Filtering and Estimation for Quantized Sensor Information

The implication of quantized sensor information on estimation and filtering problems is studied. The close relation between sampling and quantization theory was earlier reported by Widrow, Kollar and Liu (1996). They proved that perfect reconstruction of the probability density function (pdf) is possible if the characteristic function of the sensor noise pdf is band-limited. These relations are here extended by providing a class of band-limited pdfs, and it is shown that adding such dithering noise is similar to anti-alias filtering in sampling theory. This is followed up by the implications for Maximum Likelihood and Bayesian estimation. The Cramer-Rao lower bound (CRLB) is derivedfor estimation and filtering on quantized data. A particle filter (PF) algorithm that approximates the optimal nonlinear filter is provided, and numerical experiments show that the PF attains the CRLB, while second-order optimal Kalman filter approaches can perform quite bad