Abstract: This paper presents a method for identification
of a linear time invariant (LTI) autonomous all pole system
using singular value decomposition. The novelty of this paper
is two fold: First, MUSIC algorithm for estimating complex
frequencies from real measurements is proposed. Secondly,
using the proposed algorithm, we can identify the coefficients
of differential equation that determines the LTI system by
switching off our input signal. For this purpose, we need only
to switch off the input, apply our complex MUSIC algorithm
and determine the coefficients as symmetric polynomials in the
complex frequencies. This method can be applied to unstable
system and has higher resolution as compared to time series
solution when, noisy data are used. The classical performance
bound, Cramer Rao bound (CRB), has been used as a basis for
performance comparison of the proposed method for multiple
poles estimation in noisy exponential signal.
Abstract: Frequency estimation of a sinusoid in white noise using
maximum entropy power spectral estimation has been shown to be
very sensitive to initial sinusoidal phase. This paper presents use of
wavelet transform to find an analytic signal for frequency estimation
using maximum entropy method (MEM) and compared the results
with frequency estimation using analytic signal by Hilbert transform
method and frequency estimation using real data together with MEM.
The presented method shows the improved estimation precision and
antinoise performance.
Abstract: This paper presents an effective technique for harmonic current mitigation using an adaptive notch filter (ANF) to estimate current harmonics. The proposed filter consists of multiple units of ANF connected in parallel structure; each unit is governed by two ordinary differential equations. The frequency estimation is carried out based on the output of these units. The simulation and experimental results show the ability of the proposed tracking scheme to accurately estimate harmonics. The proposed filter was implemented digitally in TMS320F2808 and used in the control of hybrid active power filter (HAPF). The theoretical expectations are verified and demonstrated experimentally.
Abstract: Precise frequency estimation methods for pulseshaped echoes are a prerequisite to determine the relative velocity between sensor and reflector. Signal frequencies are analysed using three different methods: Fourier Transform, Chirp ZTransform and the MUSIC algorithm. Simulations of echoes are performed varying both the noise level and the number of reflecting points. The superposition of echoes with a random initial phase is found to influence the precision of frequency estimation severely for FFT and MUSIC. The standard deviation of the frequency using FFT is larger than for MUSIC. However, MUSIC is more noise-sensitive. The distorting effect of superpositions is less pronounced in experimental data.
Abstract: In this paper a novel method for multiple one dimensional real valued sinusoidal signal frequency estimation in the presence of additive Gaussian noise is postulated. A computationally simple frequency estimation method with efficient statistical performance is attractive in many array signal processing applications. The prime focus of this paper is to combine the subspace-based technique and a simple peak search approach. This paper presents a variant of the Propagator Method (PM), where a collaborative approach of SUMWE and Propagator method is applied in order to estimate the multiple real valued sine wave frequencies. A new data model is proposed, which gives the dimension of the signal subspace is equal to the number of frequencies present in the observation. But, the signal subspace dimension is twice the number of frequencies in the conventional MUSIC method for estimating frequencies of real-valued sinusoidal signal. The statistical analysis of the proposed method is studied, and the explicit expression of asymptotic (large-sample) mean-squared-error (MSE) or variance of the estimation error is derived. The performance of the method is demonstrated, and the theoretical analysis is substantiated through numerical examples. The proposed method can achieve sustainable high estimation accuracy and frequency resolution at a lower SNR, which is verified by simulation by comparing with conventional MUSIC, ESPRIT and Propagator Method.