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Abstract - SSAP10 |
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SSAP10.1 |
Frequency Estimation and Detection for Sinusoidal Signals with Arbitrary Envelope: A Nonlinear Least-Squares Approach O. Besson (ENSICA, France); P. Stoica (Uppsala University, Sweden) In this paper, we consider the problem of estimating the frequency of a sinusoidal signal whose amplitude could be either constant or time-varying. We present a nonlinear least-squares (NLS) approach when the envelope is time-varying. We show that the NLS estimator can be efficiently implemented using a FFT. A statistical analysis shows that the NLS frequency estimator is nearly efficient. The problem of detecting amplitude time variations is next addressed. A statistical test is formulated, based on the statistics of the difference between two frequency estimates. The test is computationally efficient and yields as a by-product consistent frequency estimates under either hypothesis (I.e. constant or time-varying amplitude). Numerical examples are included to show the performance in terms of both estimation and detection. |
| SSAP10.2 |
On Minimax Lower Bound for Time-Varying Frequency Estimation of Harmonic Signal A. Nazin (Institute of Control Science, Russia); V. Katkovnik (University of South Africa, South Africa) Estimation of the instantaneous frequency and its derivatives is considered for a harmonic signal with a time-varying phase and time-invariant amplitude. The asymptotic minimax lower bound is derived for the meansquared error of estimation provided that the phase is an arbitrary m-times piece-wise differentiable function of time. It is shown that this lower bound is different only in a constant factor from the upper bound for the mean squared errors of the local polynomial periodogram with optimal window size. |
| SSAP10.3 |
The Effect of Sampling and Quantization on Frequency Estimation A. Host-Madsen (Kwangju Institute of Science & Technology, Korea); P. Händel (Royal Institute of Technology, Sweden) The effect of sampling and quantization on frequency estimation for a single sinusoid is investigated. Cramér-Rao bound for 1 bit quantization is derived, and compared with the limit of infinite quantization. It is found that 1 bit quantization gives a slightly worse performance, however, with a dramatic increase of variance at certain freqencies. This can be avoided by using 4 times oversampling. The effect of sampling when using non-ideal anti-aliasing lowpass filters is therefore investigated. Cramér-Rao lower bounds are derived, and the optimal filters and sampling frequencies are found. Finally, fast estimators for 1 bit sampling, in particular correlation based estimators, are derived. The paper is concluded with simulation results for 4 times oversampled 1 bit quantization. |
| SSAP10.4 |
Sinusoids in White Noise: A Quadratic Programming Approach N. Moal, J. Fuchs (IRISA/Univ. de Rennes, France) We address the problem of the estimation and identification of real sinusoids in white Gaussian noise using a correlation-based method. We estimate a partial covariance sequence from the data and seek a representation of these observations as a superposition of a small number of cosines chosen from a redundant basis and the white noise contribution. We propose to minimize a quadratic program in order to choose a parsimonious decomposition among the many that allow the reconstruction. We develop optimality conditions for the criterion that can be geometrically interpreted and present a dual criterion that has an appealing physical interpretation. Some simulated examples are also presented to show the excellent performance in resolution of the approach. |
| SSAP10.5 |
Detection of Uncertain Multiple Cisioid Models R. Jonsson, J. Hagberg (Ericsson Microwave Systems AB, Sweden) The problem of detection of multiple complex sinusoidals, with uncertain parameters, is addressed in this paper. It is shown that uncertainties in amplitude and small uncertainties in frequency can be handled analytically, while unknown phases must be handled numerically. Robust detectors for some or all of the uncertainties are formulated. Performance in noise, and robustness are evaluated through simulations. Finally the applicability of the detectors for the problem of radar target recognition is discussed, and some results are presented. |
| SSAP10.6 |
Bootstrap Model Selection for Polynomial Phase Signals A. Zoubir, D. Iskander (Queensland University of Technology, Australia) We consider the problem of estimating the order of the phase of a complex valued signal, having a constant amplitude and a polynomial phase, measured in additive noise. A new method based on the bootstrap is introduced. The proposed approach does not require knowledge of the distribution of the noise, is easy to implement, and unlike existing techniques, it achieves high performance when only a small amount of data is available. The proposed technique can be easily extended to non-stationary signals which have a polynomial amplitude and phase, provided a consistent estimator for the parameters can be obtained. |
| SSAP10.7 |
Frequency Weighted Generalized Total Least Squares Linear Prediction for Frequency Estimation S. Leung, T. Lee, W. Lau (City University of Hong Kong, P R China) This paper presents a frequency weighted generalized total least squares linear prediction for estimating closely spaced sinusoids. In this method, the received data is first processed by a pole-zero prefilter and then a generalized total least squares linear prediction is applied to the prefiltered signal. A procedure of optimizing the generalized solution is introduced. By computer simulations, it is shown that the solution can outperform the existing well known total least squares solutions especially in low singal-to-noise ratio. |
| SSAP10.8 |
Bayesian Analysis for the Fault Detection of Three-phase Induction Machine M. Vieira, C. Theys (Universite de Nice-Sophia Antipolis, France) One of the most widely used techniques for obtaining information on the health state of three-phase induction machines is based on the processing of stator current. In fact, in the case of steady state operations, anomalous current spectral components, that increase if a fault occurs, allow to diagnose the presence and, in some case, the type of fault. In this paper, a Bayesian approach is proposed using a simulation technique, the Markov chain Monte Carlo (MCMC), to estimate the amplitude of some spectral components modified by machine faults and the slip, a parameter related to the load conditions, with a view to automatically detecting faults. Results on real stator current waveform are given. |
| SSAP10.9 |
On the Concept of Instantaneous Frequency P. Oliveira (Escola Naval, Portugal); V. Barroso (Instituto Superior Técnico, Portugal) The concept of Instantaneous Frequency is still not clearly defined. Current operational definitions give rise to physical paradoxes, difficulting proper interpretation of the obtained results. In this paper, we discuss why those paradoxes appear, and show how they can be avoided. We introduce a new definition of Instantaneous Frequency, which yields physically consistent results. This is confirmed with the help of several examples. |
| SSAP10.10 |
Joint Bayesian Detection and Estimation of Sinusoids Embedded in Noise C. Andrieu, A. Doucet, P. Duvaut (ENSEA-ETIS, France) In this paper we address the problem of the joint detection and estimation of sinusoids embedded in noise, from a Bayesian point of view. We first propose an original Bayesian model. A large number of parameters has to be estimated, including the number of sinusoids. No analytical developments can be performed. This lead us to design a new stochastic algorithm relying on reversible jump MCMC (Markov chain Monte Carlo). We obtain very satisfactory results. |
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