Ziv-Zakai Bound for Direct Position Estimation

Adrià Gusi-Amigó, Pau Closas, Achraf Mallat, Luc Vandendorpe

Peer Reviewed

Abstract: Direct position estimation (DPE) has arisen as an appealing alternative to the conventional two-step positioning (2SP) approach. The usual metric to assess the performance of estimators is the Cramér-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 of throwing 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).
Published in: NAVIGATION: Journal of the Institute of Navigation, Volume 65, Number 3
Pages: 463 - 475
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