A distributed robust Wasserstein estimation method resistant to sensor unknown bounded noise and intermittent impulse noise
By employing Wasserstein distance and distributed consensus mechanisms, the problems of unknown bounded noise and intermittent impulse noise in sensor networks are solved, achieving efficient and accurate state estimation and improving the accuracy and anti-interference capability of distributed fusion.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- HENAN UNIVERSITY OF TECHNOLOGY
- Filing Date
- 2026-04-07
- Publication Date
- 2026-06-30
Smart Images
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Abstract
Description
Technical Field
[0001] This invention relates to the field of distributed systems and networked control, specifically a distributed robust Wasserstein estimation method that resists unknown bounded noise and intermittent impulse noise from sensors. Background Technology
[0002] Multi-sensor information fusion achieves globally consistent, high-precision estimation by integrating the outputs of multiple local estimators. It is widely used in target localization, autonomous driving, and other fields, and is one of the key technologies in intelligent system architecture. Distributed estimation eliminates the need for a central fusion node; each node communicates only with its neighboring nodes, offering significant advantages in bandwidth usage, computational overhead, and fault tolerance. In recent years, consistency-based strategies have further propelled the development of distributed estimation.
[0003] However, existing methods still face key challenges. In real-world scenarios, sensor observation noise is often unknown and time-varying, and is easily superimposed with intermittent impulse noise, leading to biased estimations or even divergence in traditional second-order statistical filters. Traditional linear weighted consensus mechanisms are highly sensitive to outlier estimates, with even a few outliers causing global estimation bias. Existing methods mostly rely on first- and second-order statistics, making it difficult to characterize the complete distribution information of strongly nonlinear and non-Gaussian systems. Methods based on Huber functions, heavy-tailed distributions, or information theory criteria also cannot comprehensively characterize the distribution geometry and have limited ability to handle transient impulse interference.
[0004] Wasserstein distance, as a core metric in optimal transmission theory, effectively characterizes geometrical differences in distributions and does not rely on pre-defined noise distribution patterns, providing a new approach for constructing robust fusion methods. Therefore, how to organically combine the Wasserstein distance metric with distributed consensus mechanisms to build a robust fusion framework for efficient and accurate state estimation under unknown bounded noise and intermittent impulse noise interference remains a crucial technical problem that urgently needs to be solved. Summary of the Invention
[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a distributed robust Wasserstein estimation method that resists unknown bounded noise and intermittent impulse noise in sensors, solves the problem of robust state estimation of sensor networks in complex noise environments, and improves the accuracy and anti-interference capability of distributed fusion.
[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows: S1. In the absence of impulse noise or shot noise, the Dirac δ distribution is degraded, and then the Wasserstein distance between the posterior error distribution and the Dirac distribution is minimized to obtain the solution of the local adaptive Wasserstein state estimation. S2. When impulse noise or shot noise exists in the sensor network, based on the Wasserstein estimation framework established in step S1, calculate the minimum Wasserstein distance between the noise estimates of the current node and the historical time, and the minimum Wasserstein distance between the noise estimates of the current node and the neighboring nodes, respectively. S3. Based on the Wasserstein distance obtained in step S2, and combined with the noise anomaly state of the detected node and its adjacent nodes using a preset threshold, design corresponding Wasserstein dynamic weight strategies according to the normal / abnormal state of the node. S4. Each sensor node broadcasts its local estimation information to its neighboring nodes and simultaneously receives estimation information from its neighboring nodes. Based on the weight strategy obtained in step S3, it performs a consistent iterative update on the information pairs. After the iteration is completed, the global optimal state estimation result at the current moment is obtained.
[0007] Further, in step S1, the following is included: Assume the sensor measurement model for node i is defined as follows: (Its linearized measurement matrix is) ), its measurement noise It is unknown, including unknown noise. Intermittent impulse noise mean and variance It is not a fixed value; it can change over time. In the case of a nonlinear state model (Its linearized state transition matrix is) , It is the state vector at the next moment. As the random expansion vector to be estimated, its prior estimate is: ,and For prior noise estimation; the measurement model is redefined as Therefore, the linear mapping of the new posterior estimate is defined as
[0008] in, , , and , , These are the coefficient matrices for the state and the measurement, respectively.
[0009] When the new posterior estimation error Follows distribution hour, Represented as
[0010] exist hour, for
[0011] if The mean and variance of the new posterior estimation error are expressed as follows:
[0012] New posterior estimation error distribution With Dirac distribution (focused on) The 2-Wasserstein distance between the degenerate distributions at the location can be expressed as:
[0013] By minimization The solution for the locally adaptive Wasserstein state estimation with unknown measurement noise statistics is obtained.
