Consistency filtering method for distributed sensor networks with unknown colored noise

Abstract

The present invention provides a consistent filtering method for a distributed sensor network with unknown colored noise, comprising: learning the state noise and measurement noise parameters of each node in the distributed sensor network according to a given set of training data. At the same time, state expansion is performed to expand the learned colored noise parameters to the state vector, and finally the state estimation is completed using the consistent Kalman filter algorithm, so that the estimated values ​​of each sensor node converge to global consistency. In order to improve the computational efficiency, for each node, only the local measurement noise and state noise are integrated into the extended state. Simulation results show that the present invention can effectively estimate the unknown colored noise in the distributed sensor network and improve the accuracy of distributed estimation. The present invention can be applied to the fields of distributed sensor network radar, infrared target tracking, mobile robot positioning, etc.

Description

Technical Field

[0001] The invention relates to a distributed sensor network consistency filtering method with unknown colored noise. Background Art

[0002] Distributed state estimation algorithms are increasingly used in sensor networks due to their strong scalability and high fault tolerance. They have low requirements on network connectivity and system observability; maintaining global observability does not necessarily mean that each sensor is observable. In addition, the fusion center does not need to collect the original measurements of all nodes in the sensor network. Therefore, distributed strategies provide a better choice with better robustness, requiring less communication and allowing parallel processing. In contrast, centralized fusion algorithms generate a lot of communication and computational burdens at the central node.

[0003] There are three different methods for distributed state estimation: consensus algorithm, gossip algorithm and diffusion algorithm. Among them, the consensus filter is not only used for state estimation, but also for averaging new information. It is a widely used algorithm. According to the existing literature, the consensus filter methods can be divided into the following categories: consistency of estimation, consistency of measurement, consistency of information and H ∞ consistency.

[0004] Traditional consistency filtering algorithms require that the system has Gaussian noise. However, for systems in the presence of colored noise, the classic consistency algorithm cannot perform effective state estimation. For the case where there is colored noise in the measurement equations of distributed sensor networks, the state expansion and measurement difference methods can be applied to the consistency filtering algorithm, but the case of unknown colored noise is not considered. Gaussian process (GP) is an effective non-parametric estimation algorithm. When the model of the system is unknown, the Gaussian process regression model can be used to learn certain unknown parameters. The mean obtained by Gaussian process regression provides an approximation of the model state vector, while the covariance provides an estimate of the model white noise related parameters. For nonlinear models, the estimation method has also been extended from using GP Kalman filtering to using GP extensions and unscented Kalman filtering. Summary of the invention

[0005] Aiming at the problem of state estimation in distributed sensor networks, a linear dynamic system is considered in which the noise of the state equation and the observation equation are both colored noise with unknown parameters. The present invention proposes a distributed sensor network consistency filtering method with unknown colored noise. The method learns the residual output between a given state value and an approximate parameter model through Gaussian process regression to determine the covariance matrix and mean of the colored noise and the linearized colored noise function. Then, the state is extended to extend the learned noise parameters into the state vector to make it an equivalent white noise system, so that the consistency filtering algorithm based on the standard Kalman filter can be run. In addition, in order to avoid the computational burden, only the noise parameters of the node itself are extended into the state vector, and the adjacent nodes are not involved. In order to reduce the communication load, the colored noise part extended into the state vector does not participate in the consistency communication process between nodes.

[0006] The present invention is achieved through the following technical solutions.

[0007] A method for consistent filtering of a distributed sensor network with unknown colored noise comprises the following steps:

[0008] Step S1: Based on a given set of ground truth data and measurement data, determine a training set of process noise and a training set of observation noise of each sensor node for use in a Gaussian process regression model;

[0009] Step S2: Given the initial target state, the initial error variance matrix, the training set of the process noise in step S1, and the training set of the observation noise of each sensor node at each sensor node, to form initial parameters;

[0010] Step S3: using the training set of process noise in step S1, learning the process noise of each sensor node at the initial moment according to Gaussian process regression;

[0011] Step S4: using the training set of process noise in step S1 to learn process noise parameters, using the training set of observation noise of each sensor node in step S1 to learn observation noise parameters, performing a round of prediction on the target state and error variance, including initial round prediction and non-initial round prediction, and expanding state variables; wherein:

