Chirp parameter estimation from a sample covariance matrix

This paper considers the problem of estimating the bandwidth and the center frequency of a linear chirp signal. The nonstationarity property of chirp signals implies that the signal has high rank and reduces the applicability of subspace-based algorithms significantly. However, the special structure of the sample covariance matrix invites the use of regular frequency estimation algorithms. Herein, we show how subspace-type algorithms may be modified to provide accurate signal parameter estimates for linear chirp signals at reasonable complexity. The root-MUSIC algorithm is used as an example.

[1]  Petre Stoica,et al.  Markov-based eigenanalysis method for frequency estimation , 1994, IEEE Trans. Signal Process..

[2]  McMillan,et al.  Gravitational radiation from coalescing binary neutron stars. , 1994, Physical review. D, Particles and fields.

[3]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[4]  B. Friedlander,et al.  Multicomponent signal analysis using the polynomial-phase transform , 1996, IEEE Transactions on Aerospace and Electronic Systems.

[5]  Jakob Ängeby.  The Non-Linear Instantaneous Least Squares Approach to Signal Parameter Estimation , 1998 .

[6]  Philippe Forster,et al.  Operator approach to performance analysis of root-MUSIC and root-min-norm , 1992, IEEE Trans. Signal Process..

[7]  Peter Händel,et al.  Multicomponent polynomial phase signal analysis using a tracking algorithm , 1999, IEEE Trans. Signal Process..

[8]  B. R. Musicus,et al.  Frequency estimation from phase differences , 1989, International Conference on Acoustics, Speech, and Signal Processing,.

[9]  Björn E. Ottersten,et al.  Low-complexity estimators for distributed sources , 2000, IEEE Trans. Signal Process..

[10]  Petar M. Djuric,et al.  Parameter estimation of chirp signals , 1990, IEEE Trans. Acoust. Speech Signal Process..

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

[12]  S. Kadambe,et al.  Tracking of unknown non-stationary chirp signals using unsupervised clustering in the Wigner distribution space , 1988, ICASSP-88., International Conference on Acoustics, Speech, and Signal Processing.

[13]  K. S. Arun,et al.  Tracking the frequencies of superimposed time-varying harmonics , 1990, International Conference on Acoustics, Speech, and Signal Processing.

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

[15]  J. Doob.  Stochastic processes , 1953 .

[16]  Alexander Graham,et al.  Kronecker Products and Matrix Calculus: With Applications , 1981 .

[17]  Hamid Krim,et al.  Projections on unstructured subspaces , 1996, IEEE Trans. Signal Process..

[18]  P. Stoica,et al.  On the expectation of the product of four matrix-valued Gaussian random variables , 1988 .