Unknown correlation multi-sensor state and noise covariance joint estimation method

Abstract

The invention discloses an unknown related multi-sensor state and noise covariance joint estimation method. The method comprises the following steps: S1, initializing a multi-sensor system model and parameters of a local Kalman filter of each sensor; s2, on the basis of the initialized system model and filter parameters, each sensor carries out target state prediction and updating, and an innovation sequence is generated and accumulated; s3, based on the accumulated information sequence and the sliding time window with the preset length, each sensor carries out estimation to obtain a local process noise covariance and a local measurement noise covariance; s4, based on the estimated local noise covariance, distributing a fusion weight for each sensor; and S5, performing weighted fusion on the local process noise covariance and the local measurement noise covariance based on the fusion weight distributed in the step S4 to obtain global process noise covariance estimation and global measurement noise covariance estimation.

Description

Technical Field

[0001] This invention relates to the field of signal processing, and more specifically to a method for jointly estimating the covariance of unknown correlation multi-sensor states and noise. Background Technology

[0002] Kalman filters exhibit optimal performance in state estimation for linear Gaussian systems. However, in many practical systems, such as low-cost integrated navigation and positioning systems, energy-based target positioning, and fault-tolerant control systems, the covariance of process noise and measurement noise is often unknown or changes over time, and offline calibrated noise parameters may also become invalid. Improper noise covariance settings can significantly weaken the filtering effect, leading to increased state estimation bias and, in severe cases, even filter divergence. To estimate unknown noise covariance online, various algorithms utilizing historical data have been proposed, including Bayesian estimation methods, maximum likelihood estimation methods, covariance matching methods, minimax methods, subspace identification methods, and correlation function methods. Among these, the correlation function method has received widespread attention due to its moderate computational complexity and lack of special assumptions about the noise model. The correlation function method was initially developed as a three-step noise statistical estimation scheme based on the autocorrelation of the innovation sequence, which was later simplified to a single-step autocovariance least squares method. Building upon this foundation, a series of improvements have been developed, including simultaneous estimation of noise covariance and state perturbation, uniqueness conditions for noise variance estimation, optimal weight selection with minimum variance, and a novel differential estimation method for unbiased estimation under finite data. However, when available data is limited, such as when sensor sampling sequences are short, the estimation results are prone to large variances, leading to reduced reliability.

[0003] With the rise of networked sensing systems, multi-sensor information fusion has become an important means to improve estimation accuracy. Fusing the information sequences from multiple sensors can effectively increase the amount of effective data, thereby reducing estimation variance to some extent. While traditional centralized fusion methods can obtain the globally optimal estimate using data from all sensors, they suffer from high communication overhead, poor scalability, and a high risk of single-point failure. In contrast, distributed fusion can reduce communication and computational burdens and has fault tolerance, but it needs to address the impact of correlations between sensor information. When the cross-covariance between multi-sensor measurement data is known, the optimal linear fusion estimation formula can be derived from existing fusion derivations and extended to the fusion of any number of estimates. However, in practical applications, the information from different sensors often exhibits unknown correlations, making the covariance cross-calculation algorithm a common approach. This method does not require prior knowledge of the correlation between sensor estimates and can ensure the consistency of the fused estimate through conservative weighting. Initially used for conservatively fusing two estimates, it was later extended to batch fusion of multiple estimates, and improvements such as accelerated sequential fusion schemes and diffusion fusion schemes have emerged. Studies have shown that covariance cross-fusion exhibits robust optimal performance in the dual-sensor scenario, but becomes suboptimal in the multi-sensor scenario due to the conservatism of the Minkowski sum set. It should be noted that the covariance cross-fusion method is primarily used for state estimation fusion and does not offer a direct solution for the simultaneous estimation of joint state and noise covariance. Therefore, while existing technologies include distributed autocovariance least squares noise covariance estimation for multi-sensor systems, a systematic method capable of achieving high-precision joint estimation and fusion of state and noise covariance under unknown sensor correlations is still lacking. Summary of the Invention

[0004] To overcome the technical problems mentioned above, the present invention aims to overcome the shortcomings of existing noise covariance estimation methods in multi-sensor environments, such as decreased accuracy and difficulty in fusion when the correlation of sensor outputs is unknown. The invention provides a method for joint estimation and fusion of state and noise covariance in multi-sensor systems. The technical problem this method addresses is: when the observation data from multiple sensors have unknown correlations and the noise statistical parameters are uncertain, how to effectively fuse the information from each sensor to reduce the noise covariance estimation error, while ensuring the consistency of the fused estimation, so that the distributed Kalman filter can still stably track the system state with near-optimal accuracy. In other words, the present invention aims to propose a multi-sensor noise covariance adaptive fusion identification strategy that does not rely on prior correlation information, improving the robustness and reliability of distributed state estimation in complex environments, and avoiding the problems of decreased filtering accuracy or even failure caused by noise statistical parameter mismatch or data correlation in existing technologies.

