A DISCUSSION ON USING NON-GAUSSIAN NOISE TO MODEL SENSOR POSITION ERROR IN SOURCE LOCALIZATION
Yaser Dalveren, Ali Kara · 2017
Recently, experiments on radar clutter has promoted that variables in measured data are non-Gaussian. For this reason, non-Gaussian statistical modeling has gained many interests in radar detection platforms especially when heterogeneous area is desired to illustrate. However, additive zero-mean Gaussian noise has been still widely used in estimation theory for modelling measurement errors. On the other hand, it is widely known that Cramer-RaoLower Bound (CRLB) is a measure that describes a lower bound of the estimation variances of any unbiased estimators. Hence, this bound is used as a benchmark to evaluate unbiased estimators. Especially in source localization, CRLB is based on source and sensor positions along with statistical distributions of the sensor position errors and range measurement errors. However, when the measurement errors are assumed to be non-Gaussian distributed, CRLB could not be directly derived. The study that presented in this article aims to provide a discussion for using non-Gaussian noise to model sensor position error in source localization. For this purpose, given study is initiated with describing theoretical information about the CRLB. After a brief discussion on CRLB,efforts are presented to evaluate CRLB for a particular measurement and parameter vector. In this context, several multivariate non-Gaussian distributions are addressed, and then computational difficulties are discussed. It is shown that the evaluation of CRLB of the source location in non-Gaussian sensor position noise is burdensome, and seems analytically impossible in most cases.