Hybrid filtering for Markovian jump-linear systems and application to fault-tolerant attitude estimation

A recently introduced algorithm for hybrid estimation in jump Markov systems was developed via the approach of conditionally-linear (CL) filtering. The hybrid filter KCL combines a single Kalman filter for state estimation with a single CL filter for mode estimation. The KCL filter was designed with the state and mode filters interacting in an interlaced manner. The present work is concerned with the development of novel hybrid estimators for jump Markov systems. A first algorithm is developed via a reformulation of the hybrid system model as a bilinear system with respect to the state and the mode, to which standard linear filtering techniques were applied. The method is straightforward and shows satisfactory results on a simple numerical example. Good performances however require control dependent terms that enhance observabiltity. Furthermore, two novel algorithms are presented as an extension of the KCL filter. The contribution of this work consists in augmenting the estimators' design models, thereby contributing to more accurate statistical computations. The state filter block is designed with the state vector augmented by a mode estimation error. In the other block, the mode filter is designed with the mode vector augmented by a partial state estimation error. Extensive simulations are performed to illustrate the advantages and drawbacks of the method and to compare it with existing hybrid filters. The extended KCL filtering approach is applied to a problem of attitude estimation using line-of-sight observations and gyro measurements, which faulty modes are modeled via randomly appearing biases. Monte-Carlo simulations show that the proposed approach succeeds in estimating the attitude while tracking the modes conditional probabilities.