Deconvolution Estimation in Measurement Error Models: The R Package decon

Data from many scientific areas often come with measurement error. Density or distribution function estimation from contaminated data and nonparametric regression with errors in variables are two important topics in measurement error models. In this paper, we present a new software package decon for R, which contains a collection of functions that use the deconvolution kernel methods to deal with the measurement error problems. The functions allow the errors to be either homoscedastic or heteroscedastic. To make the deconvolution estimators computationally more efficient in R, we adapt the fast Fourier transform algorithm for density estimation with error-free data to the deconvolution kernel estimation. We discuss the practical selection of the smoothing parameter in deconvolution methods and illustrate the use of the package through both simulated and real examples.

The algorithm of noisy k-means

In this note, we introduce a new algorithm to deal with finite dimensional clustering with errors in variables. The design of this algorithm is based on recent theoretical advances (see Loustau (2013a,b)) in statistical learning with errors in variables. As the previous mentioned papers, the algorithm mixes different tools from the inverse problem literature and the machine learning community. Coarsely, it is based on a two-step procedure: (1) a deconvolution step to deal with noisy inputs and (2) Newton's iterations as the popular k-means

On the exact recovery of the FFT of noisy signals using a non-subtractively dither-quantized input channel

Through several algorithmic changes, the FFT and its variants have not only breathed a new lease of life into an otherwise latent classical DFT algorithm but also led to an explosion of applications in numerous areas. In all these applications of the Fourier transform, the FFT input has always been assumed to be sufficiently highly quantized so as to minimize, to a negligible level, an otherwise adverse effect of all quantization errors involved. A coarse quantization of the FFT input, with all the practical advantages that it entails, and an acceptable FFT estimation accuracy therefore seem to conflict with each other. This paper proposes a new theory that resolves this conflict for any quantization resolution used. This theory, tested with a 1-bit quantization scheme and under very noisy environments is very well supported by our simulation results. This makes the possibility of a hardware implementation of a 1-bit FFT chip a goal worth pursuing

On the exact recovery of the FFT of noisy signals using a non-subtractively dither-quantized input channel

Through several algorithmic changes, the FFT and its variants have not only breathed a new lease of life into an otherwise latent classical DFT algorithm but also led to an explosion of applications in numerous areas. In all these applications of the Fourier transform, the FFT input has always been assumed to be sufficiently highly quantized so as to minimize, to a negligible level, an otherwise adverse effect of all quantization errors involved. A coarse quantization of the FFT input, with all the practical advantages that it entails, and an acceptable FFT estimation accuracy therefore seem to conflict with each other. This paper proposes a new theory that resolves this conflict for any quantization resolution used. This theory, tested with a 1-bit quantization scheme and under very noisy environments is very well supported by our simulation results. This makes the possibility of a hardware implementation of a 1-bit FFT chip a goal worth pursuing

A new data analysis framework for the search of continuous gravitational wave signals

Continuous gravitational wave signals, like those expected by asymmetric spinning neutron stars, are among the most promising targets for LIGO and Virgo detectors. The development of fast and robust data analysis methods is crucial to increase the chances of a detection. We have developed a new and flexible general data analysis framework for the search of this kind of signals, which allows to reduce the computational cost of the analysis by about two orders of magnitude with respect to current procedures. This can correspond, at fixed computing cost, to a sensitivity gain of up to 10%-20%, depending on the search parameter space. Some possible applications are discussed, with a particular focus on a directed search for sources in the Galactic center. Validation through the injection of artificial signals in the data of Advanced LIGO first observational science run is also shown.Comment: 21 pages, 8 figure

Advanced Algorithms for Satellite Communication Signal Processing

Dizertační práce je zaměřena na softwarově definované přijímače určené k úzkopásmové družicové komunikaci. Komunikační kanály družicových spojů zahrnujících komunikaci s hlubokým vesmírem jsou zatíženy vysokými úrovněmi šumu, typicky modelovaného AWGN, a silným Dopplerovým posuvem signálu způsobeným mimořádnou rychlostí pohybu objektu. Dizertační práce představuje možné postupy řešení výpočetně efektivní digitální downkonverze úzkopásmových signálů a systému odhadu kmitočtu nosné úzkopásmových signálů zatížených Dopplerovým posuvem v řádu násobků šířky pásma signálu. Popis navrhovaných algoritmů zahrnuje analytický postup jejich vývoje a tam, kde je to možné, i analytické hodnocení jejich chování. Algoritmy jsou modelovány v prostředí MATLAB Simulink a tyto modely jsou využity pro ověření vlastností simulacemi. Modely byly také využity k experimentálním testům na reálném signálu přijatém z družice PSAT v laboratoři experimentálních družic na ústavu radioelektroniky.The dissertation is focused on software defined receivers intended for narrowband satellite communication. The satellite communication channel including deep space communication suffers from a high level of noise, typically modeled by AWGN, and from a strong Doppler shift of a signal caused by the unprecedented speed of an object in motion. The dissertation shows possible approaches to the issues of computationally efficient digital downconversion of narrowband signals and the carrier frequency estimation of narrowband signals distorted by the Doppler shift in the order of multiples of the signal bandwidth. The description of the proposed algorithms includes an analytical approach of its development and, if possible, the analytical performance assessment. The algorithms are modeled in MATLAB Simulink and the models are used for validating the performance by the simulation. The models were also used for experimental tests on the real signal received from the PSAT satellite at the laboratory of experimental satellites at the department of radio electronics.