Estimation with quantized measurements

An algorithm is described which estimates the state of a linear system from quantized measurements of the output of that system. The estimator is an unbiased minimum variance estimator which is constrained to be recursive. The form of the estimator is linear in terms of the innovation, although the gain does depend on past measurements. The basic estimator is a time-varying filter; a stationary estimator, whose gain is computed prior to the processing of any measurements, is also presented. The performance of this quantized data filter is compared with the performances of both a Kalman filter operating on the linear output and a Kalman filter which processes quantized data. The quantized data filter results in significant performance improvements when a coarse quantization characteristic with few levels is used.