Performance of Instantaneous Frequency Rate Estimation Using High-Order Phase Function

The high-order phase function (HPF) is a useful tool to estimate the instantaneous frequency rate (IFR) of a signal with a polynomial phase. In this paper, the asymptotic bias and variance of the IFR estimate using the HPF are derived in closed-forms for the polynomial phase signal with an arbitrary order. The Cramer-Rao bounds (CRBs) for IFR estimation, in both exact and asymptotic forms, are obtained and compared with the asymptotic mean-square error (MSE) of the HPF-based IFR estimator. Simulations are provided to verify our theoretical results.

[1]  A. W. Rihaczek.  Principles of high-resolution radar , 1969 .

[2]  T. Abatzoglou.  Fast Maximnurm Likelihood Joint Estimation of Frequency and Frequency Rate , 1986, IEEE Transactions on Aerospace and Electronic Systems.

[3]  T. Abatzoglou,et al.  "Fast maximum likelihood joint estimation of frequency and frequency rate" , 1986, ICASSP '86. IEEE International Conference on Acoustics, Speech, and Signal Processing.

[4]  Boaz Porat,et al.  The Cramer-Rao lower bound for signals with constant amplitude and polynomial phase , 1991, IEEE Trans. Signal Process..

[5]  B. Porat,et al.  Linear FM signal parameter estimation from discrete-time observations , 1991 .

[6]  Sailes K. Sengijpta.  Fundamentals of Statistical Signal Processing: Estimation Theory , 1995 .

[7]  Benjamin Friedlander,et al.  Asymptotic statistical analysis of the high-order ambiguity function for parameter estimation of polynomial-phase signals , 1996, IEEE Trans. Inf. Theory.

[8]  Vladimir Katkovnik.  Nonparametric estimation of instantaneous frequency , 1997, IEEE Trans. Inf. Theory.

[9]  Anna Scaglione,et al.  Product high-order ambiguity function for multicomponent polynomial-phase signal modeling , 1998, IEEE Trans. Signal Process..

[10]  Boualem Boashash,et al.  Comments on "The Cramer-Rao lower bounds for signals with constant amplitude and polynomial phase" , 1998, IEEE Trans. Signal Process..

[11]  Anna Scaglione,et al.  Autofocusing of SAR images based on the product high-order ambiguity function , 1998 .

[12]  Braham Barkat,et al.  Instantaneous frequency estimation of polynomial FM signals using the peak of the PWVD: statistical performance in the presence of additive gaussian noise , 1999, IEEE Trans. Signal Process..

[13]  P. O'Shea.  A new technique for instantaneous frequency rate estimation , 2002, IEEE Signal Processing Letters.

[14]  Peter O'Shea,et al.  A fast algorithm for estimating the parameters of a quadratic FM signal , 2004, IEEE Transactions on Signal Processing.

[15]  Christoph H. Gierull,et al.  The influence of target acceleration on velocity estimation in dual-channel SAR-GMTI , 2006, IEEE Transactions on Geoscience and Remote Sensing.

[16]  C. Gierull,et al.  Compensating the effects of target acceleration in dual-channel SAR-GMTI , 2006 .

[17]  Jianyu Yang,et al.  Generalized High-Order Phase Function for Parameter Estimation of Polynomial Phase Signal , 2008, IEEE Transactions on Signal Processing.

[18]  Boaz Porat,et al.  Digital Processing of Random Signals: Theory and Methods , 2008 .