Joint TDOA and FDOA Estimation: A Conditional Bound and Its Use for Optimally Weighted Localization

Modern passive emitter-location systems are often based on joint estimation of the time-difference of arrival (TDOA) and frequency-difference of arrival (FDOA) of an unknown signal at two (or more) sensors. Classical derivation of the associated Cramér-Rao bound (CRB) relies on a stochastic, statio...

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Bibliographic Details
Published in:IEEE transactions on signal processing 2011-04, Vol.59 (4), p.1612-1623
Main Authors: Yeredor, A, Angel, E
Format: Article
Language:English
Subjects:
Applied sciences
Arrivals
Asymptotic properties
Chirp
conditional bound
confidence ellipse
Correlation
Detection, estimation, filtering, equalization, prediction
Errors
Estimating
Exact sciences and technology
frequency-difference of arrival (FDOA)
High definition video
Information, signal and communications theory
Localization
Maximum likelihood estimation
Noise
Optimization
passive emitter location
Position (location)
Sensors
Signal and communications theory
Signal representation. Spectral analysis
Signal, noise
Telecommunications and information theory
Time frequency analysis
time-difference of arrival (TDOA)
Weighting
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Summary:Modern passive emitter-location systems are often based on joint estimation of the time-difference of arrival (TDOA) and frequency-difference of arrival (FDOA) of an unknown signal at two (or more) sensors. Classical derivation of the associated Cramér-Rao bound (CRB) relies on a stochastic, stationary Gaussian signal-model, leading to a diagonal Fisher information matrix with respect to the TDOA and FDOA. This diagonality implies that (under asymptotic conditions) the respective estimation errors are uncorrelated. However, for some specific (nonstationary, non-Gaussian) signals, especially chirp-like signals, these errors can be strongly correlated. In this work we derive a "conditional" (or a "signal-specific") CRB, modeling the signal as a deterministic unknown. Given any particular signal, our CRB reflects the possible signal-induced correlation between the TDOA and FDOA estimates. In addition to its theoretical value, we show that the resulting CRB can be used for optimal weighting of TDOA-FDOA pairs estimated over different signal-intervals, when combined for estimating the target location. Substantial improvement in the resulting localization accuracy is shown to be attainable by such weighting in a simulated operational scenario with some chirp-like target signals.
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2010.2103069