[0014] Further, in step S2, the following is included:
[0015] Consider a scenario where the measurement noise statistics are unknown and there is impulse noise / shot noise. Impulse noise / shot noise exists only in a few sensors at any given time, and the unknown noise statistics change synchronously in all sensors. If the magnitude of the innovation vector of node i exceeds the preset range, it is determined that there is an abnormality in impulse / shot noise in the sensor system.
[0016] The instantaneous noise vector follows a mean of Covariance is Given the distribution of noise, calculate the minimum 2-Wasserstein distance between the current time step and the previous time step's noise statistical estimate:
[0017] in, The distance from the previous moment. This represents the distance at the current moment.
[0018] Next, calculate the minimum 2-Wasserstein distance between node i and its neighboring node j, based on their noise statistical estimates:
[0019] in, and Based on the above distances, construct the distance matrix D for node i.
[0020] Further, in step S3, the following is included: For node i, the result obtained in step S2 With preset threshold In comparison, detect the noise anomaly state of the node itself: if the previous time... and the current moment ,or and Then the exception indicator variable ;otherwise To determine whether node i exhibits continuous noise variation or impulse noise, consider the following: or At that time, the result obtained in step S2 With threshold By comparing and combining the weighted average consistency of network topology, a Wasserstein weighting strategy is designed.
[0021] Further, in step S4, the following is included: The local estimate of node i given in step S1 is defined as... Based on the weights obtained in step S3 Wasserstein consistency update rules for design information pairs:
[0022] Where l is the number of iterations, and after L consensus iterations, the final global state estimate of node i is obtained. That is, the distributed robust Wasserstein state estimation result.
[0023] Furthermore, the present invention also proposes an electronic device including a memory and a processor, wherein the memory stores a computer program that can run on the processor, and when the processor executes the computer program, it implements the steps of the distributed robust Wasserstein estimation method against sensor unknown bounded noise and intermittent impulse noise described above.
[0024] Furthermore, the present invention also proposes a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the distributed robust Wasserstein estimation method described above for resisting unknown bounded noise and intermittent impulse noise from sensors.
[0025] Compared with the prior art, the beneficial effects of the above technical solution adopted by the present invention are as follows: This invention jointly models the target state and sensor noise into an extended state vector. Local adaptive estimation is achieved by minimizing the Wasserstein distance between the posterior error distribution and the Dirac reference distribution. This eliminates the need for prior statistical assumptions about noise, effectively adapting to unknown, time-varying bounded noise. Furthermore, it degenerates into an adaptive Kalman filter in Gaussian scenarios, exhibiting good compatibility. This invention further proposes an anomaly detection and dynamic weighting strategy based on Wasserstein distance. This strategy accurately identifies impulse noise anomalies in nodes, adaptively adjusts the fusion weights, and effectively suppresses the interference of abnormal nodes on the global estimation, thus overcoming the inherent sensitivity of traditional consensus methods to outliers. By constructing a Wasserstein consensus mechanism, this invention dynamically adjusts the fusion strategy by fusing the estimation information of the current, historical, and neighboring nodes of a node, achieving collaborative fusion of environmental perception. Attached Figure Description
[0026] Figure 1 This is a flowchart of the local and distributed robust algorithms in the embodiments of the present invention.
[0027] Figure 2 The diagram shows the tracking experimental platform in this embodiment of the invention, where (a) is the experimental platform environment, (b) is the intelligent vehicle, (c) is the radar sensor, and (d) is the sensor network.
[0028] Figure 3 The diagram shows the radar detection range and the actual target trajectory over 40 seconds in this embodiment of the invention, where (a) is the actual radar detection range, (b) is the ambiguous radar detection range, and (c) is the actual trajectory detected by the Nokov system.
[0029] Figure 4 This is a comparison chart of the position estimation errors of different methods in the embodiments of the present invention. Detailed Implementation
[0030] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and should not be used to limit the scope of protection of the present invention.
[0031] Specific Implementation Plan 1: Combining Figure 1As shown, this invention provides a distributed robust Wasserstein estimation method resistant to unknown bounded noise and intermittent impulse noise from sensors. This method jointly models the target state and sensor noise as an extended state vector. By minimizing the Wasserstein distance between the posterior error distribution and the origin Dirac reference distribution, it achieves joint adaptive estimation of the state and unknown noise without requiring prior noise assumptions. Then, based on the Wasserstein distance, an anomaly detection mechanism is designed to accurately identify anomalous nodes with impulse noise. Finally, by combining the current, historical, and neighboring node estimation information, a Wasserstein consistency mechanism is constructed to suppress interference from anomalous nodes. The specific steps are as follows:
[0032] Step 1: Solve for the optimal solution of the local adaptive Wasserstein state estimate. This is achieved by minimizing... The linear mapping between the posterior and prior state estimates and their estimated covariance is calculated as follows: and Given that the current prediction error covariance is... The measurement noise is estimated as The locally adaptive Wasserstein estimator is designed as follows:
[0033] in, , and .
