When performing measurements in an outdoor field environment, various interference factors occur. So, many studies have been performed to increase the accuracy of the localization. This paper presents a novel probability-based approach to estimating position based on Apollonius circles. The proposed algorithm is a modified method of existing trilateration techniques. This method does not need to know the exact transmission power of the source and does not require a calibration procedure. The proposed algorithm is verified in several typical environments, and simulation results show that the proposed method outperforms existing algorithms.

Let (X,Y) be a Rd R-valued random vector. In regression analysis one wants to estimate the regression function m(x):=E(Y|X=x) from a data set. In this paper we consider the convergence rate of the error for the k nearest neighbor estimators in case that m is (p,C)-smooth. It is known that the minimax rate is unachievable by any k nearest neighbor estimator for p > 1.5 and d=1. We generalize this result to any d ≥ 1. Throughout this paper, we assume that the data is independent and identically distributed and as an error criterion we use the expected L2 error.