Biased Estimation for Source Localization in Fault Tolerant Networks

Abstract

This paper considers the problem of a network that seeks to locate an emitter using biased estimation under the time difference of arrival (TDOA) method. Sensor pairings vary from disjoint (independent) pairing schemes to those with a common reference sensor. When a common sensor is shared between pairs, the network’s accuracy is highly susceptible to degradation where sensor node failures or compromise by an adversary can have drastic effects on the localization accuracy. This work develops a set of biased estimators for TDOA for any sensor pairing configuration, robust to network faults and overcomes the requirement of a common reference sensor of prior work. Two biased estimators are developed under the Minimax Trace MSE (MXTM) and the Minimax Matrix MSE (MXMM) approaches. The first biased estimator developed uses a minimax trace MSE approach, which is known to obtain a smaller trace MSE than the worst case MSE of the least squares (LS) estimator. The MXTM method, however, does not make any guarantees about the component-wise error. Thus, the second estimator uses a minimax matrix MSE approach, which ensures that the component-wise MSE is less than that of the traditional LS estimator. We observe the maximum benefit of biased estimators occurs in harsh settings characterized by: (1) low SNR, (2) low quality sensor-emitter configurations, and/or (3) small scale networks.