Instantaneous frequency estimation of multi-component Chirp signals in noisy environments

Abstract

A classical time-varying signal, the multi-component Chirp signal has been widely used and the ability to estimate its instantaneous frequency (IF) is very useful. But in noisy environments, it is hard to estimate the IF of a multi-component Chirp signal accurately. Wigner distribution maxima (WDM) are usually utilized for this estimation. But in practice, estimation bias increases when some points deviate from the true IF in high noise environments. This paper presents a new method of multi-component Chirp signal IF estimation named Wigner Viterbi fit (WVF), based on Wigner-Ville distribution (WVD) and the Viterbi algorithm. First, we transform the WVD of the Chirp signal into digital image, and apply the Viterbi algorithm to separate the components and estimate their IF. At last, we establish a linear model to fit the estimation results. Theoretical analysis and simulation results prove that this new method has high precision and better performance than WDM in high noise environments, and better suppression of interference and the edge effect. Compared with WDM, WVF can reduce the mean square error (MSE) by 50% when the signal to noise ration (SNR) is in the range of −15dB to −11dB. WVF is an effective and promising IF estimation method.

Keywords

instantaneous frequency estimation / multi-component Chirp signals / Wigner-Ville distribution / Viterbi algorithm / linear fit

References

[1] Zhang X., Bao Zeng. Nonstationary signal analysis and processing[M]. 1998, Beijing: National Defense Industry Press

[2] Boashash B. Estimating and interpreting the instantaneous frequency of a signal-part 1: fundamental[J]. Proc of IEEE, 1992, 80(4): 519-538

[3] Dai Y., Li Zhishun. Instantaneous Doppler estimation of wideband echoes based on Wigner-Ville distribution[J]. Acta Acoustica, 2002, 27(2): 137-140

[4] Rao P., Taylor F. J. Estimation of the instantaneous frequency using the discrete wigner distribution[J]. Electron Lett, 1990, 26(1): 246-248

[5] Katkovnik V., Stankovic L. Instantaneous frequency estimation using the Wigner distribution with varying and data-driven window length[J]. IEEE Trans on Signal Processing, 1998, 46(9): 2315-2326

[6] Andria G., Savino M., Trotta A. Application of Wigner-Ville distribution to measurements on transient signals[J]. IEEE Trans on Instrum Meas, 1994, 43(2): 187-193

[7] Djurovic I., Stankovic L. Influence of high noise on the instantaneous frequency estimation using time-frequency distribution[J]. IEEE Signal Processing Lett, 2000, 7(11): 317-319