Barry G. Quinn

Random coefficient autoregressive models: an introduction

1 Introduction.- 1.1 Introduction.- Appendix 1.1.- Appendix 1.2.- 2 Stationarity and Stability.- 2.1 Introduction.- 2.2 Singly-Infinite Stationarity.- 2.3 Doubly-Infinite Stationarity.- 2.4 The Case of a Unit Eigenvalue.- 2.5 Stability of RCA Models.- 2.6 Strict Stationarity 37 Appendix 2.1.- 3 Least Squares Estimation of Scalar Models.- 3.1 Introduction.- 3.2 The Estimation Procedure.- 3.3 Strong Consistency and the Central Limit Theorem.- 3.4 The Consistent Estimation of the Covariance Matrix of the Estimates.- Appendix 3.1.- Appendix 3.2.- 4 Maximum Likelihood Estimation of Scalar Models.- 4.1 Introduction.- 4.2 The Maximum Likelihood Procedure.- 4.3 The Strong Consistency of the Estimates.- 4.4 The Central Limit Theorem.- 4.5 Some Practical Aspects.- Appendix 4.1.- Appendix 4.2.- 5 A Monte Carlo Study.- 5.1 Simulation and Estimation Procedures.- 5.2 First and Second Order Random Coefficient Autoregressions.- 5.3 Summary.- 6 Testing the Randomness of the Coefficients.- 6.1 Introduction.- 6.2 The Score Test.- 6.3 An Alternative Test.- 6.4 Power Comparisons 108 Appendix 6.1.- Appendix 6.1.- 7 The Estimation of Multivariate Models.- 7.1 Preliminary.- 7.2 The Least Squares Estimation Procedure.- 7.3 The Asymptotic Properties of the Estimates.- 7.4 Maximum Likelihood Estimation.- 7.5 Conclusion.- Appendix 7.1.- 8 An Application.- 8.1 Introduction.- 8.2 A Non-Linear Model for the Lynx Data.- References.- Author And Subject Index.

Estimating frequency by interpolation using Fourier coefficients

The periodogram of a time series that contains a sinusoidal component provides a crude estimate of its frequency parameter, the maximizer over the Fourier frequencies being within O(T/sup -1/) of the frequency as the sample size T increases. In the paper, a technique for obtaining an estimator that has root mean square error of order T/sup -3/2/ is presented, which involves only the Fourier components of the time series at three frequencies, The asymptotic variance of the estimator varies between, roughly, the asymptotic variance of the maximizer of the periodogram over all frequencies (the Cramer-Rao lower bound) and three times this variance. The advantage of the new estimator is its computational simplicity. >

Estimation of frequency, amplitude, and phase from the DFT of a time series

In a previous paper, a frequency estimator using only three Fourier coefficients was introduced, which has asymptotic variance of order T/sup -3/. In this correspondence, a similar technique of Rife and Vincent (1970) is shown to have asymptotic variance of larger order. A new estimator is introduced that has asymptotic variance Less than 1.65 times the CRLB.

Application of the short‐time Fourier transform and the Wigner–Ville distribution to the acoustic localization of aircraft

The dominant feature in the acoustic spectrum of a propeller‐driven aircraft is the spectral line corresponding to the propeller blade rate that is equal to the product of the propeller shaft rotation rate and the number of blades on the propeller. The frequency of this line, when measured by a stationary observer on the ground, changes with time due to the acoustical Doppler effect. In this paper, the short‐time Fourier transform and the Wigner–Ville distribution are used to estimate the propeller blade rate at short time intervals for a turbo‐prop aircraft flying at a constant altitude and speed over an acoustic sensor located just above ground level. The temporal variation in the observed blade rate is then used to estimate the speed and altitude of the aircraft, together with the source (or rest) frequency of the blade rate. Finally, the estimated values for these parameters are compared with the actual values recorded onboard the aircraft during each of the eighteen transits formed by pairing each element of a set of speeds: 150, 200, and 250 kn, with each element of a set of aircraft altitudes: 250, 500, 750, 1000, 1250, and 1500 ft.

An extended Kalman filter frequency tracker for high-noise environments

The problem of constructing a frequency tracker for weak, narrowband signals with slowly varying frequency is considered. An extended Kalman filter is proposed that uses prior knowledge of the nature of the signal to overcome the difficulties presented by the inherent nonlinearity of the problem and the very low signal-to-noise ratios.

Threshold behavior of the maximum likelihood estimator of frequency

We present accurate simplifications of the Rife and Boorstyn (1974) performance equations for the maximum likelihood estimator of frequency. The simplicity of the result allows quick calculation of the onset of threshold as a function of sample size and signal to noise ratio (SNR). The accuracy of the new expression is demonstrated via simulation. >

Analysis of the variance threshold of Kay's weighted linear predictor frequency estimator

A theoretical approximation for the variance of Kays weighted linear predictor frequency estimator is derived. From this expression, an inequality describing the variance threshold of the estimator is found. The window weights are then optimized to improve the variance. Numerical simulations demonstrate that the variance approximations are valid for medium to high signal-to-noise ratios or for large numbers of samples. >

Stationarity and invertibility of simple bilinear models

Necessary and sufficient conditions for strict stationarity and invertibility are found for one-parameter bilinear models. These conditions involve the expectations of the logarithms of the absolute values of the input and output sequences.

Recent advances in rapid frequency estimation

There are two main types of frequency estimator-the traditional, based on FFTs, and the more modern, based on linear filtering. Statistical and computational efficiency usually have to be traded off against each other. Typically the filter-based estimators are statistically grossly inefficient. This paper discusses the extension of the Quinn-Fernandes (filter-based, statistically optimal) technique to complex-valued signals, and the use of zero-padding to improve the statistical efficiency of the Fourier transform interpolative (FTI) estimator to statistical near-optimality.

Doppler speed and range estimation using frequency and amplitude estimates

A parametric form for the received ‘‘instantaneous frequency’’ of a pure tone is derived for the case of relative straight line motion between source and receiver. Ferguson and Quinn [J. Acoust. Soc. Am. 96, 821–827 (1994)] have recently described an algorithm which, given a sequence of high‐accuracy frequency estimators, produces estimators of the closest distance between the source and receiver, the relative speed, the rest frequency, and the time at closest approach. In this paper, an improved algorithm which uses amplitude estimators as well is introduced, and the statistical behavior of the estimators derived. The technique is automatic and will work even if only a section of the Doppler track is available.