Average Fisher information optimization for quantized measurements using additive independent noise

Adding noise to nonlinear systems can enhance their performance. Additive noise benefits are observed also in parameter estimation problems based on quantized observations. In this study, the purpose is to find the optimal probability density function of additive noise, which is applied to observations before quantization, in those problems. First, optimal probability density function of noise is formulated in terms of an average Fisher information maximization problem. Then, it is proven that optimal additive “noise” can be represented by a constant signal level. This result, which means that randomization of additive signal levels is not needed for average Fisher information maximization, is supported with two numerical examples.