[0012] In the initial round of prediction, each sensor node independently performs a round of prediction on the target state and error variance using the initial parameters in step S2 and the process noise at the initial moment in step S3;

[0013] In the non-initial round prediction, a round of prediction is performed using the estimated values ​​of the target state and the own position of each sensor node obtained in step S7 of the previous round;

[0014] Step S5: Each sensor node obtains a local target state local measurement update based on its own current measurement information, and obtains a local posterior state and error variance;

[0015] Step S6: Each sensor node uses the target state posterior information of itself and its neighboring sensor nodes to perform consistency iteration, so that each sensor node tends to be globally consistent and obtains the target state estimation value;

[0016] Step S7: Each sensor node outputs the estimated value of the target state and the estimated value of the colored noise parameter, and restarts a new round of prediction from step S4.

[0017] Preferably, the step S1 comprises:

[0018] Given a set of 1: state truth values ​​for time period T0 and the measurements of each sensor node , where i∈N represents each different sensor node, and N is the set of all sensor nodes. The noise training data in the time period 1:T0 is obtained as follows:

[0019]

[0020] Therefore, the process noise training set And each sensor node observation noise training set The settings are as follows:

[0021]

[0022]

[0023] Preferably, step S2 comprises:

[0024] The initial target state is given to each sensor node. , the corresponding error variance matrix and the training set in step S1 and

[0025] Preferably, step S3 comprises:

[0026] Gaussian process regression is used to calculate the process noise of each sensor node i at time T0. The calculation formula is as follows:

[0027]

[0028] Among them, the prediction mean and variance defined by the Gaussian process are

[0029]

[0030]

[0031] k is the kernel function of the Gaussian process, and K is the n×n kernel matrix. And k * [i] = k(x * , x i ), K[i, j] = k(x i , x j ). The kernel function selects the square exponential kernel function, and the calculation formula is as follows:

[0032]

[0033] Where, θ=[W,σ f , σ n ] is the hyperparameter of the Gaussian process.

[0034] Preferably, step 4 comprises:

[0035] Step S4.1, each sensor node i learns the parameters of the process noise according to the Gaussian process regression at time k, and the calculation formula is as follows:

[0036]

[0037]

[0038]

[0039] Step S4.2, each sensor node i learns the parameters of the observation noise according to Gaussian process regression at time k, and the calculation formula is as follows:

[0040]

[0041]

[0042]

[0043] Step S4.3: Each sensor node i performs one-step state and covariance prediction on the target state and expands the variables to obtain the predicted value of the state at time k. , and the transition matrix after state expansion , Noise Variance and the predicted covariance , the calculation formula is as follows:

[0044]

[0045] Preferably, the step S5 comprises:

[0046] Each sensor node i is based on the current measurement information of the sensor And the expanded observation matrix Get the local target state local measurement update, get the local posterior state after state expansion and error variance Then calculate the information matrix and information vector The calculation formula is as follows:

[0047]

[0048] In this step, the specific processes of initial round update and non-initial round update are covered; the calculation process of initial round update and non-initial round update is the same, the only difference is that the parameter sources are different.

[0049] Preferably, step S6 comprises:

[0050] Each sensor node i uses the target posterior information matrix of itself and its neighboring node j and information vector Perform L-step consistency iteration. The calculation formula for the l-step consistency iteration is as follows:

[0051]

[0052]

[0053] The initial parameters of the iteration are set to

[0054] Preferably, step S7 comprises:

[0055] Each sensor node outputs the target state The target posterior error variance matrix after state expansion is And the colored noise parameters and

[0056] Compared with the prior art, the present invention has the following beneficial effects:

[0057] The present invention uses a Gaussian process regression model to effectively estimate unknown colored noise parameters in a distributed system and improve the estimation accuracy of a distributed consistency filtering algorithm. When performing state expansion, only the noise parameters of the local node are expanded into the state vector, avoiding the computational burden. The method is simple, effective, and easy to implement. It is particularly suitable for the application of distributed sensor network systems in the presence of unknown colored noise, and can be widely used in various fields such as robotics, intelligent transportation, air traffic control, aerospace, aviation, and navigation. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Other features, objects and advantages of the present invention will become more apparent from the detailed description of non-limiting embodiments made with reference to the following drawings:

[0059] Figure 1 A schematic diagram of a topological structure of a sensor network according to an embodiment of the present invention;

[0060] Figure 2 A schematic diagram of the estimated trajectory of the target state using different algorithms according to an embodiment of the present invention;

[0061] Figure 3 FIG. 4 is a schematic diagram of the root mean square error of target position estimation using different algorithms according to an embodiment of the present invention. DETAILED DESCRIPTION

[0062] The following is a detailed description of the embodiments of the present invention: This embodiment is implemented on the premise of the technical solution of the present invention, and a detailed implementation method and a specific operation process are given. It should be pointed out that for ordinary technicians in this field, several variations and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention.

