RANSAC as a Method for Reliable Line Identification for Efficient Estimation of the Instantaneous Frequency Rate

The random sample consensus (RANSAC) is applied as an effective approach for parameter estimation in case of presence of outliers. The CPF-RANSAC estimator is proposed and evaluated on signals embedded in high noise. Cubic phase function (CPF) is the distribution used for an efficient estimation of instantaneous frequency rate (IFR) for non-stationary signals with polynomial phase of the third order, called cubic phase (CP) signals. The most popular polynomial phase signals (PPS) are signals with the polynomial phase of the second order i.e., signals with linear frequency modulation (LFM). In real environment LFM signals are frequently distorted by additional third order component, what results in CP signals. Such signals appear as a line on the time-instantaneous frequency rate (T-IFR) plane, the parameters of which depend on the phase parameters of the signal. Thus, the problem under consideration concerns line estimation in a T-IFR plane. The IFR estimates are obtained by searching maximum of the CPF representation. Then the CPF-RANSAC strategy randomly selects a subset of data samples obtained from the CPF distribution of signals and uses them to estimate parameters of line. Optimal fitting to the line is obtained by selection of points based on the maximum likelihood (ML) criterion.