Hybrid Filtering for Markovian Jump-Linear Systems and Application to Fault-tolerant Attitude Estimation

摘要

A recently introduced algorithm for hybrid estimation in jumpMarkovsystems was developed via the approach of conditionally-linear (CL) fil-tering. The hybrid filter KCL combines a single Kalman filter for stateestimation with a single CL filter for mode estimation. The KCL filterwas designed with the state and mode filters interacting in an interlacedmanner. The present work is concerned with the development of novelhybrid estimators for jump Markov systems. A first algorithm is devel-oped via a reformulation of the hybrid system model as a bilinear systemwith respect to the state and the mode, to which standard linear filter-ing techniques were applied. The method is straightforward and showssatisfactory results on a simple numerical example. Good performanceshowever require control dependent terms that enhance observabiltity.Furthermore, two novel algorithms are presented as an extension of theKCL filter. The contribution of this work consists in augmenting theestimators’ design models, thereby contributing to more accurate sta-tistical computations. The state filter block is designed with the statevector augmented by a mode estimation error. In the other block, themode filter is designed with the mode vector augmented by a partial stateestimation error. Extensive simulations are performed to illustrate theadvantages and drawbacks of the method and to compare it with exist-ing hybrid filters. The extended KCL filtering approach is applied to aproblem of attitude estimation using line-of-sight observations and gyromeasurements, which faulty modes are modeled via randomly appear-ing biases. Monte-Carlo simulations show that the proposed approachsucceeds in estimating the attitude while tracking the modes conditionalprobabilities.