Widely linear estimation of quaternion signals with intermittent observations

This paper is concerned with the optimal quaternion estimation problem for linear discrete-time stochastic systems with intermittent observations by using a widely linear processing. The uncertainty of the observations is modeled by a Bernoulli distributed quaternion variable with known parameters. An augmented linear state-space model is developed to describe the evolution of both the quaternion state and their noisy observations. On the basis of that model, the optimal widely linear filter, predictor and smoothers (fixed-point and fixed-interval), that only depend on probabilities, are obtained via an innovation analysis approach. The special case of semi-widely linear estimators, which appears under Cη-properness, is also studied. Simulation examples demonstrate the effectiveness and applicability of the proposed estimators.