Alpha-trimmed means of multiple location estimates

Abstract

Localization by distance measurements is a common technique for solving this contemporary problem. The methods which achieve the theoretically optimum solutions have generally iterative structures. That is why when limited computational load is required, suboptimum methods described by closed form formulas like the one of Coope which depends on orthogonal decomposition of sensor coordinates, are preferred. In this method, when there are more than necessary distance measurements required for localization, the location will be found as the arithmetic average of the estimates obtained using the all three-combinations of distance measurements. In the averaging, eliminating the outlier estimates will increase the performance. In this case discarding the estimates making the ratio of alpha which are farthest away from the arithmetic average, one attains the socalled alpha-trimmed mean of the estimates. Applying this technique, the disturbing effects of impulsive mixture of Gaussian contamination are eliminated and similar performances as in the case of Gaussian distance measurements are attained in localization.