Optimal Quantization of Signals for System Identification

In this technical note, we examine the optimal quantization of signals for system identification. We deal with memoryless quantization for the output signals and derive the optimal quantization schemes. The objective functions are the errors of least squares parameter estimation subject to a constraint on the number of subsections of the quantized signals or the expectation of the optimal code length for either high or low resolution. The optimal quantizer has the property that it is coarse near the origin of its output and becomes dense away from the origin in the usual situation. Finally the required quantity of data to decrease the total parameter estimation error, caused by quantization and noise, is discussed.