Unlike some traditional polynomial phase signal (PPS) parameter estimation methods restricted to monocomponent case, this paper focuses on the parameter estimation of multicomponent PPSs mixed in a single channel, which is more sophisticated and always involves the cross-term issue. In this investigation, based on the model of multicomponent PPSs in additional white Gaussian noise, we partition the maximum likelihood estimation into two consecutive steps. The first one involving estimation of polynomial coefficients is intensively studied using importance sampling, while the second one involving the estimation of amplitude and initial phase is trivial. Numerical experiments show satisfactory estimation performance even if the parameters are closely spaced.
2. Angeby, J., "Estimating signal parameters using the nonlinear instantaneous least squares approach," IEEE Transactions on Signal Processing, Vol. 48, No. 10, 2721-2732, 2000.
3. Pham, D. S. and A. M. Zoubir, "Analysis of multicomponent poly-nomial phase signals," IEEE Transactions on Signal Processing, Vol. 55, No. 1, 56-65, 2007.
4. Peleg, S. and B. Porat, "Estimation and classification of polynomial-phase signals," IEEE Transactions on Information Theory, Vol. 37, No. 2, 422-430, 1991.
5. Peleg, S. and B. Friedlander, "The discrete polynomial-phase transform," IEEE Transactions on Signal Processing, Vol. 43, No. 8, 1901-1914, 1995.
6. Porat, B. and B. Friedlander, "Asymptotic statistical analysis of the high-order ambiguity function for parameter estimation of polynomial-phase signals ," IEEE Transactions on Information Theory, Vol. 42, No. 3, 995-1001, 1996.
7. Peleg, S. and B. Friedlander, "Multicomponent signal analysis using the polynomial-phase transform," IEEE Transactions on Aerospace and Electronic Systems, Vol. 32, No. 1, 378-387, 1996.
8. Kay, S. and S. Saha, "Mean likelihood frequency estimation," IEEE Transactions on Signal Processing, Vol. 48, No. 7, 1937-1946, 2000.
9. Saha, S. and S. M. Kay, "Maximum likelihood parameter estimation of superimposed chirps using Monte Carlo importance sampling ," IEEE Transactions on Signal Processing, Vol. 50, No. 2, 224-230, 2002.
10. Kay, S. M., Fundamentals of Statistical Signal Processing, Volume I: Estimation Theory, 1993.
11. Pincus, M., "A closed form solution for certain programming problems," Oper. Res., 690-694, 1962.
12. Stoica, P. and A. Nehorai, "MUSIC, maximum likelihood, and Cramer-Rao bound," IEEE Transactions on Acoustics, Speech and Signal Processing, Vol. 37, No. 5, 720-741, 1989.
13. Yau, S. F. and Y. Bresler, "A compact Cramer-Rao bound expression for parametric estimation of superimposed signals," IEEE Transactions on Signal Processing, Vol. 40, No. 5, 1226-1230, 1992.