This paper presents a method of estimating the speed of an induction motor using a measurement of the stator current. Speed-induced current harmonics are identified in the stator current using the fast orthogonal search (FOS) algorithm. The frequencies of these estimated harmonics are in turn used to estimate the speed of the motor given the number of rotor slots in the motor. Several optimizations of the FOS algorithm are presented to allow for real-time performance on an embedded digital signal processor. Experimental results of speed estimates on a 1/4 horsepower motor are presented to verify this approach.

The fast orthogonal search (FOS) algorithm has been shown to accurately model various types of time series by implicitly creating a specialized orthogonal basis set to fit the desired time series. When the data contain periodic components, FOS can find frequencies with a resolution greater than the discrete Fourier transform (DFT) algorithm. Frequencies with less than one period in the record length, called subharmonic frequencies, and frequencies between the bins of a DFT, can be resolved. This paper considers the resolution of subharmonic frequencies using the FOS algorithm. A new criterion for determining the number of non-noise terms in the model is introduced. This new criterion does not assume the first model term fitted is a dc component as did the previous stopping criterion. An iterative FOS algorithm called FOS first-term reselection (FOS-FTR), is introduced. FOS-FTR reduces the mean-square error of the sinusoidal model and selects the subharmonic frequencies more accurately than does the unmodified FOS algorithm.

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The accuracy of computer-aided diagnosis (CAD) for early detection and classification of breast cancer in dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is dependent upon the features used by the CAD classifier. Here, we show that fast orthogonal search (FOS), which provides a more efficient iterative manner of computing stepwise regression feature selection, can select features with predictive value from a set of kinetic and texture candidate features computed from dynamic contrast-enhanced magnetic resonance images. FOS can in minutes search candidate feature sets of millions of terms, which may include cross-products of features up to second-, third- or fourth-order. This method is tested on a set of 83 DCE-MRI images, of which 20 are for cancerous and 63 for benign cases, using a leave-one-out trial. The features selected by FOS were used in a FOS predictor and nearest-neighbour predictor and had an area under the receiver operating curve (AUC) of 0.889 and 0.791 respectively. The FOS predictor AUC is significantly improved over the signal enhancement ratio predictor with an AUC of 0.706 (p = 0.0035 for the difference in the AUCs). Moreover, using FOS-selected features in a support vector machine increased the AUC over that resulting when the features were manually selected.

In both military and civilian applications, the inertial navigation system (INS) and the global positioning system (GPS) are two complementary technologies that can be integrated to provide reliable positioning and navigation information for land vehicles. The accuracy enhancement of INS sensors and the integration of INS with GPS are the subjects of widespread research. Wavelet de-noising of INS sensors has had limited success in removing the long-term (low-frequency) inertial sensor errors. The primary objective of this research is to develop a novel inertial sensor accuracy enhancement technique that can remove both short-term and long-term error components from inertial sensor measurements prior to INS mechanization and INS/GPS integration. A high resolution spectral analysis technique called the fast orthogonal search (FOS) algorithm is used to accurately model the low frequency range of the spectrum, which includes the vehicle motion dynamics and inertial sensor errors. FOS models the spectral components with the most energy first and uses an adaptive threshold to stop adding frequency terms when fitting a term does not reduce the mean squared error more than fitting white noise. The proposed method was developed, tested and validated through road test experiments involving both low-end tactical grade and low cost MEMS-based inertial systems. The results demonstrate that in most cases the position accuracy during GPS outages using FOS de-noised data is superior to the position accuracy using wavelet de-noising.