[0063] The present invention relates to a consistency filtering method based on Gaussian process regression (GPR) and state extension, which can be applied to the fields of collaborative state estimation, target tracking, etc. of distributed sensor networks in the presence of colored noise.

[0064] This embodiment provides a distributed sensor network consistency filtering method with unknown colored noise, comprising the following steps:

[0065] Step 1: Determine the training set of unknown colored noise of the system based on a given set of true state values ​​and measurement values.

[0066] Given a set of 1: state truth values ​​for time period T0 and the measurements of each sensor node Where i∈N represents each different sensor node, and N is the set of all sensor nodes. The input and output of the Gaussian process with colored noise is determined by the residual:

[0067]

[0068]

[0069] Therefore, the training set of process noise and the training set of observation noise of each sensor node for:

[0070]

[0071]

[0072] Step 2: Initialize each sensor node to form initial parameters.

[0073] The initial target state is given to each sensor node. The corresponding error variance matrix Process noise training set And the training set of each sensor node measurement noise

[0074] Step 3: Calculate the process noise of each sensor node at the initial moment.

[0075] The training set of process noise is used to learn the process noise of each sensor node at the initial time T0 according to Gaussian process regression.

[0076]

[0077] Step 4: Gaussian process regression is used to learn the process noise of each sensor node at each moment.

[0078] According to the mean value of the process noise at the previous moment At each time point k, each sensor node i uses Gaussian process regression to learn the mean of the process noise variance and the colored process noise function

[0079]

[0080]

[0081]

[0082] Step 5: Gaussian process regression is used to learn the measurement noise of each sensor node at each moment.

[0083] According to the mean value of the measured noise at the last moment At each time point k, each sensor node i uses Gaussian process regression to learn the mean of the process noise variance and the colored measurement noise function

[0084]

[0085]

[0086]

[0087] Step six, expand the state variables and perform prediction updates at each node in the sensor network.

[0088] Each sensor node i performs one-step state and covariance prediction on the target state and expands the variables. In order to avoid the computational burden, only the noise parameters of the node itself are expanded into the state vector without involving adjacent nodes. The predicted value of the state at time k is obtained. And the transition matrix after state expansion Noise variance and the predicted covariance

[0089]

[0090]

[0091]

[0092]

[0093] Step 7: Each sensor node i measures the current moment of the sensor And the expanded observation matrix Get the local target state local measurement update, get the local posterior state after state expansion and error variance

[0094]

[0095]

[0096]

[0097]

[0098] Based on the posterior state and error variance, calculate the information matrix and information vector

[0099]

[0100] Step 8: Each sensor node i uses the target posterior information matrix of itself and its neighboring node j and information vector Perform L-step consistency iteration. The calculation formula for the l-step consistency iteration is as follows:

[0101]

[0102]

[0103] The initial parameters of the iteration are set to Get the target state after consistency averaging and the error variance matrix

[0104]

[0105] In order to reduce the communication load, the colored noise part extended into the state vector does not participate in the consistency communication process between nodes.

[0106] Step 9: Each sensor node outputs the target state The target posterior error variance matrix after state expansion is And the colored noise parameters and

[0107]

[0108]

[0109] The technical solution of this embodiment is further described in detail below in conjunction with the accompanying drawings.