[0005] To achieve the above objectives, this invention provides a method for joint estimation of the state and noise covariance of unknown correlated multi-sensor systems, comprising the following steps:

[0006] S1. Initialize the multi-sensor system model and the parameters of the local Kalman filter for each sensor;

[0007] S2. Based on the initialized system model and filter parameters, each sensor performs target state prediction and update, generating and accumulating the information sequence;

[0008] S3. Based on the accumulated information sequence, each sensor estimates the local process noise covariance and the local measurement noise covariance based on a sliding time window of a preset length.

[0009] S4. Assign fusion weights to each sensor based on the estimated local noise covariance;

[0010] S5. Based on the fusion weights allocated in S4, the local process noise covariance and the local measurement noise covariance are weighted and fused to obtain the global process noise covariance estimate and the global measurement noise covariance estimate.

[0011] Preferably, S1 includes:

[0012] Establish a state-space model and a measurement model for the target motion;

[0013] Initialize the state estimates and covariance matrices of the local Kalman filters for each sensor;

[0014] Set the initial process noise covariance matrix and the initial measurement noise covariance matrix for the local Kalman filter of each sensor.

[0015] Preferably, S2 includes: each sensor acquiring the observation value at the current moment; predicting the target state and the predicted observation based on the state space model constructed in S1 and using the time update step of the local Kalman filter; calculating the observation information and performing the measurement update step of the local Kalman filter based on the observation information to obtain the corrected state estimate and the updated estimated covariance; and accumulating the observation information by adding it to the information sequence of the local Kalman filter.

[0016] Preferably, S3 includes:

[0017] For each sensor, collect the innovation sequence within the sliding time window; calculate the sample autocovariance set of the innovation sequence; based on the system's state transition matrix, observation matrix, and current Kalman gain matrix, construct a system of linear equations about the unknown process noise covariance and the unknown measurement noise covariance; solve the system of linear equations to obtain the local process noise covariance estimate and the local measurement noise covariance estimate for the sensor.

[0018] Preferably, step S4 includes: calculating the upper bound of the estimated variance based on the residual statistics of the local noise covariance estimation of each sensor; and assigning fusion weights to the corresponding sensors according to the proportion of their normalized inverses based on the upper bounds of the estimated variances.

[0019] Preferably, S5 includes:

[0020] The local process noise covariance estimate of each sensor and its corresponding uncertainty measure, as well as the local measurement noise covariance estimate of each sensor and its corresponding uncertainty measure, are used as inputs.

[0021] By applying the batch covariance cross-fusion formula and combining it with the fusion weights allocated in step S4, the global process noise covariance estimate and its uncertainty, as well as the global measurement noise covariance estimate and its uncertainty, are calculated.

[0022] Preferably, the method further includes: using the global process noise covariance estimate and the global measurement noise covariance estimate obtained in S5 to update the corresponding noise covariance parameters in the local Kalman filters of each sensor, respectively.

[0023] Preferably, the method further includes: adaptively adjusting the image segmentation threshold in the target detection stage based on the updated global process noise covariance estimate, wherein the segmentation threshold is positively correlated with the norm or weighted sum of the process noise covariance.

[0024] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0025] This invention significantly improves the estimation accuracy of noise covariance and the performance of state filtering even when sensor observation data are correlated and noise statistics are unknown. By fusing information from multiple sensors, it avoids the problem of increased variance caused by insufficient data from a single sensor, making the estimates of process noise and measurement noise more accurate and stable. The covariance cross-fusion strategy ensures the consistency of the estimation, preventing the underestimation of uncertainty due to unknown correlations, thus avoiding the adverse consequences of over-reliance or even divergence in the fusion filter. Simulation results show that, compared with traditional methods, this invention can significantly reduce the error of noise covariance estimation. For example, for the estimation of process noise covariance in a two-dimensional system, the root mean square error is reduced by about 70% compared to the single-sensor ALS method; the measurement noise variance estimation error is reduced by more than 80%. Furthermore, the state estimation error of the fusion filter is also significantly reduced; for example, in target tracking experiments, the global state root mean square error is reduced by more than 15% compared to local estimation alone. This demonstrates that this invention can effectively solve the estimation difficulties caused by unknown noise correlations in multi-sensor environments, enabling the filter to maintain stable operation and achieve near-optimal estimation accuracy even in complex scenarios with mismatched noise statistical models or correlation between sensor data. Therefore, this invention improves the robustness of distributed state estimation and filtering systems to noise uncertainties, meeting the needs of high-precision and high-reliability state perception in practical engineering. Attached Figure Description

