CN109582914B

CN109582914B - Parallel fusion estimation method of noise-related deviation system

Info

Publication number: CN109582914B
Application number: CN201910079209.4A
Authority: CN
Inventors: 葛泉波; 王宏; 张建朝; 牛竹云; 何美光
Original assignee: Hangzhou Dianzi University
Current assignee: Hangzhou Dianzi University
Priority date: 2019-01-28
Filing date: 2019-01-28
Publication date: 2023-08-18
Anticipated expiration: 2039-01-28
Also published as: CN109582914A

Abstract

The invention relates to a parallel fusion estimation method of a noise-related deviation system. Aiming at the filtering problem of a multi-sensor measuring system with dynamic deviation and related noise which influence the system state and measurement, the invention provides a method for estimating the system with deviation based on a solution correlation technology and a parallel multi-sensor fusion idea. The invention solves the problem of filtering accuracy degradation caused by the correlation of process noise and measurement noise in estimation.

Description

Parallel fusion estimation method of noise-related deviation system

Technical Field

The invention belongs to the field of filtering estimation, and particularly relates to an estimation method of a deviation system based on a noise decorrelation technology and a parallel fusion structure.

Background

When dynamic bias exists and affects the system process or measurement, the system as the basis of the estimation adds a bias equation, and in order to obtain a more accurate filtered estimate, the bias needs to be estimated.

In view of the problem of state estimation including dynamic deviation, a common method is to synthesize the deviation and the state into a new state for estimation, and the method is easy to understand, but the calculation of the method involves the calculation of a high-dimensional matrix, and the calculation amount is large. On the basis, the introduction of the two-stage Kalman filter provides a solution to the problem, and the estimation method has the following thought: and adding a noise self-adaptive covariance matrix and a conversion matrix concept, decomposing the filter process in an enhanced state into an unbiased filter and a deviation filter by utilizing a matrix inversion theorem and the conversion matrix, and compensating the unbiased filter by utilizing the deviation filter to obtain an estimated value of a system state.

The multi-sensor information fusion system is advantageous in performance over a single sensor. When a single sensor is used for state estimation, the source of measurement data is single and problems easily occur, so that the accuracy of filter estimation cannot be ensured; when a plurality of sensors are used for state estimation, the sources of measurement data are numerous, the measurement data are unlikely to be problematic at the same time, and the estimation accuracy is ensured. The present invention therefore focuses on the estimation problem of systems with bias that are noise dependent.

Disclosure of Invention

In order to cope with the above-mentioned noise correlation and dynamic deviation situations, the present invention introduces a noise decorrelation technique to obtain a two-stage kalman filter under noise correlation conditions. Based on the filters, parallel fusion is carried out on a plurality of unbiased state filters and deviation filters respectively, and a noise-related parallel two-stage Kalman filtering fusion estimation method is provided.

The present invention may be divided into five parts in general. The first part is system model establishment; the second part introduces a decorrelation technology, and reestablishes an equivalent model of uncorrelated noise; in the third part, obtaining a plurality of local two-stage Kalman filters according to the measurement data; the fourth part respectively carries out parallel fusion on the unbiased filter and the biased filter; and finally, combining the two fusion results to obtain an estimated value of the system state.

The invention has the beneficial effects that: noise correlations can be processed and more accurate estimates of the no-bias condition and bias can be obtained relative to a single two-stage kalman filter.

Drawings

FIG. 1 is a recursive process of the method of the present invention.

Fig. 2 shows the detailed process of steps 4 and 5 in the present invention.

Detailed Description

The invention is further described below with reference to the accompanying drawings.

As shown in fig. 1, the present invention includes the steps of:

step 1, modeling a system

Taking a common multi-sensor system with deviation into consideration, the state equation, the deviation equation and the measurement equation of the system with related noise are described as follows, wherein the statistical characteristics of the noise in the system process are known:

wherein k represents a time series; x is x _k ,b _k And y _i,k The system is respectively an n-dimensional state vector, an m-dimensional deviation vector and a p-dimensional observation vector of an ith sensor;and v _i,k The system state noise vector, the system deviation noise vector and the measurement noise vector of the ith sensor are respectively; a is that _k+1,k ∈R ^n×n Is a state transition matrix; c (C) _i,k ∈R ^p×n Is the state observation matrix of the ith sensor. The process noise, the bias noise and the measurement noise are zero-mean Gaussian white noise sequences: /> v _i,k ～N(0,V _i,k ) And->

Step 2, introducing a decorrelation technology to reestablish an equivalent model of uncorrelated noise

