Chair: Anthony J. Weiss, Tel-Aviv University (ISRAEL)
Stephen D. Casey, The American University
Brian M. Sadler, Army Research Laboratory (USA)
A modified Euclidean algorithm is presented for determining the period from a sparse set of noisy measurements. The set may arise from measuring the occurrence time of noisy zero-crossings of a sinusoid with very many missing observations. The procedure is computationally simple, stable with respect to noise, and converges quickly. Its use is justified by a theorem that shows that, for a set of randomly chosen positive integers, the probability that they do not all share a common prime factor approaches one quickly as the cardinality of the set increases. Simulations are presented to demonstrate the proposed algorithm.
Jakob Angeby, Ericsson Infocom Consultants AB (SWEDEN)
A new approach to estimate the phase and amplitude signal parameters of a quite general class of complex valued signals is presented. The proposed algorithm can estimate the signal parameters of a sum of complex signals, the amplitudes may be time varying and the phase functions are modelled by some continuous functions $a_l(t)$. The data can be evenly or unevenly sampled in time. The signal parameter estimates minimizes a loss function based on the prediction errors of a new, time dependent, structured autoregressive filter. The instantaneous phase and frequency is easily obtained from the estimated signal parameters. The structured AR filter is a model based time-frequency representation.
T. Ganesan, Motorola India Electronics Ltd. (INDIA)
A frequency estimator for complex sinusoids in white noise is proposed for very low SNR scenario. This algorithm possesses the computational simplicity of Discrete Fourier Transform (DFT) and resolution advantages of signal eigenvector methods. Asymptotic expressions are derived to explain the behaviour of the estimator for high and low SNR. Simulation results shows that the estimator provides reasonably good estimates even at lower SNR as compared to the existing techniques.
Olivier Besson, ENSICA (FRANCE)
In this paper, a new method for estimating the frequency of a random amplitude sinusoid is proposed. It is based upon solving Overdetermined Yule-Walker equations using constrained least-squares techniques. A Gauss-Newton algorithm is derived for proceeding to the constrained minimization. Simulation results prove the superiority of the new method over the unconstrained method, specially for a small number of equations.
C.S. Ramalingam, University of Rhode Island (USA)
R. Kumaresan, University of Rhode Island (USA)
In this paper we examine the effect of model mismatch when modeling a signal consisting of multiple non-stationary sinusoids. The envelopes and frequencies of the components were modeled as polynomials of low order over short intervals of time and the coefficients estimated using the least-squares error criterion. If the block length and model orders are not properly chosen, unacceptable errors occurred in the estimated frequency tracks. The errors tended to increase as the number of components increased. Using the simpler constant envelope, constant frequency sinewave model for short, heavily overlapping blocks and smoothing the resulting frequency tracks gave surprisingly good results when analyzing a long duration multicomponent signal. We conclude that the more complex polynomial model may not always yield the expected increase in accuracy in signal modeling.
Stuart Golden, University of California at Davis (USA)
In this paper we approximate arbitrary complex signals by modeling both the logarithm of the amplitude and the phase of the complex signal as finite-order polynomials in time. We refer to a signal of this type as an Exponential Polynomial Signal (EPS). We propose an algorithm to estimate any desired coefficient for this signal model. We also show how the mean-squared error of the estimate can be determined by using a first-order perturbation analysis. A Monte Carlo simulation is used to verify the validity of the perturbation analysis. The performance of the algorithm is illustrated by comparing the mean-squared error of the estimate to the Cramer-Rao bound for a particular example.
Gary D. Brushe, Defence Science and Technology Organisation
Langford B. White, Australian National University (AUSTRALIA)
A method of jointly estimating the parameters of a number of superimposed convolutional coded communications signals incident on an antenna array and demodulating these signals is presented in this paper. The method would allow simpler arrays to be designed due to the threshold extension obtained by this method. It also has the potential to increase the throughput of current Multiple Access channel systems, for example, Satellite communications and digital Mobile Cellular Phones, by using an antenna array. The contribution of the paper is the use of sequence estimation combined jointly with parameter estimation in array processing problems. In the simulations it is shown that a significant improvement in the accuracy of the demodulated signals and in the estimation of the signal's angle of arrivals is obtained compared to a deterministic Maximum Likelihood estimation method.
Joanna M. Spanjaard, Cooperative Research Centre for Robust and Adaptive Systems
Langford B. White, Defense Science and Technology Organization (AUSTRALIA)
The problem of period uncertainty when evaluating spectrum estimates for wide sense cyclostationary processes is addressed in this paper. In paricular, the extended Kalman filter and a parallel bank of Kalman filters are investigated as different methods for adaptive estimation of a time-varying period. An example is given concerning an AR(1) process and a number of time-varying periods are adaptively tracked for different periodic functions. Convergence characteristics are also assessed. Finally, a combined detection-estimation approach is also investigated.
Alain Ducasse, ENSEEIHT/GAPSE (FRANCE)
Corinne Mailhes, ENSEEIHT/GAPSE (FRANCE)
Francis Castanie, ENSEEIHT/GAPSE (FRANCE)
The Prony method is a technique for modeling a data set of N samples using a linear combination of p exponentials (N>p) in a least square estimation procedure. In this paper, a study of the amplitude and phase estimator is presented. In particular, theoretical results are given for bias and variance, which are confirmed by simulations. An optimal number of equations in the corresponding least square estimation procedure is derived, minimizing estimation errors.
Boaz Porat, Israel Institute of Technology (ISRAEL)
Benjamin Friedlander, University of California (USA)
The paper develops a method of error analysis for Fourier-transform based sinusoidal frequency estimation in the presence of nonrandom interferences. A general error formula is derived, and then specialized to the cases of additive and multiplicative interferences. Approximate error formulas are derived for the case of additive polynomial- phase interference. Finally, an application to error-analysis in estimating the parameters of multiple polynomial-phase signals is discussed in detail.