A Hybrid Adaptive Unscented Kalman Filter Algorithm

Abstract

Abstract:In order to overcome the limitation of the traditional adaptive Unscented Kalman Filtering (UKF) algorithm in noise covariance estimation for statement and measurement, we propose a hybrid adaptive UKF algorithm based on combining Maximum a posteriori (MAP) criterion and Maximum likelihood (ML) criterion, in this paper. First, to prevent the actual noise covariance deviating from the true value which can lead to the state estimation error and arouse the filtering divergence, a real-time covariance matrices estimation algorithm based on hybrid MAP and ML is proposed for obtaining the statement and measurement noises covariance, respectively; and then, a balance equation the two kinds of covariance matrix is structured in this proposed to minimize the statement estimation error. Compared with the UFK based MAP and based ML, the proposed algorithm provides better convergence and stability.

An ASVSF-SLAM Algorithm with Time-Varying Noise Statistics Based on MAP Creation and Weighted Exponent

“…Then, since (93)-(100) are derived completely, both state transition in (33) and measurement function in (35) are satisfied. Next, + can be calculated as follows:…”

“…However, in the real-case application, the system is inaccurately modeled, and the prior knowledge of the noise statistics is unknown or partially known. An inaccuracy of modeling the system might enlarge the estimation error [4,26,35]. The internal and external uncertainties also might affect the change of the statistical characteristic which undoubtedly leads to the divergences of the filter performance [4,24,26,35].…”

“…First, the improved SVSF was derived based on the one-step smoothing technique [24,42,43]. Then by referring to the prior knowledge, the noise statistics parameter of SVSF was estimated based on the maximum a posteriori (MAP) creation [4,14,15,24,26,27,35] and weighted exponent concept [4,24,26,27]. It aims to produce the time-varying of those parameters.…”

An improved adaptive FastSLAM algorithm with time‐varying noise estimator

“…here, b is a fading factor, which is set to 0.96 [31]. Thanks to fading factor, the effect of the last collected data on the noise statistics estimator is increased [32]. The mean value of the measurement noise is…”

“…$$$ {d}_k $$$ is weighting coefficient, which is calculated as $$$$ {d}_k=\frac{1-b}{1-{b}^k}; $$$$ here, $$$ b $$$ is a fading factor, which is set to 0.96 [31]. Thanks to fading factor, the effect of the last collected data on the noise statistics estimator is increased [32]. The mean value of the measurement noise is $$$$ {\hat{r}}_k={\hat{r}}_{k-1}+{d}_k\left[\left(I-H{K}_k\right){e}_{z,k}\right] $$$$ …”