Parametric System Identification Using Quantized Data

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 that is based on the Gauss-Markov theorem. The general theory is first described and the estimator is then applied to both DC and AC input signals with unknown characteristics. By using simulations and experimental results it is shown that the new estimator outperforms conventional estimators in both problems, by removing the estimation bias.

Quick Estimation of Periodic Signal Parameters From 1-Bit Measurements

“…The variance of each component of Y can be approximated using a Taylor series expansion of −1 (p h ) about the mean value ofp h . In [19], it is shown that this calculation provides…”

“…Previous research on this subject considered the estimation of systems parameters when the input sequence is known [17], [18] and when the input signal is synchronously sampled, that is, when the ratio between the sampling sequence period and the signal period is a rational number [19]. Several other papers have addressed a wide class of similar problems in the context of system identification [20]- [27].…”

“…The estimator working principle is based on the estimation of the probability with which, for a given value of x j , the quantizer outputs a logical 0, that is [19],…”

“…Finally, an estimate of is obtained by using the weighted least squares estimator [45] = ( A T W A) −1 A T WY (20) where W is a H × H diagonal matrix that contains the reciprocal of the variance of each estimator, 1 /σ 2 Y h , on the principal diagonal [45], estimated according to (19). An estimate of the estimator covariance matrix is given by [45]…”

“…Thus, either θ 1 or T must be known if the other parameter needs to be estimated. 3) When σ is unknown, both left-hand and right-hand terms in ( 12) can be divided by σ ; in this case, a new estimation problem can be setup if T is known and if the reciprocal of σ is defined as a new parameter to be estimated [19]. 4) The observation model (12) assumes that 0 <p h < 1, ∀h.…”