Kalman filtering method for recursive estimation under condition that observation noise covariance matrix is unknown

Abstract

The invention provides a Kalman filtering method for recursive estimation under the condition that an observation noise covariance matrix of a discrete time time-invariant system is unknown, wherein the method solves the problem of system state filtering estimation under the condition that the observation noise covariance matrix of the discrete time time-invariant system is completely unknown. The method includes the steps that (1) a new statistic sequence is built by means of an observation sequence; (2) a recursion formula of the covariance matrix of the new statistic sequence is calculated; (3) an estimation sequence (f(R)k)of the observation noise covariance matrix is calculated; (4) an estimation sequence of the covariance matrix is calculated, and then real-time estimation of the observation noise covariance matrix is calculated through an algebraic relation; (5) an estimation sequence substitution true value of the observation noise covariance matrix is put into a standard Kalman filtering method, and real-time state estimation of the system and a covariance matrix of state estimation deviation are calculated.

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 observation noise covariance matrix recursive estimation. Background technique [0002] Due to its own superiority, after more than 50 years of development, different forms of Kalman filter theory have been theoretically promoted and applied in different engineering fields. [0003] 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, imp...

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Problems solved by technology

[0008] In view of this, the present invention provides a Kalman filter method with unknown observation noise covariance matrix recursive estimation for discrete time time invariant systems, the purpose is to solve the observation noise covariance in discrete time linear time invariant systems When the variance matrix is ​​completely unknown, the problem of system state filtering estimation taking into account the real-time requirements of the filtering algorithm

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