State estimation with multi-level vector quantisation and communication uncertainty

In this paper, we design a state estimation algorithm for vector state-vector measurement systems over wireless sensor networks subject to bandwidth limitation and communication uncertainty. With the aid of Mahalanobis transformation, vector measurement innovations are decorrelated into the normalised ones to facilitate parallel quantisation. Then, taking account of Gaussian channel noises, a generalised multi-level quantisation mechanism and the minimum mean square error (MMSE) estimator are jointly designed, where optimal quantisation parameters can be solved by minimising the estimation error covariance with given quantisation level. The proposed MMSE estimator not only has a similar recursive structure as the classical Kalman filter, but also dramatically reduces the sensor-to-estimator communication requirement with only a slight deterioration of estimation performance. The combined effect of quantisation mechanism and communication uncertainty on estimation performance is also discussed. Finally, Monte Carlo simulation results illustrate the effectiveness and efficiency of the proposed quantised estimator.