TY - JOUR
T1 - Joint TDOA and FDOA estimation
T2 - A conditional bound and its use for optimally weighted localization
AU - Yeredor, Arie
AU - Angel, Eyal
PY - 2011/4
Y1 - 2011/4
N2 - 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.
AB - 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.
KW - Chirp
KW - conditional bound
KW - confidence ellipse
KW - frequency-difference of arrival (FDOA)
KW - passive emitter location
KW - time-difference of arrival (TDOA)
UR - http://www.scopus.com/inward/record.url?scp=79952661216&partnerID=8YFLogxK
U2 - 10.1109/TSP.2010.2103069
DO - 10.1109/TSP.2010.2103069
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AN - SCOPUS:79952661216
SN - 1053-587X
VL - 59
SP - 1612
EP - 1623
JO - IEEE Transactions on Signal Processing
JF - IEEE Transactions on Signal Processing
IS - 4
M1 - 5678660
ER -