Robust Fundamental Frequency Estimation in Coloured Noise

Most parametric fundamental frequency estimators make the implicit assumption that any corrupting noise is additive, white Gaus-sian. Under this assumption, the maximum likelihood (ML) and the least squares estimators are the same, and statistically efficient. However, in the coloured noise case, the estimators differ, and the spectral shape of the corrupting noise should be taken into account. To allow for this, we here propose two schemes that refine the noise statistics and parameter estimates in an iterative manner, one of them based on an approximate ML solution and the other one based on removing the periodic signal obtained from a linearly constrained minimum variance (LCMV) filter. Evaluations on real speech data indicate that the iteration steps improve the estimation accuracy, therefore offering improvement over traditional non-parametric fundamental frequency methods in most of the evaluated scenarios

Auto-regressive model based polarimetric adaptive detection scheme part I: Theoretical derivation and performance analysis

This paper deals with the problem of target detection in coherent radar systems exploiting polarimetric diversity. We resort to a parametric approach and we model the disturbance affecting the data as a multi-channel autoregressive (AR) process. Following this model, a new polarimetric adaptive detector is derived, which aims at improving the target detection capability while relaxing the requirements on the training data size and the computational burden with respect to existing solutions. A complete theoretical characterization of the asymptotic performance of the derived detector is provided, using two different target fluctuation models. The effectiveness of the proposed approach is shown against simulated data, in comparison with alternative existing solutions

Maximum Likelihood Estimation of Exponentials in Unknown Colored Noise for Target Identification in Synthetic Aperture Radar Images

This dissertation develops techniques for estimating exponential signals in unknown colored noise. The Maximum Likelihood (ML) estimators of the exponential parameters are developed. Techniques are developed for one and two dimensional exponentials, for both the deterministic and stochastic ML model. The techniques are applied to Synthetic Aperture Radar (SAR) data whose point scatterers are modeled as damped exponentials. These estimated scatterer locations (exponentials frequencies) are potential features for model-based target recognition. The estimators developed in this dissertation may be applied with any parametrically modeled noise having a zero mean and a consistent estimator of the noise covariance matrix. ML techniques are developed for a single instance of data in colored noise which is modeled in one dimension as (1) stationary noise, (2) autoregressive (AR) noise and (3) autoregressive moving-average (ARMA) noise and in two dimensions as (1) stationary noise, and (2) white noise driving an exponential filter. The classical ML approach is used to solve for parameters which can be decoupled from the estimation problem. The remaining nonlinear optimization to find the exponential frequencies is then solved by extending white noise ML techniques to colored noise. In the case of deterministic ML, the computationally efficient, one and two-dimensional Iterative Quadratic Maximum Likelihood (IQML) methods are extended to colored noise. In the case of stochastic ML, the one and two-dimensional Method of Direction Estimation (MODE) techniques are extended to colored noise. Simulations show that the techniques perform close to the Cramer-Rao bound when the model matches the observed noise

Maximum Likelihood Estimation of Exponentials in Unknown Colored Noise for Target in Identification Synthetic Aperture Radar Images

This dissertation develops techniques for estimating exponential signals in unknown colored noise. The Maximum Likelihood ML estimators of the exponential parameters are developed. Techniques are developed for one and two dimensional exponentials, for both the deterministic and stochastic ML model. The techniques are applied to Synthetic Aperture Radar SAR data whose point scatterers are modeled as damped exponentials. These estimated scatterer locations exponentials frequencies are potential features for model-based target recognition. The estimators developed in this dissertation may be applied with any parametrically modeled noise having a zero mean and a consistent estimator of the noise covariance matrix. ML techniques are developed for a single instance of data in colored noise which is modeled in one dimension as 1 stationary noise, 2 autoregressive AR noise and 3 autoregressive moving-average ARMA noise and in two dimensions as 1 stationary noise, and 2 white noise driving an exponential filter. The classical ML approach is used to solve for parameters which can be decoupled from the estimation problem. The remaining nonlinear optimization to find the exponential frequencies is then solved by extending white noise ML techniques to colored noise. In the case of deterministic ML, the computationally efficient, one and two-dimensional Iterative Quadratic Maximum Likelihood IQML methods are extended to colored noise. In the case of stochastic ML, the one and two-dimensional Method of Direction Estimation MODE techniques are extended to colored noise. Simulations show that the techniques perform close to the Cramer-Rao bound when the model matches the observed noise

