Image Jacobian Matrix Estimation Based on Fuzzy Adaptive Robust Kalman Filter

Abstract

Aiming at the problem of image Jacobian matrix estimation, this paper proposes a method to get the motion state estimation of the object feature point at the current time by using the combination of robust Kalman filter and fuzzy adaptive method from the image feature space, and the estimation of the image Jacobian matrix can be obtained. Firstly, an adaptive robust decorrelation Kalman filter algorithm with colored measurement noise is proposed by reconstructing process equation and measurement equation and combining the mathematical characteristics of the standard Kalman filter noise. Secondly, by monitoring if the ratio between theoretical residual and actual residual is near 1, the fuzzy inference system constantly adjust the weighted measurement noise covariance and recursively correct the measurement noise covariance of the adaptive Kalman filter, and thus be able to estimate the position and velocity of the object feature point at the current time in the image space more accurately, then the estimation of image Jacobian matrix can be achieved accurately under unknown dynamic environment. The feasibility and superiority of the proposed method can be verified by the simulation and experimental results.