[0026] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0027] Figure 1 This is a block diagram of a cooperative tracking system architecture based on adaptive Kalman filtering.

[0028] Figure 2 The estimation results of the state noise and observation noise covariance matrices Q and R for dynamic target tracking using an adaptive Kalman filter are shown in the figure.

[0029] Figure 3 The flowchart for fusion weight allocation shows how to calculate and allocate fusion weights based on the upper bound of the variance estimated by the local noise covariance of each sensor.

[0030] Figure 4 To illustrate the comparative experimental flowchart, this paper demonstrates the execution flow and performance evaluation process of the method of this invention and two comparative methods (DKF and DKF-ACLS) under the same experimental conditions. Detailed Implementation

[0031] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0032] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0033] Example 1

[0034] This embodiment provides a method for joint estimation of the state and noise covariance of unknown correlation multi-sensor systems, and verifies the accuracy of the invention in the joint estimation direction through comparative experiments. The specific steps include:

[0035] S1. Initialize the multi-sensor system model and the parameters of the local Kalman filter for each sensor.

[0036] Establish a system model of the target motion (including a state-space model and a measurement model), such as Figure 1 As shown in the process, the Kalman filter state is initialized. and covariance Given the initial process noise covariance matrix and the measurement noise covariance matrix. and .

[0037] This embodiment designs a scenario where a fully connected static sensor network consisting of 10 sensors (radar sensors used for tracking moving targets such as vehicles or pedestrians) tracks the same dynamic target. System Status ,Measurement The state-space model is as follows:

[0038] .

[0039] Among them, process noise Noise measured by each sensor All noise is zero-mean Gaussian white noise. Let the noise covariance of the actual process be... The actual measured noise covariance is (Scalar, here the noise variance of the 10 sensors is the same). The initial state truth value x0 is randomly generated, initial state estimation. Take the true value, add a small perturbation, and let the initial estimated covariance be... Without knowing the true noise covariance, we first give an imprecise initial guess: assume an initial value for the process noise covariance that is too large. And the relatively large initial values ​​of the measurement noise variance of each sensor. This is to simulate model mismatch.

[0040] Based on the initial parameters described above, Kalman filtering is run. After the initial convergence of the state estimation for each sensor, its Kalman gain matrix also tends to a steady state. In order to evaluate the performance of different methods under the condition of unknown correlation, this embodiment assumes that the observation noise of each sensor is independent. However, since they share the same system state and are driven by common process noise, there is actually an implicit correlation between the information sequences of different sensors. This provides a basis for testing the effectiveness of the fusion algorithm.

[0041] S2. Based on the initialized system model and filter parameters, each sensor performs target state prediction and update, generating and accumulating the information sequence, as follows: Figure 2 As shown.

[0042] The Kalman filter time update step predicts the target state based on the state-space model constructed in S1. and predictive observation The observational information is calculated using the measurement model constructed based on S1. According to the predicted covariance Calculating Kalman gain by measuring noise covariance And perform filtered measurement updates to obtain the corrected state estimate. and the updated estimated covariance .

[0043] S3. Based on the accumulated information sequence, each sensor estimates the local process noise covariance and the local measurement noise covariance based on a sliding time window of a preset length.

[0044] This embodiment uses a sliding time window method to periodically estimate the noise covariance. During the filtering process, whenever noise covariance is collected... When processing data at a step size, covariance estimation and fusion are performed on the innovation sequences of each sensor within this window. Specifically, innovation sequences of length 150 are collected for each sensor. The lag order is calculated as follows: (Including 0, a total of 5 values) The new information autocovariance sequence Combining the known F and H matrices of the system with the current steady-state gain K i Construct the design matrix A of sensor i i and observation vector b i This leads to a linear equation. ,in It includes the covariance elements of the process noise and measurement noise to be estimated. The local noise covariance estimate for each sensor is obtained by least squares solution with regularization constraints. and .

