To verify the tracking performance of the algorithm, we compared it with different algorithms and observed its performance by changing the number of consensus steps. Figure 1 It can be seen that the algorithm has high tracking accuracy; under random sensor networks, the actual trajectory and the tracked trajectory almost coincide, as shown in the simulation. Figures 2-3 The RMSE comparison chart shows that the tracking error of this algorithm is consistently lower than that of AC-DMHE under a fixed communication step size, indicating higher tracking accuracy. Figure 4 This demonstrates that the algorithm can achieve higher estimation accuracy with fewer consensus steps, confirming that the likelihood consensus-based tracking method proposed in this invention has good tracking performance.

Claims

1. A tracking method based on distributed likelihood consensus, used to track all targets within the sensor range in a nonlinear sensor network, characterized in that, Includes the following steps: S1. System modeling, considering a nonlinear dynamic system as follows: ， ， in, This represents the state of the system at time t; For the observation of the i-th sensor; and Let represent the nonlinear dynamic function and the measurement function of sensor i at time t, respectively; and It is bounded noise; S2, Local MHE Construction: For each sensor, a local cost function is constructed based on a sliding window of length T. ， in, This represents the predicted state of node i at time t. It is a positive definite weight matrix used for quantization state estimation. Compared with the predicted value The differences between them; This is the weight matrix, used to measure the importance of dynamic noise; N represents the set of sensor nodes. This represents the state estimate of node i at time t. With measured value The relevant likelihood function; The likelihood function is the weighted Euclidean distance: ， in, Here is the positive definite weight matrix to be designed; S3, Likelihood Consensus: Measurement function of the sensor Perform a first-order Taylor expansion: ， in, To predict the state, Given the Jacobian matrix, the likelihood function after linearization becomes: ， in, For equivalent observation; Initialize consensus parameters: ， ， The sensor exchanges and updates local likelihood parameters with its neighbors: ， ， Among them, consensus weight All are positive numbers and satisfy Define N i Let l be the set of in-neighbor nodes of node i, and l be the current consensus count. , This represents the total number of consensuses. Reconstruct the global likelihood function after reaching a consensus: ； S4. Introducing the consensus likelihood into the cost function, we obtain the cost function required for the final estimate as follows: ， in, As a compensation factor, to ensure that the likelihood function after consensus remains consistent with its original form, it is usually taken as... ; S5. By minimizing the cost function to obtain the state estimation sequence, the predicted state and weight matrix for the next time step are updated to achieve recursive estimation: ， ， Where α is any scalar satisfying 0 < α < 1. Let represent any chosen positive definite scaling matrix, and we have: ， ， ， ， ， ， 。

Images