Polynomial Method of Unscented Kalman Filter Based on Higher Order Moment Matching

Abstract

The invention discloses a polynomial method of an unscented Kalman filter based on high-order moment matching, and belongs to the technical field of nonlinear filtering. It includes the following steps: establish the state equation and measurement equation of the nonlinear system; determine the random distribution characteristics of the initial state, including its mean, covariance and higher-order moments, the distribution characteristics of noise, and the initial measurement value; based on the state of the previous moment Estimation and state equations, using multi-layer unscented transformation to calculate the distribution characteristics of random variables for one-step state prediction; based on the state prediction and measurement equations of step 3, using MUT to calculate the distribution characteristics of state prediction measurements; using Kalman gain to fuse states Predict and measure the data to calculate the distribution characteristics of the optimal state, and complete the one-step estimation task of the nonlinear system. This method is used to solve the accuracy and calculation stability problems of nonlinear filters in the actual application process. Combining with the existing sampling strategy, high-order moments and multiple symmetric sampling are used to improve the accuracy.

Description

technical field [0001] The invention belongs to the technical fields of information fusion such as nonlinear filtering, digital signal processing, and target positioning and tracking, and relates to a polynomial method of an unscented Kalman filter based on high-order moment matching. Background technique [0002] At present, in the fields of aircraft navigation, target tracking and industrial control. Almost all real-world systems are nonlinear. For example: in the process of target positioning and tracking, when the radar is used to observe the air target, the radar can obtain the azimuth angle of the air target relative to itself, but this observation contains noise, and the azimuth observation of the radar in the observation equation is the target position parameter to be estimated Nonlinear functions cannot directly use the linear filtering method to obtain the motion state of the target. It is essentially a nonlinear filtering problem, which is a common problem in the...

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Problems solved by technology

[0004] Compared with the unscented Kalman filter, the EKF has the following three disadvantages: (1) When the high-order terms of the nonlinear function Taylor expansion cannot be ignored, linearization will cause a large error in the system, and even the filter Difficult to be stable; (2) In many practical problems, it is difficult to obtain the Jacobian matrix of nonlinear functions, or even does not exist; (3) EKF needs to be derived, so it is necessary to clearly understand the specific form of nonlinear functions, and black boxes cannot be achieved package, making it difficult to modularize application

[0006] At present, the UKF used in the field of target tracking is the second-order UKF method. For Gaussian nonlinear systems, the estimation accuracy of the second-order UKF can only reach the cubic Taylor expansion of the nonlinear function, which has limited accuracy and poor stability. In applications, there is an urgent need for a sampling strategy that takes into account accuracy, stability, and computational efficiency

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