[0110] Consider a two-dimensional plane tracking problem. Consider a distributed sensor network consisting of 10 sensor nodes, each sensor is randomly deployed on a plane space of 5000m×5000m, and each sensor can only communicate with adjacent nodes within its communication range. The topology of the sensor network is as follows: Figure 1 As shown in Figure 2. The target adopts a uniform motion model, and the sensor measures the position of the target. The noise in the prediction equation and the measurement equation is colored noise. The prediction equation of the system is

[0111] x k =F k-1 x k-1 +Φ k-2 w k-2 +η k-1 ,

[0112] The measurement equation is

[0113]

[0114] in,

[0115]

[0116] Φ k =diag(0.9 0.9 0.9 0.9),

[0117]

[0118] η k ~N(0, diag([1.25 0.5 1.25 0.5])),

[0119]

[0120] The system state vector is Contains position and velocity. The state of the target at the initial moment is:

[0121]

[0122]

[0123] The target's trajectory is Figure 2 Given a set of training data, we can get the training set of the system with colored noise. and At the same time, the colored noise parameters of each sensor node at the initial time are obtained and After determining the above initial values ​​and simulation parameters, in each simulation cycle, the specific steps are as follows:

[0124] Step S1: Calculate process noise

[0125]

[0126]

[0127]

[0128] Step S2: Calculate the observation noise

[0129]

[0130]

[0131]

[0132] Step S3: Calculate prior state estimates and extended variables

[0133]

[0134]

[0135]

[0136]

[0137] Step S4: Measurement update

[0138]

[0139]

[0140]

[0141]

[0142]

[0143] Step S5: Consistency averaging of posterior information

[0144] make (Set the initial value of variational iteration for each node),

[0145] For l=1, ..., L (for each l=1, ..., L, perform the following operation),

[0146]

[0147]

[0148] End,

[0149]

[0150] Step S6: Each sensor node outputs target state estimation and colored noise parameters:

[0151]

[0152]

[0153] This embodiment uses Matlab language to test the proposed algorithm and compares the filtering results of different distributed state estimation algorithms on the dynamic equation.

[0154] The first case gives the accurate parameters of the colored noise system, so there is no need to run a Gaussian process regression model, and the standard Kalman filter (AKF) can be directly performed after state expansion.

[0155] The second case is the condition we mentioned in the previous analysis. The colored noise of the process and measurement models is unknown. The state estimation is performed using the Gaussian process-based consistency filtering algorithm (GP-KF) under colored noise conditions proposed in this paper.

[0156] In the third case, we still assume that the colored noise of the process and measurement models are unknown, but do not estimate them. We use the traditional consistency-based Kalman filter algorithm and simply treat the colored noise as white noise (KF).

[0157] Figure 3 The root mean square error (RMSE) of the position after 10 Monte Carlo simulations is given. The traditional consistent Kalman filter algorithm that simply treats colored noise as white noise will have divergent errors. At the same time, Table 1 shows the average root mean square error (ARMSE, i.e., the mean of the total error at K moments) of the three algorithms under different consistency iteration steps. From Table 1 and Figure 3 It can be seen that the proposed algorithm is always more accurate than the traditional state expansion algorithm in estimating the state, which further confirms the effectiveness of Gaussian process regression for colored noise estimation.

[0158] Table 1 Algorithm comparison

[0159] Consistency Steps GP-KF KF AKF L＝1 7.92 37.55 12.33 L＝2 7.84 35.54 11.55 L＝3 7.03 32.17 10.95

[0160] In summary, the method proposed in this embodiment can effectively estimate the colored noise parameters of the distributed sensor network and improve the estimation accuracy when the model is inaccurate.

[0161] The present embodiment provides a distributed sensor network consistency filtering method with unknown colored noise, which is a distributed consistency filtering method based on Gaussian process in a colored noise environment. Specifically, when there is unknown colored noise in both the state model and the observation model, the Gaussian process regression model is used to learn the relevant noise parameters, and the state is expanded, and finally the state estimation is completed using the consistency Kalman filter algorithm. Compared with the traditional consistency algorithm, the algorithm with the addition of the Gaussian process regression model has a more accurate estimate of the noise parameters, and the method can achieve higher accuracy. Simulation results show that the present embodiment can improve the estimation accuracy of each node on the target in a distributed sensor network with unknown colored noise. The present embodiment can be applied to the fields of distributed sensor network radar, infrared target tracking, etc.

[0162] The above describes the specific embodiments of the present invention. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art may make various modifications or variations within the scope of the claims, which do not affect the essence of the present invention.

