Quantile Process with Applications : Chirp Signal Model

<p>The parameters in the well-known chirp signal model controls the frequency fluctuations of the signals, and consequently, the estimation of the parameters has received considerable attention in the literature of statistical signal processing. In the same spirit with a broader view, this article investigates the quantile estimator of parameters involved in the chirp signal model, which enables us to provide basic features of the entire distribution of the signals. In the course of this study, we establish the limiting behaviour of the associated stochastic process, which we call quantile process. As the applications of this result, we obtain the limiting distributions of various quantile based measures of descriptive statistics, which give us summarized features of the fluctuations of the signals in various senses. Finally, along with extensive simulation study, the practicability of the proposed methodology is shown on a few benchmark real datasets closely related with various chirp signal models.<br></p>

Quantile Process with Applications : Chirp Signal Model

<p>The parameters in the well-known chirp signal model controls the frequency fluctuations of the signals, and consequently, the estimation of the parameters has received considerable attention in the literature of statistical signal processing. In the same spirit with a broader view, this article investigates the quantile estimator of parameters involved in the chirp signal model, which enables us to provide basic features of the entire distribution of the signals. In the course of this study, we establish the limiting behaviour of the associated stochastic process, which we call quantile process. As the applications of this result, we obtain the limiting distributions of various quantile based measures of descriptive statistics, which give us summarized features of the fluctuations of the signals in various senses. Finally, along with extensive simulation study, the practicability of the proposed methodology is shown on a few benchmark real datasets closely related with various chirp signal models.<br></p>

Super-resolution multi-reference alignment

We study super-resolution multi-reference alignment, the problem of estimating a signal from many circularly shifted, down-sampled and noisy observations. We focus on the low SNR regime, and show that a signal in ${\mathbb{R}}^M$ is uniquely determined when the number $L$ of samples per observation is of the order of the square root of the signal’s length ($L=O(\sqrt{M})$). Phrased more informally, one can square the resolution. This result holds if the number of observations is proportional to $1/\textrm{SNR}^3$. In contrast, with fewer observations recovery is impossible even when the observations are not down-sampled ($L=M$). The analysis combines tools from statistical signal processing and invariant theory. We design an expectation-maximization algorithm and demonstrate that it can super-resolve the signal in challenging SNR regimes.

A novel FastICA algorithm based on improved secant method for Intelligent drive

Blind Source Separation(BSS) is one of the research hotspots in the field of signal processing. In order to improve the accuracy of speech recognition in driving environment, the driver’s speech signal must be enhanced to improve its signal to noise ratio(SNR). Independent component analysis (ICA) algorithm is the most classical and efficient blind statistical signal processing technique. Compared with other improved ICA algorithms, fixed-point algorithm (FastICA) is well known for its fast convergence speed and good robustness. However, the convergence of FastICA algorithm is comparatively susceptible to the initial value selection of the original demixing matrix and the calculation of the iterative process is relatively large. In this paper, the gradient descent method is used to reduce the effect of initial value. What’s more, the improved secant method is proposed to speed up the convergence rate and reduce the amount of computation. As the results of mixed speech separation experiment turn out, the improved algorithm is of better performance relative to the standard FastICA algorithm. Experimental results show that the proposed algorithm improves the speech quality of the target driver. It is suitable for speech separation in driving environment with low SNR.

Cross-Layer Inference in WSN: From Methods to Experimental Validation

In this chapter, the fundamentals of distributed inference problem in wireless sensor networks (WSN) is addressed and the statistical theoretical foundations to several applications is provided. The chapter adopts a statistical signal processing perspective and focusses on distributed version of the binary-hypothesis test for detecting an event as correctly as possible. The fusion center is assumed to be equipped with multiple antennas collecting and processing the information. The inference problem that is solved, primarily concerns the robust detection of a phenomenon of interest (for example, environmental hazard, oil/gas leakage, forest fire). The presence of multiple antennas at both transmit and receive sides resembles a multiple-input-multiple-output (MIMO) system and allows for utilization of array processing techniques providing spectral efficiency, fading mitigation and low energy sensor adoption. The problem is referred to as MIMO decision fusion. Subsequently, both design and evaluation (simulated and experimental) of these fusion approaches is presented for this futuristic WSN set-up.