[0034] When the measurement noise follows a Gaussian distribution At that time, It has a mean ,variance and new information At this point, it degenerates into a traditional Kalman-type adaptive filter.
[0035] Step 2: Calculate the Wasserstein distance and construct the distance matrix. Consider a scenario where the measurement noise statistics are unknown and impulse noise / shot noise exists. Impulse noise / shot noise exists only in a few sensors at any given time, and the unknown noise statistics change synchronously in all sensors. If the magnitude of the innovation vector of node i exceeds a preset range, it is determined that the sensor system has an abnormal impulse / shot noise.
[0036] The instantaneous noise vector follows a mean of Covariance is Given the distribution of noise, calculate the minimum 2-Wasserstein distance between the current time step and the previous time step's noise statistical estimate:
[0037] in, The distance from the previous moment. This represents the distance at the current moment.
[0038] Next, calculate the minimum 2-Wasserstein distance between node i and its neighboring node j, based on their noise statistical estimates:
[0039] in, and Based on the above distances, construct the distance matrix D for node i.
[0040] Step 3: Anomaly Detection and Dynamic Weight Design. For node i, the weights obtained in Step 2 are... With preset threshold In comparison, detect the noise anomaly state of the node itself: if the previous time... and the current moment ,or and Then the exception indicator variable ;otherwise The system determines whether node i exhibits continuous noise changes or impulse noise. Based on the above strategy, the anomaly detection and dynamic weight design are as follows: like The result obtained in step two With threshold For comparison, the detection rules are as follows: in, This indicates that the adjacent node j is normal; otherwise, it is abnormal. Combining the weighted average consistency of the network topology, the Wasserstein weight strategy can be designed using the Metropolis weight standard.
[0041] in, and Obtained using the Metropolis weighting standard.
[0042] like The result obtained in step two With threshold By comparison, the anomaly detection rules are obtained as follows:
[0043] in, This indicates that sensor node i is abnormal while its neighboring nodes are normal; otherwise, all its noise statistics are altered. The Wasserstein weighting strategy is designed as follows: Step 4: Consistency Iteration and Global Estimation. The local estimates for node i given in Step 1 are defined as... Based on the weights obtained in step three Wasserstein consistency update rules for design information pairs:
[0044] Where l is the number of iterations, and after L consensus iterations, the final global state estimate of node i is obtained: The final result is the Distributed Robust Wasserstein State Estimation (DRWSE).
[0045] Specific Implementation Scheme Two: This invention uses a real target tracking experimental platform to verify its performance. For example... Figure 2 As shown, the platform consists of the following components: 1) Target device: A smart car measuring 28cm×18cm, moving along a circular path with a radius of 95cm, with a movement cycle of 40s and an average speed of 75cm / s; 2) Measurement equipment: The detection range of low-precision radar and the ambiguity range within the target trajectory are respectively as follows: Figure 3 (a) and (b), four 24GHz ranging radar sensors form a distributed sensor network with a sampling period of 100ms and a ranging accuracy of 5cm; 3) Truth-of-fact device: Nokov motion capture system, which includes 6 Mars 2 cameras, with a 3D positioning accuracy of ±0.3mm and a sampling frequency of 60Hz, used to provide the truth value of the target position.
[0046] During the experiment, the ideal trajectory was as follows: Figure 3 As shown in (c), within the motion interval of [10s, 35s], artificial baffles are added to radars 2 and 3 every 2s to generate intermittent pulse noise, simulating electromagnetic interference and obstruction in a real-world scenario. The process noise includes interference from ground friction and the motor, and the vehicle exhibits small lateral oscillations as it moves in a circle around the copper coil. These disturbances are appropriately modeled as zero-mean Gaussian noise, i.e. .
[0047] Parameter settings: Provided by the Nokov system, the initial state and corresponding covariance are set as follows: and The anomaly detection thresholds are 0.1 and 0.15, respectively, and the number of consistency iterations is L=5.
[0048] Comparison techniques: Three typical techniques in the field of distributed fusion estimation were selected as references: distributed volumetric information filtering, distributed adaptive volumetric information filtering, and robust distributed filtering based on Wasserstein weighted consistency. All comparison techniques were set according to the optimal parameter configuration criteria published in their original literature.
[0049] This experiment uses three metrics to evaluate the algorithm's performance: mean, median, MAE (mean absolute error), and STD (standard deviation). The performance comparison results for position estimation are shown in Table 1, and the position estimation error curves are shown in Figure 1. Figure 4 As shown in Table 1 and Figure 4 It can be seen that despite the combined challenges of low-precision radar (≈5 cm) positioning errors, vehicle positioning errors, and artificial impulse noise, the algorithm still achieves a positioning accuracy of approximately 5.19 cm. Compared with local estimation, Metropolis weighted rule, or adaptive distribution estimation, this fusion method improves the estimation accuracy by approximately 2 times, while also enhancing error stability and robustness. Experimental results show that, in scenarios with unknown bounded noise and intermittent impulse noise, the estimation accuracy and error stability of this invention are significantly superior to existing mainstream algorithms, achieving the intended purpose of the invention.
