Bayesian Parameter Estimation Using Periodic Cost Functions

In this paper, a new method for Bayesian periodic parameter estimation is derived using periodic cost functions. The method, named parameter estimation via root finding (PERF), is based on Fourier series representation of the Bayes periodic-risk functions. The PERF method is implemented for minimum cyclic error, minimum absolute periodic error, and minimum mean-square-periodic-error (MSPE) estimators and the corresponding estimators are derived. The periodic estimators are applied to direction-of-arrival and phase estimation problems and compared with the minimum mean-square-error and maximum a posteriori probability estimators, and the periodic Ziv-Zakai lower bound in terms of MSPE.

[1]  Robert Boorstyn,et al.  Single tone parameter estimation from discrete-time observations , 1974, IEEE Trans. Inf. Theory.

[2]  R. Durrett.  Probability: Theory and Examples , 1993 .

[3]  K. Mardia.  Statistics of Directional Data , 1972 .

[4]  José M. N. Leitão,et al.  A nonlinear filtering approach to estimation and detection in mobile communications , 1998, IEEE J. Sel. Areas Commun..

[5]  L. Scharf,et al.  Modulo-2 Pi Phase Sequence Estimation. , 1978 .

[6]  R. Reggiannini.  A lower performance bound for phase estimation over slowly-fading Ricean channels , 1995, Proceedings of GLOBECOM '95.

[7]  Louis L. Scharf,et al.  Modulo-2 Pi phase sequence estimation (Corresp.) , 1980, IEEE Trans. Inf. Theory.

[8]  Yoram Bresler,et al.  A global lower bound on parameter estimation error with periodic distortion functions , 2000, IEEE Trans. Inf. Theory.

[9]  F. Gini,et al.  Multibaseline ATI-SAR for robust ocean surface velocity estimation , 2001, IEEE Transactions on Aerospace and Electronic Systems.

[10]  Yossef Steinberg,et al.  Extended Ziv-Zakai lower bound for vector parameter estimation , 1997, IEEE Trans. Inf. Theory.

[11]  A. Gualtierotti.  H. L. Van Trees, Detection, Estimation, and Modulation Theory, , 1976 .

[12]  Visa Koivunen,et al.  Robust ML-estimation of the Transmitter Location , 2004 .

[13]  Alan S. Willsky,et al.  Fourier series and estimation on the circle with applications to synchronous communication-I: Analysis , 1974, IEEE Trans. Inf. Theory.

[14]  Ruggero Reggiannini,et al.  A fundamental lower bound to the performance of phase estimators over Rician-fading channels , 1997, IEEE Trans. Commun..

[15]  Alan Lee,et al.  Circular data , 2010 .

[16]  M. Zakai,et al.  Some Classes of Global Cramer-Rao Bounds , 1987 .

[17]  J. Rosenthal.  A First Look at Rigorous Probability Theory , 2000 .

[18]  Fredrik Athley,et al.  Angle and frequency estimation using sensor arrays , 2001 .

[19]  J. Tabrikian,et al.  Optimal Bayesian parameter estimation with periodic criteria , 2010, 2010 IEEE Sensor Array and Multichannel Signal Processing Workshop.

[20]  Ioannis Pitas,et al.  Nonlinear processing and analysis of angular signals , 1998, IEEE Trans. Signal Process..

[21]  Joseph Tabrikian,et al.  Periodic CRB for non-Bayesian parameter estimation , 2011, 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[22]  Feller William,et al.  An Introduction To Probability Theory And Its Applications , 1950 .

[23]  James Ting-Ho Lo,et al.  Exponential Fourier densities and optimal estimation and detection on the circle , 1977, IEEE Trans. Inf. Theory.

[24]  H. L. Van Trees,et al.  Comparison of Performance Bounds for Doa Estimation , 1994 .

[25]  H. V. Trees.  Detection, Estimation, And Modulation Theory , 2001 .

[26]  R. S. Bucy,et al.  An Optimal Phase Demodulator , 1975 .

[27]  S. R. Jammalamadaka,et al.  Topics in Circular Statistics , 2001 .

[28]  Tretiak,et al.  Estimation for Rotational Processes with One Degree Sf Freedom-part I: Introduction and Contimuous-time Processes , 1975 .