A fast and accurate chirp rate estimation algorithm based on the fractional Fourier transform

Abstract

Abstract-In this work, a fast and accurate chirp-rate estimation algorithm is presented. The algorithm is based on the fractional Fourier transform. It is shown that utilization of the golden section search algorithm to find the maximum magnitude of the fractional Fourier transform domains not only accelerates the process, but also increases the accuracy in a noisy environment. Simulation results validate the proposed algorithm and show that the accuracy of parameter estimation nearly achieves the Cramer-Rao lower bound for SNR values as low as −7dB.

Efficient Rotational Angular Velocity Estimation of Rotor Target via Modified Short-Time Fractional Fourier Transform

“…Several comparative experimental results based on both simulated data and measured data are implemented to verify the effectiveness of the proposed algorithm in solving the contradiction between the estimation accuracy and the efficiency and avoiding the problem of local iterative convergence in the matched transform order estimation. From the results, we can conclude that the proposed algorithm is more effective and stable in rotational angular velocity estimation than GSS-based FRFT method proposed in [35] and other mentioned time-frequency analysis estimation algorithms.…”

“…Figure 18 shows the estimated RMSE and SD of rotational angular velocity am the proposed algorithm, the Hough-GSS-based STFRFT algorithm, and other tim quency analysis algorithms, where the received signal is added with white Gau noise, and each value of RMSE and SD are obtained and averaged by 1000 Montetrails. It should be pointed out that the rotational angular velocity estimation proc the Hough-GSS-based STFRFT algorithm is the same as that of the algorithm propos this paper, except that the Hough-GSS-based STFRFT algorithm adopts the GSS-b FRFT method proposed in [35] when estimating the matched transform order. As a parison, we give the rotational angular velocity estimation results of the method desc in Section 3.1, in which the matched transform order is estimated by searching the m mum amplitude value of FRFT in the traditional method, which is labeled as Hough-STFRFT in Figure 18.…”

“…Therefore, it is of great significance to study an effective and fast matched transform order estimation algorithm for the application of FRFT or STFRFT. Serbes and Aldimashki [35] proposed a fast and accurate matched transform order estimation method using the golden section search (GSS)-based FRFT algorithm. Guan et al [36] proposed a grading iterative search method to increase the estimation accuracy and calculation speed of the matched transform order.…”

A Block Method Using the Chirp Rate Estimation for NLFM Radar Pulse Reconstruction

“…If the used signal is characterized by a linearly modulated frequency, the estimation problem is not complicated, and in the literature many methods can be found. One of the most popular and precise approaches is a fractional Fourier transform [14], which is the generalized Fourier transform allowing intermediate signal representation between the time and frequency domains to be obtained. Cyclostationary analysis is also employed in many applications, but because of noise sensitivity and the requirement of several pulses this approach is not very suitable for radar techniques.…”

Polynomial phase signal parameter estimates refinement

“…The representative estimator of TFR based estimators is the quasi‐maximum likelihood estimator [10, 11], which avoids the disadvantages of phase differentiation based estimators. In addition, we have to mention the recent rising interest for the use of fractional Fourier transform for chirp rate estimation [12] and also, gradient methods for parameter estimation [13, 14]. Based on TFR, Djurovic and Stankovic [15] have proposed an algorithm for complex PPS parameter estimation, combining the intersection of the confidence intervals (ICI) rule [16] and O'Shea refinement procedure [17].…”