951941
A fast algorithm for estimating the parameters of a quadratic FM signal
This paper describes a fast algorithm that can be used for estimating the parameters of a quadratic frequency modulated (FM) signal. The proposed algorithm is fast in that it requires only one-dimensional (1-D) maximizations. The optimal maximum likelihood method, by contrast, requires a three-dimensional (3-D) maximization, which can only be realized with an exhaustive 3-D grid search. Asymptotic statistical results are derived for all the estimated parameters. The amplitude estimate is seen to be optimal, whereas the phase parameters are, in general, suboptimal. Of the four phase parameter estimates, two approach optimality as the signal-to-noise ratio (SNR) tends to infinity. The other two have mean-square errors that are within 50% of the theoretical lower bounds for high SNR. Simulations are provided to support the theoretical results. Extensions to multiple components and higher order FM signals are also discussed.
121721485
Linear FM signal parameter estimation from discrete-time observations
The authors consider the problem of estimating the parameters of a complex linear FM signal from a finite number of noisy discrete-time observations. An estimation algorithm is proposed, and its asymptotic (large sample) performance is analyzed. The algorithm is computationally simple, consisting of two fast Fourier transforms (FFTs) accompanied by one-dimensional searches for maxima. The variance of the estimates is shown to be close to the Cramer-Rao lower bound when the signal-to-noise ratio is 0 dB and above. The authors applied the algorithm to the problem of estimating the kinematic parameters of an accelerating target by pulse-Doppler radar. A representative test case was used to exhibit the usefulness of the algorithm for this problem, and to verify the analytical results by Monte Carlo simulations. >
122768186
"Fast maximum likelihood joint estimation of frequency and frequency rate"
A Fast Maximum Likelihood Algorithm for the Joint estimation of the Frequency and Frequency rate of a sinusoid in Gaussian white noise is presented here. The novelty of this algorithm is the use of Newton's method for finding the zero of a function to determine the maximum of the log-likelihood function. The rate of convergence of Newton's method is extremely fast. Simulation of the algorithm shows that the RMSEs for frequency and frequency-rate are practically equal to the Cramer-Rao bound for allSNR \geq 15dB.
2382373
Single tone parameter estimation from discrete-time observations
Estimation of the parameters of a single-frequency complex tone from a finite number of noisy discrete-time observations is discussed. The appropriate Cramer-Rao bounds and maximum-likelihood (MI.) estimation algorithms are derived. Some properties of the ML estimators are proved. The relationship of ML estimation to the discrete Fourier transform is exploited to obtain practical algorithms. The threshold effect of one algorithm is analyzed and compared to simulation results. Other simulation results verify other aspects of the analysis.
37078028
Polynomial phase signal analysis based on the polynomial derivatives decompositions
An exact decomposition of the derivatives of any order of a polynomial /spl phi/(t) is proposed in terms of /spl phi/(t-t/sub 0/), ..., /spl phi/(t-t/sub n/). This result allows us to introduce generalized time-frequency distributions for studying signals having a polynomial phase and a constant amplitude in order to determine the degree and the coefficients of the corresponding phase. The relationships between these distributions and the already known polynomial distributions, i.e., the polynomial phase transform and the polynomial Wigner-Ville distribution, are discussed. Illustrations by example are proposed.
2766724
Polynomial Wigner-Ville distributions and their relationship to time-varying higher order spectra
The Wigner-Ville distribution (WVD) has optimal energy concentration for linear frequency modulated (FM) signals. This paper presents a generalization of the WVD in order to effectively process nonlinear polynomial FM signals. A class of polynomial WVD's (PWVD's) that give optimal concentration in the time-frequency plane for FM signals with a modulation law of arbitrary polynomial form are defined. A class of polynomial time-frequency distributions (PTFD's) are also defined, based on the class of PWVD's. The optimal energy concentration of the PWVD enables it to be used for estimation of the instantaneous frequency (IF) of polynomial FM signals. Finally, a link between PWVD's and time-varying higher order spectra (TVHOS) is established. Just as the expected value of the WVD of a nonstationary random signal is the time-varying power spectrum, the expected values of the PWVD's have interpretations as reduced TVHOS
34225189
The discrete polynomial-phase transform
The discrete polynomial-phase transform (DPT) is a new tool for analyzing constant-amplitude polynomial-phase signals. The main properties of the DPT are its ability to identify the degree of the phase polynomial and to estimate its coefficients. The transform is robust to deviations from the ideal signal model, such as slowly-varying amplitude, additive noise and nonpolynomial phase. The authors define the DPT, derive its basic properties, and use it to develop computationally efficient estimation and detection algorithms. A statistical accuracy analysis of the estimated parameters is also presented. >
29551518
Multicomponent signal analysis using the polynomial-phase transform
We consider the problem of estimating signals consisting of multiple components of the form b(n)exp{J/spl phi/(n)} where b(n) is a constant or a slowly varying amplitude, and the /spl phi/(n) is a polynomial function of time. We present an estimation algorithm based on the discrete polynomial transform and illustrate its performance by several examples. The proposed algorithm is computationally much simpler than the maximum likelihood estimator for this problem.
15883569
Parameter estimation of chirp signals
The problem of the parameter estimation of chirp signals is addressed. Several closely related estimators are proposed whose main characteristics are simplicity, accuracy, and ease of online or offline implementation. For moderately high signal-to-noise ratios they are unbiased and attain the Cramer-Rao bound. Monte Carlo simulations verify the expected performance of the estimators. It should be easy to extend this approach to signals having polynomials of any degree in the exponent. All the derivations will be done under the assumption that the signal-to-noise ratio is sufficiently high. >
9531651
Design of higher order polynomial Wigner-Ville distributions
The polynomial Wigner-Ville distribution (PWVD) is a time-frequency signal analysis tool for representing polynomial frequency modulated (FM) signals. We present an optimization procedure to design PWVDs and discuss the need for higher order PWVDs.
5096069
Asymptotic statistical analysis of the high-order ambiguity function for parameter estimation of polynomial-phase signals
The high-order ambiguity function (HAF) is a nonlinear operator designed to detect, estimate, and classify complex signals whose phase is a polynomial function of time. The HAF algorithm, introduced by Peleg and Porat (1991), estimates the phase parameters of polynomial-phase signals measured in noise. The purpose of this correspondence is to analyze the asymptotic accuracy of the HAF algorithm in the case of additive white Gaussian noise. It is shown that the asymptotic variances of the estimates are close to the Cramer-Rao bound (CRB) for high SNR. However, the ratio of the asymptotic variance and the CRB has a polynomial growth in the noise variance.