For the multi-sensor system with deviation provided in step 1, there is correlation between the process noise and each measurement noise, and a two-stage Kalman filter cannot be directly used. Therefore, a noise decorrelation technology is introduced, and equivalent transformation is carried out on a system state equation to obtain new system state noise which is irrelevant to measurement noise. The reconstruction process is as follows: first, in the equation of system state, N zero-added equations:

taking outThe new state noise is uncorrelated with the bias noise, the measurement noise, i.e

The model of the original system can be rewritten as

Step 3, according to the ith measurement equation, obtaining the estimated information of the ith noise-related two-stage Kalman filter of the system state, wherein the estimated information is specifically as follows:

obtaining a non-deviation state, prediction of deviation, an estimated value and a covariance matrix thereof through the i-th noise-related two-stage Kalman filter, and obtaining estimated information of the i-th noise-related two-stage Kalman filter of a system state through combination.

Step 4. Based on the noise-related two-stage Kalman filter, a parallel fusion mode is added in the multi-sensor information fusion mode (before combination, a plurality of unbiased filters and a plurality of biased filters are respectively fused)

In a linear system consisting of multiple sensors, each local unbiased filter i makes its own estimate of the unbiased state; meanwhile, the local deviation filter i makes its own estimation value for the deviation. The N partial unbiased filters are fused in a parallel mode to obtain a better unbiased state estimation value; the N partial deviation filters are fused in the same mode to obtain a better deviation estimation value.

Based on the estimation information of the plurality of unbiased filters, obtaining the state estimation value and covariance matrix thereof after the unbiased filters are fused, wherein the state estimation value and covariance matrix thereof are respectively as follows:

in the method, in the process of the invention,and the state estimation value is the state estimation value and the covariance matrix of the i-th filter after fusion of the unbiased filters.

Based on the estimation information of the plurality of deviation filters, obtaining a deviation estimation value and a covariance matrix thereof after the fusion of the deviation filters, wherein the deviation estimation value and the covariance matrix are respectively as follows:

wherein b is _i,k+1/k ,And the state estimation value is the state estimation value after the fusion of the deviation filter of the ith filter and the covariance matrix of the state estimation value.

Step 5, combining the two estimated values through a linear combination formula to obtain estimated information x of the system state _k+1/k+1 ,

Wherein V is _k+1 Is a fusion factor. Fig. 2 shows the detailed procedure of steps four and five.

Claims

1. The parallel fusion estimation method of the noise-related deviation system is characterized by comprising the following steps of:

step 1, modeling a system;

wherein k represents time; x is x _k ,b _k And y _i,k The system is respectively an n-dimensional state vector, an m-dimensional deviation vector and a p-dimensional observation vector of an ith sensor;and v _i,k The system state noise vector, the system deviation noise vector and the measurement noise vector of the ith sensor are respectively; a is that _k+1,k ∈R ^n×n Is a state transition matrix; c (C) _i,k ∈R ^p×n A state observation matrix for the ith sensor; the process noise, the bias noise and the measurement noise are zero-mean Gaussian white noise sequences: /> v _i,k ～N(0,V _i,k ) And->

Step 2, introducing a decorrelation technology, and reestablishing an equivalent model of uncorrelated noise;

because of the correlation between the state noise and the measurement noise, the system state equation needs equivalent transformation, and the reconstruction process is as follows:

first, in the equation of system state, N zero-added equations:

The equivalent model of the original system is

Step 3, according to the ith measurement equation, obtaining an estimated value of the ith noise-related two-stage Kalman filter of the system state, wherein the estimated value is specifically as follows:

obtaining a non-deviation state, prediction and estimation values of deviation and a covariance matrix thereof through an i-th noise-related two-stage Kalman filter, and obtaining the estimation values of the i-th noise-related two-stage Kalman filter of a system state through combination;

step 4, adding a parallel fusion mode into the multi-sensor information fusion mode based on a noise-related two-stage Kalman filter;

based on the filtering estimation information of the plurality of unbiased filters, obtaining the state estimation values after fusion of the unbiased filters and covariance matrixes thereof are respectively as follows:

in the method, in the process of the invention,the state estimation value after fusion of the unbiased filter of the ith filter and the covariance matrix thereof;

based on the filtering estimation information of the plurality of deviation filters, obtaining the deviation estimation values after the fusion of the deviation filters and covariance matrixes thereof are respectively as follows:

wherein b is _i,k+1/k ,The state estimation value after fusion of the deviation filter of the ith filter and the covariance matrix of the state estimation value are obtained;

step 5, combining the unbiased state estimated value and the bias estimated value which are respectively fused to obtain estimated information x of the system state _k+1/k+1 ,