Parametric System Identification Using Quantized Data

TL;DR

This paper introduces a quantile-based estimator for signal parameter estimation from quantized data, demonstrating improved accuracy and bias removal over traditional methods through simulations and experiments.

Contribution

It presents a novel quantile-based estimator for parameter estimation from quantized data, outperforming conventional methods in bias reduction.

Findings

The new estimator removes bias in constant and sinewave parameter estimation.

Simulations and experiments confirm the estimator's superior performance.

It effectively handles unknown signal characteristics.

Abstract

The estimation of signal parameters using quantized data is a recurrent problem in electrical engineering. As an example, this includes the estimation of a noisy constant value and of the parameters of a sinewave, that is, its amplitude, initial record phase, and offset. Conventional algorithms, such as the arithmetic mean, in the case of the estimation of a constant, are known not to be optimal in the presence of quantization errors. They provide biased estimates if particular conditions regarding the quantization process are not met, as it usually happens in practice. In this paper, a quantile-based estimator is presented, which is based on the Gauss-Markov theorem. The general theory is first described and the estimator is then applied to both direct current and alternate current input signals with unknown characteristics. Using simulations and experimental results, it is shown that the new estimator outperforms conventional estimators in both problems, by removing the estimation bias.