Systematic Bias Correction in Source Localization

A novel analytical approach is proposed to approximate and correct the bias in localization problems in n-dimensional space (n = 2 or 3) with N (N >= n) independently usable measurements (such as distance, bearing, time difference of arrival (TDOA), etc.). Here, N is often but not always the same as the number of sensors. This new method mixes Taylor series and Jacobian matrices to determine the bias and leads in the case when N = n to an easily calculated analytical bias expression; however, when N is greater than n, the nature of the calculation is more complicated in that a further step is required. The proposed novel method is generic, which means that it can be applied to different types of measurements. To illustrate this approach we analyze the proposed method in three situations. Monte Carlo simulation results verify that, when the underlying geometry is a good geometry (which allows the location of the target to be obtained with acceptable mean square error (MSE)), the proposed approach can correct the bias effectively in space of dimension 2 or 3 with an arbitrary number of independent usable measurements. In addition the proposed method is applicable irrespective of the type of measurement (range, bearing, TDOA, etc.).