[0045] The current new information e k When a new information sequence window is added, and the accumulated amount of new information data reaches the preset window length or a specified update interval, the autocovariance least squares (ALS) algorithm is used to estimate the current process noise covariance. and measurement noise covariance Specifically, this includes: selecting a sliding time window of length N to collect the new information sequence. Calculate the set of sample autocovariances of the innovation sequence within the window. Constructing information about process noise covariance and measurement noise covariance linear equations ,in The coefficient matrix is ​​determined by the Kalman filter state transition matrix and the observation matrix. To be and A vector formed by arranging unknown elements in a vector. for The expanded vector is obtained by solving the problem. Restored and In this embodiment, the linear equations are solved using the least squares closed-form solution. get.

[0046] S4. Assign fusion weights to each sensor based on the estimated local noise covariance.

[0047] Will get and The feedback is used in the Kalman filtering process of subsequent frames, where Used to update the process noise covariance in S2 Used to update the measurement noise covariance in S2; and based on Adjust the threshold for object detection in the next frame The threshold adjustment rule is as follows: ,in, From A function to extract the measure of motion uncertainty.

[0048] For robustness, this embodiment performs Monte Carlo simulation sampling on the above process, repeats the independent experiment 500 times, and takes the average of the obtained noise covariance estimates as the final result. , The fusion weights are selected by normalizing the inverse of the variance traces of each estimate, thus giving greater weight to more accurate sensor estimates, such as... Figure 3 The process is shown. The result after fusion... and The filter parameters will be used to calibrate each sensor.

[0049] S5. Based on the fusion weights allocated in S4, the local process noise covariance and the local measurement noise covariance are weighted and fused to obtain the global process noise covariance estimate and the global measurement noise covariance estimate.

[0050] Utilize each The upper bound of the estimated variance is calculated using residual statistics. According to the batch CI fusion algorithm proposed in this embodiment, Normalized reciprocal proportional weighting .Will Substituting into the CI fusion formula, for and We perform weighted fusion to obtain a global noise covariance estimate. and .

[0051] Example 2

[0052] To verify the superiority of this invention over the prior art, this embodiment sets up three cases as control experiments, the process of which is as follows: Figure 4 As shown.

[0053] Utilize the fused and After reconfiguring the Kalman filter for each sensor, the system state was continued to be tracked and estimated, and the performance of each scheme was evaluated. For comparison, the following three methods were tested under the same conditions in this embodiment:

[0054] a) DKF (Noise Covariance Unknown): Directly use the initial guess. , Run a distributed Kalman filter (i.e., without correcting noise statistics).

[0055] b) DKF-ACLS (Single Sensor Identification): Each sensor is independently estimated using the ACLS method. , Then, the states are fused using their respective filters.

[0056] c) DKF-ACLS-BCI (Method of this invention): First obtain , Then, state fusion estimation is performed.

[0057] Simulation results show that the method (c) of this invention significantly outperforms the other two comparative methods in terms of state estimation accuracy. Specific quantification results are as follows: for the two diagonal elements of the process noise covariance... , fusion estimate The deviation from the true value is significantly smaller than that of any single sensor. ; calculated through 500 experiments and The estimated root mean square errors are 0.20 and 0.12 for method (c), and 0.72 and 0.41 for method (b). Method (a) is not comparable here because it does not update the covariance, indicating that the method of the present invention reduces the process noise variance estimation error by approximately 2 / 3. For measurement noise variance... The estimated root mean square error of method (c) is 0.0019, which is much lower than that of method (b) (0.0128).

[0058] More importantly, by combining information from multiple sensors, the variance of the estimated values ​​is significantly reduced: for example, the uncertainty matrix of the fused estimate... The trace is approximately 57.08, estimated by only a single sensor. The variance is 1 / 10 of the trace (approximately 570.8), indicating that the method of this invention effectively reduces the estimation variance and achieves information utilization efficiency close to that of centralized methods under unknown correlation conditions. Regarding state estimation, method (c) achieves the minimum estimation error variance throughout the simulation process. Taking the state estimation error at the final time step as an example, the root mean square error of state for method (a) is 10.791 (due to inaccurate noise parameter settings, the filtering deteriorates to some extent), method (b) improves to 10.083, and method (c) further reduces it to 8.771. Compared to the case without corrected noise statistics, applying the method of this invention reduces the state estimation error by approximately 18.7%; even compared to the scheme that only corrects noise locally, the error is reduced by approximately 13%. This fully demonstrates the effect of fusion noise covariance estimation on improving filtering accuracy.

