Kalman filtering method with unknown process noise covariance matrix recursive estimation

Abstract

The invention provides a Kalman filtering method with unknown process noise covariance matrix recursive estimation and aims at a discrete time time-invariant system and aims at solving the system state filtering estimation problem of the discrete time time-invariant system under the condition that an observation noise covariance matrix is completely unknown. The Kalman filtering method comprises step one, constructing a new statistical sequence {xik} according to an observation sequence {yk}; step two, calculating a covariance matrix recursion formula of {xik}; step three, calculating a process noise covariance matrix estimation sequence according to an algebraic relationship between real-time estimation values Covk(xi) of the observation noise covariance matrix and a new statistical sequence covariance matrix; step four, calculating an estimation sequence as the following formula of a covariance matrix according to the relationship between f(Q) and a process noise covariance matrix Q; substituting the process noise covariance matrix estimation sequence as the following formula replacing a truth value into a standard Kalman filtering method to calculate a system real-time state estimation and a state estimation deviation covariance matrix.

Description

technical field [0001] The invention belongs to the field of discrete time self-adaptive filtering, in particular to a Kalman filtering method with unknown process noise covariance matrix recursive estimation. Background technique [0002] The Kalman filter method is a time-domain state estimation method. Because it uses the description method of the state space, and its recursive form is easy to implement by computer, the state estimation based on the state space can be applied to the advanced control method in modern control theory , to obtain good system performance. For the system described by the linear state space model, the standard Kalman filter method can obtain the estimation of the internal state of the system from the observation sequence with observation noise, improve the system control performance, and better complete the system control goal. When the system equation and the measurement equation are known, the signal is estimated, and the following informatio...

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Problems solved by technology

[0007] In view of this, the present invention provides a kind of Kalman filtering method based on recursive covariance matrix estimation method for discrete-time time-invariant systems, the purpose is to solve the observation noise covariance in a class of discrete-time linear time-invariant systems System State Filtering Estimation Problem Considering the Real-time Requirement of Filtering Algorithm in the Case of Completely Unknown Matrix

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