Wavelet de-noising is the current state of the art technique used in the accuracy enhancement of inertial sensors [3,4] and is therefore used as a standard of comparison in this research. The surveyed literature indicated that the Daubechies family of wavelets and soft thresholding employing the principles of Stein’s Unbiased Risk Estimate (SURE) are typically kinase inhibitor Crizotinib used in pre-filtering inertial sensors.The proposed technique employs the fast orthogonal search (FOS) algorithm [5,6] to estimate the low frequency spectrum, which contains the vehicle motion dynamics and long Inhibitors,Modulators,Libraries term noise, with a high frequency resolution and small number of frequency terms. The high-resolution spectral analysis capabilities Inhibitors,Modulators,Libraries of FOS will result in modeling the low frequencies with a small number of Inhibitors,Modulators,Libraries terms.
The dynamic noise threshold of FOS should accept the vehicle motion dynamics while rejecting the long term noise since the motion dynamics Inhibitors,Modulators,Libraries will likely have higher power than the long term noise terms.2.?Fast Orthogonal Search (FOS)The fast orthogonal search (FOS) algorithm [5�C9] is a general purpose modeling technique, which can be applied to spectral estimation and time-frequency analysis. The algorithm uses an arbitrary set of non-orthogonal candidate functions pm(n) and finds a functional expansion of an input y(n) in order to minimize the mean squared error (MSE) between the input and the functional expansion.The functional expansion of the input y(n) in terms of the arbitrary candidate functions pm(n) is given by:y(n)=��m=0Mampm(n)+��(n)(1)where am are the weights of the functional expansion, and ��(n) is the modeling error.
By choosing non-orthogonal candidate functions, there is no unique solution for Equation (1). However, FOS may model the input with fewer model terms than an orthogonal functional expansion [5]. For example, the fast Fourier transform (FFT) uses a basis set of Dacomitinib complex sinusoidal functions that Sorafenib Raf-1 have an integral number of periods in the record length [10]. For the FFT to model a frequency that does not have an integral number of periods in the record length, energy is spread into all the other frequencies, which is a phenomena known as spectral leakage [5,9,11]. By using candidate functions that are non-orthogonal, FOS may be able to model this frequency between two FFT bins with a single term resulting in many fewer weighting terms in the model [5,9].