Narrowband signal processing techniques with applications to distortion product otoacoustic emissions.

by Ma Wing-Kin.Thesis (M.Phil.)--Chinese University of Hong Kong, 1997.Includes bibliographical references (leaves 121-124).Chapter 1 --- Introduction to Otoacoustic Emissions --- p.1Chapter 1.1 --- Introduction --- p.1Chapter 1.2 --- Clinical Significance of the OAEs --- p.2Chapter 1.3 --- Classes of OAEs --- p.3Chapter 1.4 --- The Distortion Product OAEs --- p.4Chapter 1.4.1 --- Measurement of DPOAEs --- p.5Chapter 1.4.2 --- Some Properties of DPOAEs --- p.8Chapter 1.4.3 --- Noise Reduction of DPOAEs --- p.8Chapter 1.5 --- Goal of this work and Organization of the Thesis --- p.9Chapter 2 --- Review to some Topics in Narrowband Signal Estimation --- p.11Chapter 2.1 --- Fourier Transforms --- p.12Chapter 2.2 --- Periodogram ´ؤ Classical Spectrum Estimation Method --- p.15Chapter 2.2.1 --- Signal-to-Noise Ratios and Equivalent Noise Bandwidth --- p.17Chapter 2.2.2 --- Scalloping --- p.18Chapter 2.3 --- Maximum Likelihood Estimation --- p.19Chapter 2.3.1 --- Finding of the ML Estimator --- p.19Chapter 2.3.2 --- Properties of the ML Estimator --- p.21Chapter 3 --- Review to Adaptive Notch/Bandpass Filter --- p.23Chapter 3.1 --- Introduction --- p.23Chapter 3.2 --- Filter Structure --- p.24Chapter 3.3 --- Adaptation Algorithms --- p.25Chapter 3.3.1 --- Least Squares Method --- p.25Chapter 3.3.2 --- Least-Mean-Squares Algorithm --- p.27Chapter 3.3.3 --- Recursive-Least-Squares Algorithm --- p.28Chapter 3.4 --- LMS ANBF Versus RLS ANBF --- p.31Chapter 3.5 --- the IIR filter Versus ANBF --- p.31Chapter 4 --- Fast RLS Adaptive Notch/Bandpass Filter --- p.33Chapter 4.1 --- Motivation --- p.33Chapter 4.2 --- Theoretical Analysis of Sample Autocorrelation Matrix --- p.34Chapter 4.2.1 --- Solution of Φ (n) --- p.34Chapter 4.2.2 --- Approximation of Φ (n) --- p.35Chapter 4.3 --- Fast RLS ANBF Algorithm --- p.37Chapter 4.4 --- Performance Study --- p.39Chapter 4.4.1 --- Relationship to LMS ANBF and Bandwidth Evaluation . --- p.39Chapter 4.4.2 --- Estimation Error of Tap Weights --- p.40Chapter 4.4.3 --- Residual Noise Power of Bandpass Output --- p.42Chapter 4.5 --- Simulation Examples --- p.43Chapter 4.5.1 --- Estimation of Single Sinusoid in Gaussian White Noise . --- p.43Chapter 4.5.2 --- Comparing the Performance of IIR Filter and ANBFs . . --- p.44Chapter 4.5.3 --- Harmonic Signal Enhancement --- p.45Chapter 4.5.4 --- Cancelling 50/60Hz Interference in ECG signal --- p.46Chapter 4.6 --- Simulation Results of Performance Study --- p.52Chapter 4.6.1 --- Bandwidth --- p.52Chapter 4.6.2 --- Estimation Errors --- p.53Chapter 4.7 --- Concluding Summary --- p.55Chapter 4.8 --- Appendix A: Derivation of Ts --- p.56Chapter 4.9 --- Appendix B: Derivation of XT(n)Λ(n)ΛT(n)X(n) --- p.56Chapter 5 --- Investigation of the Performance of two Conventional DPOAE Estimation Methods --- p.58Chapter 5.1 --- Motivation --- p.58Chapter 5.2 --- The DPOAE Signal Model --- p.59Chapter 5.3 --- Preliminaries to the Conventional Methods --- p.60Chapter 5.3.1 --- Conventional Method 1: Constrained Stimulus Generation --- p.60Chapter 5.3.2 --- Conventional Method 2: Windowing --- p.61Chapter 5.4 --- Performance Comparison --- p.63Chapter 5.4.1 --- Sidelobe Level Reduction --- p.63Chapter 5.4.2 --- Estimation Accuracy --- p.65Chapter 5.4.3 --- Noise Floor Level --- p.67Chapter 5.4.4 --- Additional Loss by Scalloping --- p.68Chapter 5.5 --- Simulation Study --- p.69Chapter 