Iterative Fast Orthogonal Search for Modeling by a Sum of Exponentials or Sinusoids

Abstract

Accurate sinusoidal series models of biological time-series data may be obtained using a modeling algorithm known as fast orthogonal search (FOS). FOS does not require equally spaced data, and can resolve sinusoidal frequencies much more closely spaced than can a discrete Fourier transform. FOS has been less successful at obtaining accurate exponential series models. We here consider a modification of FOS in which iteration of the original procedure is used to further reduce the mean-squared error (m.s.e.) between model and data, approaching a minimum in the m.s.e. Iteration of the FOS procedure greatly improves the accuracy of estimated exponential series models. The application of iterative FOS (IFOS) to exponential and sinusoidal series models is described. Finally, the use of FOS and IFOS procedures for finding a single model from the results of multiple experiments is described.

Particle-Filter-Based WiFi-Aided Reduced Inertial Sensors Navigation System for Indoor and GPS-Denied Environments

“…The problem then is reduced to a search in the space of N columns to find C columns that if they are used as basis functions in (9) they would achieve the minimum total mean square error over all data columns ( [27]. Finding such columns set is equivalent to finding the most informative "true" APs in the radiomap.…”

“…In orthogonal basis function space, the coefficient g m that minimizes the mean square error over the observations is given by [27] …”

“…The fast orthogonal search procedure [27] makes use of the fact that it is not necessary to create the orthogonal functions W m [n] explicitly. Only their correlations with P m [n], the data Y [n], and with themselves are required.…”

“…In Orthogonal Search techniques [27], Gram-Schmidt procedure is used to replace the functions P m [n] in (9) by a set of orthogonal basis functions W m [n] where the model for a specific j in (9) is represented by the following corresponding model:…”

A New High-Resolution GPS Multipath Mitigation Technique Using Fast Orthogonal Search

“…a ratio of the MSE over the mean squared value of the measured correlation function (Korenberg and Adeney, 1998) or an acceptably small percentage of the variance of the time-series being modelled). The search may also stop when a certain number of terms have been fitted.…”