Signal tracking approach for simultaneous estimation of phase and instantaneous frequency

Phase estimation plays an important role in various signal processing areas like Radar, Sonar, power systems, speech analysis, communications and many others. The phase of the analytic form of the non stationary signals can be used to find instantaneous frequency. This paper addresses the problem of simultaneous phase and instantaneous frequency estimation from polynomial phase signals embedded in Gaussian noise. Here we have introduced the modified signal tracking approach which is then realized using unscented Kalman filter. The state space model is derived using Taylor series expansion of the phase of polynomial phase signal as process model while Polar to Cartesian conversion as measurement model. Proposed method, compared with state-of-the-art, performs better for signals with higher order polynomial phase variations at lower Signal-to-Noise-Ratio (0-5dB). We also present the simulation results for phase estimation.

[1]  Deepak Mishra,et al.  Signal tracking approach for phase estimation in digital holographic interferometry. , 2014, Applied optics.

[2]  J. Angeby.  Estimating signal parameters using the nonlinear instantaneous least squares approach , 2000 .

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

[4]  Maree Farquharson,et al.  Estimating the parameters of polynomial phase signals , 2006 .

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

[6]  Steven A. Tretter,et al.  Estimating the frequency of a noisy sinusoid by linear regression , 1985, IEEE Trans. Inf. Theory.

[7]  Ioan Nafornita,et al.  Identification of polynomial phase signals by extended Kalman filtering , 2008, 2008 16th European Signal Processing Conference.

[8]  W. Rudin.  Principles of mathematical analysis , 1964 .

[9]  Ioan Nafornita,et al.  The estimation of chirp signals parameters by an extended Kalman filtering algorithm , 2011, ISSCS 2011 - International Symposium on Signals, Circuits and Systems.

[10]  Xiang-Gen Xia,et al.  Discrete chirp-Fourier transform and its application to chirp rate estimation , 2000, IEEE Trans. Signal Process..

[11]  Jeffrey K. Uhlmann,et al.  Unscented filtering and nonlinear estimation , 2004, Proceedings of the IEEE.

[12]  Benjamin Friedlander,et al.  The discrete polynomial-phase transform , 1995, IEEE Trans. Signal Process..

[13]  Boaz Porat,et al.  Estimation and classification of polynomial-phase signals , 1991, IEEE Trans. Inf. Theory.

[14]  Amy T. Neel.  Formant detail needed for vowel identification , 2004 .

[15]  Sergio Barbarossa,et al.  Analysis of polynomial-phase signals by the integrated generalized ambiguity function , 1997, IEEE Trans. Signal Process..

[16]  I. Nafornita,et al.  Estimation of Chirp Signals in Gaussian Noise by Kalman Filtering , 2007, 2007 International Symposium on Signals, Circuits and Systems.

[17]  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..

[18]  Ananthram Swami,et al.  On polynomial phase signals with time-varying amplitudes , 1996, IEEE Trans. Signal Process..

[19]  Gerard Ledwich,et al.  Estimation of Time-Varying Mains Frequencies , 2003 .