[0050]
[0051] Specific Implementation Scheme 3: The present invention provides an electronic device, including a memory and a processor. The memory stores a computer program that can run on the processor. When the processor executes the computer program, it implements the steps of the distributed robust Wasserstein estimation method against sensor unknown bounded noise and intermittent impulse noise described above.
[0052] Specific Implementation Scheme 4: The present invention provides a computer-readable storage medium storing a computer program thereon. When the computer program is executed by a processor, it implements the distributed robust Wasserstein estimation method against unknown bounded noise and intermittent impulse noise described above.
[0053] The specific embodiments of the present invention have been given above, but the present invention is not limited to the described embodiments. Under the concept given by the present invention, the technical means in the above embodiments can be changed, replaced, or modified in a way that is easy for those skilled in the art to conceive of, and the effect is basically the same as the corresponding technical means in the present invention, and the purpose of the invention is also basically the same. The technical solution formed in this way is a fine-tuning of the above embodiments, and such technical solution still falls within the protection scope of the present invention.
Claims
1. A distributed robust Wasserstein estimation method resistant to sensor unknown bounded noise and intermittent impulse noise, applied to a distributed sensor network system containing multiple sensor nodes, comprising local state estimation of measurement data from each sensor node and distributed fusion through information exchange between neighboring nodes, characterized in that, Includes the following steps: S1. In the absence of impulse noise or shot noise, the Dirac δ distribution is degraded, and then the Wasserstein distance between the posterior error distribution and the Dirac distribution is minimized to obtain the solution of the local adaptive Wasserstein state estimation. S2. When impulse noise or shot noise exists in the sensor network, based on the Wasserstein estimation framework established in step S1, calculate the minimum Wasserstein distance between the noise estimates of the current node and the historical time, and the minimum Wasserstein distance between the noise estimates of the current node and the neighboring nodes, respectively. S3. Based on the Wasserstein distance obtained in step S2, and combined with the noise anomaly state of the detected node and its adjacent nodes using a preset threshold, design corresponding Wasserstein dynamic weight strategies according to the normal / abnormal state of the node. S4. Each sensor node broadcasts its local estimation information to its neighboring nodes and simultaneously receives estimation information from its neighboring nodes. Based on the weight strategy obtained in step S3, it performs a consistent iterative update on the information pairs. After the iteration is completed, the global optimal state estimation result at the current moment is obtained.
2. The distributed robust Wasserstein estimation method against unknown bounded noise and intermittent impulse noise of sensors according to claim 1, characterized in that: Step S1 includes: Given a nonlinear state model Its linearized state transition matrix is Sensor model of node i Its linearized measurement matrix is Assume the measurement noise is unknown bounded noise. Its mean and variance can change over time, and when there is no impulse noise or shot noise. By minimizing the Wasserstein distance, a linear mapping between the posterior and prior state estimates and their estimated covariance is calculated, and a locally adaptive Wasserstein estimator is designed.
3. The distributed robust Wasserstein estimation method against unknown bounded noise and intermittent impulse noise of sensors according to claim 1, characterized in that: In step S2, considering the scenario where the measurement noise statistics are unknown and there is impulse noise / shot noise, the minimum 2-Wasserstein distance between the noise statistics estimates before and after the time step and between adjacent nodes is calculated.
4. The distributed robust Wasserstein estimation method against unknown bounded noise and intermittent impulse noise of sensors according to claim 1, characterized in that: In step S3, the minimum distance from step S2 will be... With preset threshold Compare and detect the noise state of node i: if in the previous time step and the current moment ,or and Then the exception indicator variable ;otherwise Determine whether node i contains continuously changing noise or impulse noise; Based on this, a Wasserstein weighting strategy was designed.
5. The distributed robust Wasserstein estimation method against unknown bounded noise and intermittent impulse noise of sensors according to claim 1, characterized in that: In step S4, the local estimation pair of node i given in step S1 and the weights obtained in step S3 are used as the basis. We design Wasserstein consistency update rules for information pairs and obtain distributed robust Wasserstein state estimation results.
6. An electronic device comprising a memory and a processor, wherein the memory stores a computer program executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the distributed robust Wasserstein estimation method against sensor unknown bounded noise and intermittent impulse noise as described in any one of claims 1 to 5.
7. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the distributed robust Wasserstein estimation method against sensor unknown bounded noise and intermittent impulse noise as described in any one of claims 1 to 5.