A High-Order Kalman Filter Method for Fusion Estimation of Motion Trajectories of Multi-Robot Formation

Abstract

Multi-robot motion and observation generally have nonlinear characteristics; in response to the problem that the existing extended Kalman filter (EKF) algorithm used in robot position estimation only considers first-order expansion and ignores the higher-order information, this paper proposes a multi-robot formation trajectory based on the high-order Kalman filter method. The joint estimation method uses Taylor expansion of the state equation and observation equation and introduces remainder variables on this basis, which effectively improves the estimation accuracy. In addition, the truncation error and rounding error of the filtering algorithm before and after the introduction of remainder variables, respectively, are compared. Our analysis shows that the rounding error is much smaller than the truncation error, and the nonlinear estimation performance is greatly improved.

Kalman Filter for Linear Discrete-Time Rectangular Singular Systems Considering Causality

“…State estimation has always been an important topic in practical applications. Since the least squares method was proposed, many state estimation methods for linear systems have been proposed [1][2][3][4][5]. Among these, the Kalman filter [6] is the optimal state estimation method for linear Gaussian systems.…”