Our article “Ziv-Zakai Bound for Direct Position Estimation” was recently accepted:
A. Gusi-Amigó, P. Closas, A. Mallat, and L. Vandendorpe, “Ziv-Zakai Bound for Direct Position Estimation”, Navigation, accepted!
Abstract: Direct Position Estimation (DPE) has arisen as an appealing alternative to the conventional two steps positioning (2SP) approach. The usual metric to assess the performance of estimators is the Cramer-Rao Bound (CRB). However, the ´ CRB is only accurate in the high signal-to-noise ratio (SNR) region. In the lower SNR regions, high estimation errors take place and the variance of the estimates approach the a priori domain of the parameter. The DPE approach is expected to overcome the 2SP approach in such conditions. With the objective to throw light on this aspect, this paper shows the derivation of an approximate Ziv-Zakai Bound (ZZB) for the DPE approach and a mean square error (MSE) performance approximation based on the ZZB for the conventional approach. The derived bounds are compared with their associated CRBs and also with the performance of the corresponding Maximum Likelihood Estimator (MLE).