Optimal Quantizer for Mixed Probabilistic/Deterministic Parameter Estimation

In this paper, we analyse the optimal quantization of signals for parameter estimation under constraints on admissible error bounds. We deal with simple FIR models where the input is a stochastic variable of uniform distribution. Then, we consider to derive the optimal memoryless quantization schemes for the output signals, which maximize the probability that the hard bounds of the estimated system parameters consist with the given error bounds. The analytic form of the optimal quantizer is given explicitly and it represents the relation between the accuracy of parameter estimation, system parameters and the necessary information