A Bound on Mean-Square Estimation Error Accounting for System Model Mismatch
Abstract
In typical array processing problems the signal observation is a function of the parameter set to be estimated as well as some background system model assumed known. The modeled background could differ from the true one, leading to biased estimates even at high signal-to-noise ratio (SNR). To analyze this system model mismatch problem, a Ziv-Zakai-type lower bound on the mean-square error is developed based on the mismatched likelihood ratio test (MLRT). At high SNR, the bound incorporates the increase in mean-square error due to estimation bias; at low SNR, it includes the threshold effect due to estimation ambiguity. The kernel of the bound's evaluation is the error probability associated with the MLRT. A closed-form expression for this error probability is derived under a data model typical of the array problem assuming random signal embedded in random noise, both of which can be spatially correlated and potentially mismatched. The development is applied to plane-wave bearing estimation with array shape mismatch and matched-field source localization with channel parameter mismatch. Examples demonstrate that the developed bound describes the simulations of the maximum likelihood estimate well, including the sidelobe-introduced threshold behavior and the bias at high SNR.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 20, 2004
- Accession Number
- ADA432923
Entities
People
- Arthur Bernard Baggeroer
- Christ D. Richmond
- Kristine L. Bell
- Xu Wen