5.5.1 --- Sidelobe Suppressions of the Windows --- p.69Chapter 5.5.2 --- Mean Level Estimation --- p.70Chapter 5.5.3 --- Mean Squared Error Analysis --- p.71Chapter 5.6 --- Concluding Summary --- p.75Chapter 5.7 --- Discussion --- p.75Chapter 5.8 --- Appendix A: Cramer-Rao Bound of the DPOAE Level Estimation --- p.76Chapter 6 --- Theoretical Considerations of Maximum Likelihood Estimation for the DPOAEs --- p.77Chapter 6.1 --- Motivation --- p.77Chapter 6.2 --- Finding of the MLEs --- p.78Chapter 6.2.1 --- First Form: Joint Estimation of DPOAE and Artifact Pa- rameter --- p.79Chapter 6.2.2 --- Second Form: Artifact Cancellation --- p.80Chapter 6.3 --- Relationship of CM1 to MLE --- p.81Chapter 6.4 --- Approximating the MLE --- p.82Chapter 6.5 --- Concluding Summary --- p.84Chapter 6.6 --- Appendix A: Equivalent Forms for the Minimum Least Squares Error --- p.85Chapter 7 --- Optimum Estimator Structure and Artifact Cancellation Ap- proaches for the DPOAEs --- p.87Chapter 7.1 --- Motivation --- p.87Chapter 7.2 --- The Optimum Estimator Structure --- p.88Chapter 7.3 --- References and Frequency Offset Effect --- p.89Chapter 7.4 --- Artifact Canceling Algorithms --- p.92Chapter 7.4.1 --- Least-Squares Canceler --- p.93Chapter 7.4.2 --- Windowed-Fourier-Transform Canceler --- p.93Chapter 7.4.3 --- FRLS Adaptive Canceler --- p.95Chapter 7.5 --- Time-domain Noise Rejection --- p.97Chapter 7.6 --- Regional Periodogram --- p.98Chapter 7.7 --- Experimental Results --- p.99Chapter 7.7.1 --- Artifact Cancellation via External Reference --- p.99Chapter 7.7.2 --- Artifact Cancellation via Internal Reference --- p.99Chapter 7.7.3 --- Artifact Cancellation in presence of Transient Noise --- p.101Chapter 7.7.4 --- Illustrative Example: DPgrams --- p.102Chapter 7.8 --- Conclusion and Discussion --- p.111Chapter 7.9 --- Appendix A: Derivation of the Parabolic Interpolation Method . --- p.113Chapter 7.10 --- Appendix B: Derivation of Weighted-Least-Squares Canceler . . --- p.114Chapter 8 --- Conclusions and Future Research Directions --- p.118Chapter 8.1 --- Conclusions --- p.118Chapter 8.2 --- Future Research Directions --- p.119Bibliography --- p.12

Maximum Likelihood Estimation of Signals in Autoregressive Noise

Time series modeling as the sum of a deterministic signal and an autoregressive (AR) process is studied. Maximum likelihood estimation of the signal amplitudes and AR parameters is seen to result in a nonlinear estimation problem. However, it is shown that for a given class of signals, the use of a parameter transformation can reduce the problem to a linear least squares one. For unknown signal parameters, in addition to the signal amplitudes, the maximization can be reduced to one over the additional signal parameters. The general class of signals for which such parameter transformations are applicable, thereby reducing estimator complexity drastically, is derived. This class includes sinusoids as well as polynomials and polynomial-times-exponential signals. The ideas are based on the theory of invariant subspaces for linear operators. The results form a powerful modeling tool in signal plus noise problems and therefore find application in a large variety of statistical signal processing problems. We briefly discuss some applications such as spectral analysis, broadband/transient detection using line array data, and fundamental frequency estimation for periodic signals. Copyright © 1994 by the Institute of Electrical and Electronics Engineers, Inc