Benefits of Averaging Lateration Estimates Obtained Using Overlapped Subgroups of Sensor Data

Abstract

In this paper, we suggest averaging lateration estimates obtained using overlapped subgroups of distance measurements as opposed to obtaining a single lateration estimate from all of the measurements directly if a redundant number of measurements are available. Least squares based closed form equations are used in the lateration. In the case of Gaussian measurement noise the performances are similar in general and for some subgroup sizes marginal gains are attained. Averaging laterations method becomes especially beneficial if the lateration estimates are classified as useful or not in the presence of outlier measurements whose distributions are modeled by a mixture of Gaussians (MOG) pdf. A new modified trimmed mean robust averager helps to regain the performance loss caused by the outliers. If the measurement noise is Gaussian, large subgroup sizes are preferable. On the contrary, in robust averaging small subgroup sizes are more effective for eliminating measurements highly contaminated with MOG noise. The effect of high-variance noise was almost totally eliminated when robust averaging of estimates is applied to QR decomposition based location estimator. The performance of this estimator is just 1 cm worse in root mean square error compared to the Cramér–Rao lower bound (CRLB) on the variance both for Gaussian and MOG noise cases. Theoretical CRLBs in the case of MOG noise are derived both for time of arrival and time difference of arrival measurement data.