Variance analysis of unbiased least ℓpℓp-norm estimator in non-Gaussian noise

• Theoretical performance of unbiased linear and nonlinear estimators is studied.
• Variance expressions based onℓpℓp-norm minimization in non-Gaussian noise are derived.
• To find the minimum variance under different noise types, the optimum p is computed.

Modeling time and space series in various areas of science and engineering require the values of parameters of interest to be estimated from the observed data. It is desirable to analyze the performance of estimators in an elegant manner without the need for extensive simulations and/or experiments. Among various performance measures, variance is the most basic one for unbiased estimators. In this paper, we focus on the estimator based on the ℓpℓp-norm minimization in the presence of zero-mean symmetric non-Gaussian noise. Four representative noise models, namely, αα-stable, generalized Gaussian, Student׳s tt and Gaussian mixture processes, are investigated, and the corresponding variance expressions are derived for linear and nonlinear parameter estimation problems at p≥1p≥1. The optimal choice of pp for different noise environments is studied, where the global optimality and sensitivity analyses are also provided. The developed formulas are verified by computer simulations and are compared with the Cramér-Rao lower bound.