Unknown Random Bias Research Articles

Two‐Stage Cubature Kalman Filtering Based on T‐Transform and Its Application

According to the actual application system model which has bias, this paper analyzes the shortage of the conventional augmented algorithm, the two‐stage cubature Kalman filtering algorithm, which is presented on the basis of a two‐stage nonlinear transformation. The core ideas of the algorithm are to obtain the block diagonalization of the covariance matrix using the matrix transformation and avoid calculating the covariance of the state and bias to reduce the amount of calculation and ensure a smooth filtering process. Then, the equivalence of the two‐stage cubature Kalman filtering algorithm and the cubature Kalman filtering algorithm is proved by updating equivalent transformation. Through the experiment of trajectory tracking of a wheeled robot, it is verified that the two‐stage cubature Kalman filtering algorithm can obtain good tracking accuracy and stability with the presence of unknown random bias. Simultaneously, the equivalence of the two‐stage cubature Kalman filtering algorithm and cubature Kalman filtering algorithm is verified again using the contrast experiment.

Two-stage information filters for single and multiple sensors, and their square-root versions

Accurate states and unknown random bias estimation for well- and ill-conditioned systems are crucial for several applications. In this paper, a fusion of a two-stage Kalman filter and an information filter, and its extensions are considered to estimate the state variables and unknown random bias. Specifically, we propose four extensions of two-stage Kalman filters: two-stage information filter (TSIF), multi-sensor two-stage information filter (M-TSIF) and their square-root versions. The TSIF deals with single-sensor systems whereas the M-TSIF is capable to handle multi-sensor systems. For ill-conditioned systems, numerically stable square-root versions of TSIF and M-TSIF are developed. The performance of the proposed filters (along with the existing two-stage Kalman filter), for well- and ill-conditioned cases, is demonstrated on a quadruple-tank model.

The stability analysis of the adaptive two‐stage Kalman filter

AbstractRecently, the adaptive two‐stage Kalman filter, which can track unknown random bias, was proposed. This filter can be used for systems with unknown random bias on the assumption that the stochastic information of a random bias is incomplete. This paper analyses the stability of the adaptive two‐stage Kalman filter. Copyright © 2007 John Wiley & Sons, Ltd.

Adaptive Two-Stage EKF for INS-GPS Loosely Coupled System with Unknown Fault Bias

This paper proposes an adaptive two-stage extended Kalman filter (ATEKF) for estimation of unknown fault bias in an INS-GPS loosely coupled system. The Kalman filtering technique requires complete specifications of both dynamical and statistical model parameters of the system. However, in a number of practical situations, these models may contain parameters, which may deviate from their nominal values by unknown random bias. This unknown random bias may seriously degrade the performance of the filter or cause a divergence of the filter. The two-stage extended Kalman filter (TEKF), which considers this problem in nonlinear system, has received considerable attention for a long time. The TEKF suggested until now assumes that the information of a random bias is known. But the information of a random bias is unknown or partially known in general. To solve this problem, this paper firstly proposes a new adaptive fading extended Kalman filter (AFEKF) that can be used for nonlinear system with incomplete information. Secondly, it proposes the ATEKF that can estimate unknown random bias by using the AFEKF. The proposed ATEKF is more effective than the TEKF for the estimation of the unknown random bias. The ATEKF is applied to the INS-GPS loosely coupled system with unknown fault bias.

Adaptive two‐stage Kalman filter in the presence of unknown random bias

AbstractThe well‐known conventional Kalman filter gives the optimal solution but requires an accurate system model and exact stochastic information. In a number of practical situations, the system model has unknown bias and the Kalman filter with unknown bias may be degraded or even diverged. The two‐stage Kalman filter (TKF) to consider this problem has been receiving considerable attention for a long time. Until now, the optimal TKF for system with a constant bias or a random bias has been proposed by several researchers. In case of a random bias, the optimal TKF assumes that the information of a random bias is known. But the information of a random bias is unknown or incorrect in general. To solve this problem, this paper proposes two adaptive filters, such as an adaptive fading Kalman filter (AFKF) and an adaptive two‐stage Kalman filter (ATKF). Firstly, the AFKF is designed by using the forgetting factor obtained from the innovation information and the stability of the AFKF is analysed. Secondly, the ATKF to estimate unknown random bias is designed by using the AFKF and the performance of the ATKF is verified by simulation. Copyright © 2006 John Wiley & Sons, Ltd.