Fault-tolerant spacecraft attitude determination via conditionally-linear filtering

Spacecraft are complex systems that are prone to sub-systems failures. Failure of the Attitude and Orbit Control System (AOCS), for instance, may be caused by failures of its components such as the attitude sensors, i.e., gyros, Sun sensors, horizon sensors, Earth magnetometers, etc. The increasing requirements on the spacecraft performances lead to more autonomy in estimation and health monitoring, as well as in reconfiguration, which emphasizes the necessity for fault-tolerant AOCS systems. A widely used mathematical paradigm for modeling random faulty systems is that of stochastic jump systems, i.e. a specific class of hybrid systems combining continuous valued state variables with discrete-valued state variables and where the discrete variable ("the mode") can jump among a finite number of possible values according to a priori transition probabilities. It is known, however, that the combined estimation of the continuous and of the discrete states via optimal filtering techniques does not lend itself to finite dimensional algorithms. The area of approximate hybrid estimation has thus been an area of intense research, yielding to practical algorithms, like the popular Interactive Multiple Model (IMM) estimator. Recently, a novel algorithm for mode estimation was developed via the approach of Conditionally-Linear (CL) filtering. That mode estimator proved to compare well with the optimal nonlinear mode estimator (Wonham filter) in simple cases, and could furthermore handle cases where the assumptions of the Wonham filter were not valid. It was efficiently applied to spacecraft gyros failures monitoring. The CL filter, however, only estimated the mode. This work presents an extension of the CL filter to mode and state estimation. The proposed hybrid filter combines a CL filter for mode estimation and a Kalman filter for state estimation. The overall architecture is simple since a single filter is needed for each of the tasks, and there is no need to compute likelihood functions via specific distribution functions. This is contrary to the IMM which requires a bank of filters to run in parallel for the state estimation, and which relies on the Gaussian assumption for the likelihood functions evaluation.