Optimum FFT-based frequency acquisition with application to COSPAS-SARSAT

Abstract

In the case of a single sinusoid or multiple weD-separated sinusoids, a coarse estimator consisting of a windowed Fourier transform foDowed by a rme estimator which is an interpolator is a good approximation to an optimal frequency acquisition and measurement algorithm. The design tradeoffs are described, and for the fine frequency estimator it is shown that a simple and good method is to fit a Gaussian function to the fast Fourier transform (F�'T) peak and its two neighbors. This method is able to achieve a frequency standard-deviation and a frequency bias in the order of ouly a few percent of a bin. In the case of short-time stationarity a proper compromise between FTT length and number of averages has to be made. We show here that for IDlderate nUlmer of averages and for an adaptive threshold detector, only between 0.5 and 1 dB is lost when averaging is traded off for FFT length, as contrasted to the asymptotic result of 1.5 dB.The COSPAS-SARSAT satellite system for emergency detection and localization is used to illustrate the concepts described. It is based on emergency locator transmitters and emergency position indicating radio beacons existing prior to sateOite systelJL These beacons have spectra] characteristics that are nonideal for Doppler positiOning. The described algorithm is analyzed theoreticaJIy and good agreement is found with test results.

Improved position estimation method for locating an encrypted COSPAS‐SARSAT beacon

“…Basically, a conventional COSPAS-SARSAT estimates time of arrival (TOA) and frequency of arrival (FOA) at the signal processing level to obtain the position of the beacon in distress, in which TOA and FOA are obtained by correlating the incoming signal with the locally generated signal. An optimum fast Fourier transformation (FFT)-based method for frequency acquisition and measurement was proposed in Holm [6], in which a windowed Fourier transform, which is a close approximation to an optimal acquisition algorithm, is employed in the first step as a coarse estimator. Then, the curve fitting of Gaussian function is applied to the FFT peak and its two neighbours in the second step to obtain a fine estimate.…”

Airborne ultrasound data communications: the core of an indoor positioning system

“…There is no absolute value for the maximum sound pressure level (SPL) for shouted speech. We have found values such as 1 Pa (94 dB), 90 dB SPL at 0.3 m [9] and 88 dB SPL at 1 m. We will assume a threshold for detection in the range assumed in optimal detection theory of 15-20 dB-Hz [13]. Here we will use 20 dBHz.…”

Indoors Data Communications using Airborne Ultrasound

“…The threshold for detection is in the range 15-20 dB [13], and here the more conservative value will be used. An analysis of speech for SL = 88 dB and a noise level, NS = 30... 40 dB in eq.…”