Cramer-Rao lower bounds for estimation of phase in LBI based localization systems

This paper derives the Cramer-Rao lower bound (CRLB) on estimates of phase in long baseline interferometry (LBI) based localization systems. LBI localization is a classical method for finding the location of a non-cooperative emitter by estimating the phase difference between received signals by two sensors spatially separated on a single platform. In this paper, we derive the CRLB for phase difference in LBI-based systems by modelling the received signal as a deterministic unknown; that is, its samples are considered as nuisance parameters to be estimated. Consequently, the CRLB computations become much more complicated in this case. Finally, we provide the discussion for our results.

[1]  S. Kay.  Fundamentals of statistical signal processing: estimation theory , 1993 .

[2]  T. Moon,et al.  Mathematical Methods and Algorithms for Signal Processing , 1999 .

[3]  Mark L. Fowler.  Analysis of single-platform passive emitter location with terrain data , 2001 .

[4]  K. Becker.  An efficient method of passive emitter location , 1992 .

[5]  N. E. Wu,et al.  Aperture error mitigation via local-state estimation for frequency-based emitter location , 2003 .

[6]  Mark L. Fowler,et al.  Cramer-Rao lower bound on doppler frequency of coherent pulse trains , 2008, 2008 IEEE International Conference on Acoustics, Speech and Signal Processing.

[7]  K. Becker.  Passive localization of frequency-agile radars from angle and frequency measurements , 1999 .

[8]  Mark L. Fowler,et al.  Sensor network distributed computation for Direct Position Determination , 2012, 2012 IEEE 7th Sensor Array and Multichannel Signal Processing Workshop (SAM).

[9]  Mark L. Fowler,et al.  A LBI based emitter location estimator with platform trajectory optimality , 2009, 2009 Conference Record of the Forty-Third Asilomar Conference on Signals, Systems and Computers.

[10]  Don Torrieri,et al.  Statistical Theory of Passive Location Systems , 1984, IEEE Transactions on Aerospace and Electronic Systems.

[11]  Mark L. Fowler,et al.  Spatial sparsity based emitter localization , 2012, 2012 46th Annual Conference on Information Sciences and Systems (CISS).

[12]  K. Becker.  New algorithm for frequency estimation from short coherent pulses of a sinusoidal signal , 1990 .

[13]  K. Deergha Rao,et al.  A new method for finding electromagnetic emitter location , 1994 .

[14]  Jill K. Nelson,et al.  Target tracking via a sampling stack-based approach , 2009, 2009 Conference Record of the Forty-Third Asilomar Conference on Signals, Systems and Computers.

[15]  Arie Yeredor,et al.  Joint TDOA and FDOA Estimation: A Conditional Bound and Its Use for Optimally Weighted Localization , 2011, IEEE Transactions on Signal Processing.

[16]  N. Levanon.  Interferometry against differential Doppler: performance comparison of two emitter location airborne systems , 1989 .