No / This paper presents a new approach to estimate the unknown frequencies of the constituent sinusoids in a noiseless signal. The signal comprising of unknown number of sinusoids of unknown amplitudes and unknown phases is measured in the time domain. The Hankel matrix of measured samples is used as a basis for further analysis in the Pisarenko harmonic decomposition. A new constraint, the Existence Factor (EF), has been introduced in the methodology based on the relationship between the frequencies of the unknown sinusoids and the eigenspace of Hankel matrix of signal's samples. The accuracy of the method has been tested through multiple simulations on different signals with an unknown number of sinusoidal components. Results showed that the proposed method has efficiently estimated all the unknown frequencies.

The Range Limited Antenna (RLA) has the ability to track and pin-point RF devices operating within a certain accepted range. Using two antenna arrays, each made up of several elements, direction-finding algorithms such as MUSIC and Modified Root Pisarenko (MRP) are used to estimate the angles of arrival of incoming signals. Using the estimated angles of arrival, a range estimation algorithm is used to estimate the distance of the emitter from the antenna array. The aim of this thesis is to check the sensitivity of the range estimation and to form a statistical analysis for such conditions. Conditions of error are introduced into the system and several extensive Monte Carlo simulations are run for both MUSIC and MRP. Upon simulating physical errors in the antenna set-up, it is realized that the range estimation algorithm is sensitive to the slightest of phase shift differences, cable loss differences, mixer mismatches, and antenna mismatches. / Master of Science

Darbe atlikta eksponentinių-sinusinių modelių įvertinimo specialiu mažiausių kvadratų metodu analizė. Apžvelgti pagrindiniai signalo parametrai. Aprašyti signalo modeliai bei jų formos. Išnagrinėtas visuminių mažiausių kvadratų metodas bei jam alternatyvūs metodai: kovariacinis, Tufts-Kumaresan ir Pisarenko. Pateikti šių metodų matematiniai aprašymai. Signalų modelių parametrų analizei sukurtos MATLAB programos bei pateikti jų programiniai kodai. Skaitiniais eksperimentais ištirta, kaip kiekvienas iš metodų veikia, esant skirtingam signalo-triukšmo santykiui. Gauti rezultatai iliustruoti grafiškai. Remiantis sumodeliuotais rezultatais, suformuluotos išvados apie nagrinėjamų metodų galimybes. / The aim of this study is to explore exponential-sinusoidal signal model estimation by a special least squares method. The main signal parameters are considered. Signal models and their forms are described. The total least squares method as well as its alternatives – the covariance, Tufts-Kumaresan and Pisarenko methods – are analysed. The mathematical description of these methods is given. MATLAB–based programs to analyse signal model parameters are developed and their codes are presented. We investigated the performance of each of these methods for different signal noise ratio values. The results obtained are illustrated graphically. Conclusions about the method properties are drawn on the basis of simulation experiments.