Recursive Estimation with Quantized and Censored Measurements

In this paper, we extend the Tobit Kalman filter for quantized measurements. Quantization occurs in many applications and systems and can usually be neglected in cases where the quantization interval is small. If this is not the case, the quantization effects cannot be ignored, and the nonlinearity induced by the quantizer must be addressed. Particle filters can be used, but are computationally expensive. Recently, the Tobit Kalman filter has been used to provide estimates when the measurement is a piecewise nonlinear censored regression model. The Tobit Kalman filter for quantized measurements derived in this paper is a computationally efficient algorithm, which converges to the optimal Kalman filter when quantization intervals become small. The derived estimator is compared to the Cramer Rao lower bound and the particle filter.