Claims

1. A method for consistent filtering of distributed sensor networks with unknown colored noise, characterized in that: The following steps are involved: Step S1: According to a given set of ground truth data and measurement data, a training set of unknown colored noise is determined for use in a Gaussian process regression model, wherein the training set of unknown colored noise includes: a training set of process noise and a training set of observation noise of each sensor node; Step S2: Given the initial target state, the initial error variance matrix, the training set of the process noise in step S1, and the training set of the observation noise of each sensor node at each sensor node, to form initial parameters; Step S3: using the training set of process noise in step S1, learning the process noise of each sensor node at the initial moment according to Gaussian process regression; Step S4: Use the training set of process noise in step S1 to learn process noise parameters, use the training set of observation noise of each sensor node in step S1 to learn observation noise parameters, perform a round of prediction on the target state and error variance, including initial round prediction and non-initial round prediction, and expand the state variables, where: In the initial round prediction, each sensor node independently performs a round of prediction on the target state and error variance using the initial parameters in step S2 and the process noise at the initial moment in step S3; In the non-initial round prediction, the target state and error variance are predicted in one round using the estimated value of the target state output by each sensor node and the estimated value of its own position obtained in step S7 of the previous round; Step S5: Each sensor node obtains a local target state local measurement update based on its own current measurement information, and obtains a local posterior state and error variance; Step S6: Each sensor node uses the target state posterior information of itself and its neighboring sensor nodes to perform consistency iteration, so that each sensor node tends to be globally consistent and obtains the target state estimation value; Step S7: After each sensor node outputs the estimated value of the target state and the estimated value of the colored noise parameter, a new round of prediction starts again from step S4.

2. The method for consistent filtering of a distributed sensor network with unknown colored noise according to claim 1, characterized in that: In step S1, a set of state truth values ​​of time period 1:T0 is given. and the measurements of each sensor node Where i∈N represents different sensor nodes, N is the set of all sensor nodes, and the noise training data in the time period 1:T0 is as follows: Therefore, the training set of process noise and the training set of observation noise of each sensor node The setup is as follows:

3. The method for consistent filtering of a distributed sensor network with unknown colored noise according to claim 2, characterized in that: In step S2, each sensor node is given an initial target state. The corresponding initial error variance matrix and the training set in step S1 and 4. The method for consistent filtering of a distributed sensor network with unknown colored noise according to claim 3, characterized in that: In step S3, Gaussian process regression is used to calculate the process noise of each sensor node i at time T0, and the calculation formula is as follows: Among them, the prediction mean and variance defined by the Gaussian process are Among them, k is the kernel function of the Gaussian process, K is the n×n kernel matrix; and there are k * [i] = k(x * , x i ), K[i, j] = k(x i , x j ); the kernel function selects the square exponential kernel function, and the calculation formula is as follows: Where, θ=[W,σ f , σ n ] is the hyperparameter of the Gaussian process.

5. The method for consistent filtering of a distributed sensor network with unknown colored noise according to claim 4, characterized in that: The step S4 comprises: Step S4.1, each sensor node i learns the noise parameters according to the Gaussian process regression at time k, and the calculation formula is as follows: Step S4.2, each sensor node i observes the noise parameter according to Gaussian process regression learning at time k, and the calculation formula is as follows: Step S4.3: Each sensor node i performs one-step state and covariance prediction on the target state and expands the variables to obtain the predicted value of the state at time k. And the transition matrix after state expansion Noise variance and the predicted covariance The calculation formula is as follows:

6. The method for consistent filtering of a distributed sensor network with unknown colored noise according to claim 5, characterized in that: In step S5, each sensor node i generates a signal based on its own current measurement information. And the expanded observation matrix Get the local target state local measurement update, get the local posterior state after state expansion and error variance Then calculate the information matrix and information vector The calculation formula is as follows:

7. The method for consistent filtering of a distributed sensor network with unknown colored noise according to claim 6, characterized in that: In step S6, each sensor node i uses the target posterior information matrix of itself and its neighboring node j and information vector Perform L-step consistency iterations. The calculation formula for the l-th step consistency iteration is as follows: The initial parameters of the iteration are set to 8. The method for consistent filtering of a distributed sensor network with unknown colored noise according to claim 7, characterized in that: In step S7, each sensor node outputs an estimated value of the target state The target posterior error variance matrix after state expansion is and estimates of the colored noise parameters and

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