Development of frequency estimation algorithms

Abstract

My project title is frequency estimation which means determine the frequency of a received signal. The aim of this project is to develop a single-tone frequency estimation base on linear prediction technique. In this project, we don’t know the original frequency(ω) of the original signal, what we get is just a noisy signal. We try to use different approaches to retrieve the original signal and the frequency from the noisy received signals. After that, we calculate the difference between the original frequency(ω) and estimated frequency(ω) in order to evaluate its performance (by the help of CRLB). We have three main tasks to complete a) To implement the single-tone methods which is either biased estimators or unbiased estimators 1) Biased estimators includes: modified covariance (MC), Pisarenko Harmonic Decomposer (PHD) 2) Unbiased estimators includes: Reformed Pisarenko Harmonic Decomposer (RPHD), Maximum Likelihood (ML), Two stage Autocorrelation, Modified Pisarenko Harmonic Decomposition (MPHD) b) To implement the performance bound. There are two performance bounds implement in this project namely Cramer-Rao Lower Bound (CRLB). These performance bounds are in terms of minimum achievable variance provided by any unbiased estimator. c) To observe and compare the performance of different methods with the help of Cramer-Rao Lower Bound( CRLB). All the implementations are carried out under the environment of Matlab.