Kalman filtering method under the condition of unknown process noise covariance matrix Q

Abstract

The invention provides a Kalman filtering method under the condition of an unknown process noise covariance matrix Q. The method specifically comprises the steps of: 1, judging whether a system model satisfies a preset condition, going to a step two if the system model satisfies the preset condition, and stopping the method if the system model does not satisfy the preset condition; 2, establishing a system generalized output matrix E; 3, utilizing the matrix E determine a coupled vector [delta]i output by a system; 4, establishing linear coupling output by the system according to the coupled vector [delta]I, based on the linear coupling, estimating the process noise covariance matrix Q by utilizing a law of large numbers, and recording an estimated result as Q<->; and 5, taking the real-time estimated result Q<-> of the process noise covariance matrix into a standard Kalman filter, and obtaining a filtering result. According to the invention, the Kalman filtering under the condition of the unknown process noise covariance matrix Q is realized.

Description

technical field [0001] The invention relates to a Kalman filter method under the condition that the process noise covariance matrix Q is unknown, and belongs to the technical field of the Kalman filter method. Background technique [0002] Kalman filtering is a time-domain filtering method. It uses the state-space method to describe the system. The algorithm uses a recursive form. The data storage is small, and it is very convenient to execute on a computer. It can not only deal with stationary random processes, but also deal with multidimensional non-stationary random processes. When the system model and noise prior information are known and the noise satisfies the Gaussian white noise assumption, it can be proved that the Kalman filtering result is the minimum variance unbiased estimate. Because the Kalman filtering method is simple and easy to operate, the result is accurate and reliable, and has advantages that other filtering methods do not have, Kalman filtering is wi...

AI Technical Summary

Problems solved by technology

The uncertainty of statistical characteristics will directly lead to a large deviation between the Q used in the filtering algorithm and the real Q, and this deviation will make the Kalman filtering algorithm lose its optimality, and the estimation accuracy will be greatly reduced. cause filter divergence

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