[0059] This embodiment also observes that, near steady state, the statistical characteristics of the innovation sequences of each sensor filter are closer to white noise, indicating that the method of this invention effectively corrects the noise statistical model, enabling the Kalman filter to once again meet the theoretically optimal performance assumptions. In summary, this embodiment verifies the effectiveness of the invention: by collaboratively processing multi-sensor data with unknown correlations, accurate estimation of noise covariance and high-precision fusion estimation of distributed states are achieved, demonstrating significant advantages over traditional methods under the mean square error criterion.

[0060] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for joint estimation of the state and noise covariance of multiple sensors with unknown correlations, characterized in that, Includes the following steps: S1. Initialize the multi-sensor system model and the parameters of the local Kalman filter for each sensor; S2. Based on the initialized system model and filter parameters, each sensor performs target state prediction and update, generating and accumulating the information sequence; S3. Based on the accumulated information sequence, each sensor estimates the local process noise covariance and the local measurement noise covariance based on a sliding time window of a preset length. S4. Assign fusion weights to each sensor based on the estimated local noise covariance; S5. Based on the fusion weights allocated in S4, the local process noise covariance and the local measurement noise covariance are weighted and fused to obtain the global process noise covariance estimate and the global measurement noise covariance estimate.

2. The method for joint estimation of unknown correlation multi-sensor state and noise covariance according to claim 1, characterized in that, S1 includes: Establish a state-space model and a measurement model for the target motion; Initialize the state estimates and covariance matrices of the local Kalman filters for each sensor; Set the initial process noise covariance matrix and the initial measurement noise covariance matrix for the local Kalman filter of each sensor.

3. The method for joint estimation of unknown correlation multi-sensor state and noise covariance according to claim 1, characterized in that, S2 includes: each sensor acquiring the observation value at the current moment; predicting the target state and the predicted observation based on the state space model constructed in S1 and the time update step of the local Kalman filter; calculating the observation information and performing the measurement update step of the local Kalman filter based on the observation information to obtain the corrected state estimate and the updated estimated covariance; and accumulating the observation information by adding it to the information sequence of the local Kalman filter.

4. The method for joint estimation of unknown correlation multi-sensor state and noise covariance according to claim 1, characterized in that, S3 includes: For each sensor, collect the innovation sequence within the sliding time window; calculate the sample autocovariance set of the innovation sequence; based on the system's state transition matrix, observation matrix, and current Kalman gain matrix, construct a system of linear equations about the unknown process noise covariance and the unknown measurement noise covariance; solve the system of linear equations to obtain the local process noise covariance estimate and the local measurement noise covariance estimate for the sensor.

5. The method for joint estimation of unknown correlation multi-sensor state and noise covariance according to claim 1, characterized in that, S4 includes: calculating the upper bound of the estimated variance based on the residual statistics of the local noise covariance estimation of each sensor; and assigning fusion weights to the corresponding sensors according to the proportion of their normalized reciprocals based on the upper bound of each estimated variance.

6. The method for joint estimation of unknown correlation multi-sensor state and noise covariance according to claim 1, characterized in that, S5 includes: The local process noise covariance estimate of each sensor and its corresponding uncertainty measure, as well as the local measurement noise covariance estimate of each sensor and its corresponding uncertainty measure, are used as inputs. By applying the batch covariance cross-fusion formula and combining it with the fusion weights allocated in step S4, the global process noise covariance estimate and its uncertainty, as well as the global measurement noise covariance estimate and its uncertainty, are calculated.

7. The method for joint estimation of unknown correlation multi-sensor state and noise covariance according to claim 1, characterized in that, The method further includes using the global process noise covariance estimate and the global measurement noise covariance estimate obtained in S5 to update the corresponding noise covariance parameters in the local Kalman filters of each sensor.

8. The method for joint estimation of unknown correlation multi-sensor state and noise covariance according to claim 7, characterized in that, The method further includes: adaptively adjusting the image segmentation threshold in the target detection stage based on the updated global process noise covariance estimate, wherein the segmentation threshold is positively correlated with the norm or weighted sum of the process noise covariance.

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