Eric Moisan

Phase tracking: what do we gain from optimality? particle filtering versus phase-locked loops

This paper studies the problem of tracking a Brownian phase with linear drift observed to within one digital modulation and one additive white Gaussian noise. This problem is of great importance as it models the problem of carrier synchronization in digital communications. The ultimate performances achievable for this problem are evaluated and are compared to the performances of three solutions of the problem. The optimal filter cannot be explicitly calculated and one goal of the paper is to implement it using recent sequential Monte-Carlo techniques known as particle filtering. This approach is compared to more traditional loops such as the Costas loop and the decision feedback loop. Moreover, since the phase has a linear drift, the loops considered are second-order loops. To make fair comparisons, we exploit all the known information to put the loops in their best configurations (optimal step sizes of the loops). We show that asymptotically, the loops and the particle filter are equivalent in terms of mean square error. However, using Monte-Carlo simulations we show that the particle filter outperforms the loops when considering the mean acquisition time (convergence rate), and we argue that the particle filter is also better than the loops when dealing with the important problem of mean time between cycle slips.

Blind source separation using order statistics

This paper shows the possibility to blindly separate instantaneous mixtures of sources by means of a criterion exploiting order statistics. Properties of higher order statistics and second-order methods are first underlined. Then a brief description of the order statistics shows that they gather all these properties and a new criterion is proposed. Next an iterative algorithm able to simultaneously extract all the sources is developed. The last part is comparison of this algorithm with well-known methods (JADE and SOBI). The most striking result is the possibility to exploit together independence and correlation through the use of order statistics.

Compressed and Quantized Correlation Estimators

In passive monitoring using sensor networks, low energy supplies drastically constrain sensors in terms of calculation and communication abilities. Designing processing algorithms at the sensor level that take into account these constraints is an important problem in this context. Here we study the estimation of correlation functions between sensors using compressed acquisition and one-bit-quantization. The estimation is achieved directly using compressed samples, without considering any reconstruction of the signals. We show that if the signals of interest are far from white noise, estimation of the correlation using M compressed samples out of N ≥ M can be more advantageous than estimation of the correlation using M consecutive samples. The analysis consists of studying the asymptotic performance of the estimators at a fixed compression rate. We provide the analysis when the compression is realized by a random projection matrix composed of independent and identically distributed entries. The framework includes widely used random projection matrices, such as Gaussian and Bernoulli matrices, and it also includes very sparse matrices. However, it does not include subsampling without replacement, for which a separate analysis is provided. When considering one-bit-quantization as well, the theoretical analysis is not tractable. However, empirical evidence allows the conclusion that in practical situations, compressed and quantized estimators behave sufficiently correctly to be useful in, for example, time-delay estimation and model estimation.

Optimal Asymmetric Binary Quantization for Estimation Under Symmetrically Distributed Noise

Estimation of a location parameter based on noisy and binary quantized measurements is considered in this letter. We study the behavior of the Cramér-Rao bound as a function of the quantizer threshold for different symmetric unimodal noise distributions. We show that, in some cases, the intuitive choice of threshold position given by the symmetry of the problem, placing the threshold on the true parameter value, can lead to locally worst estimation performance.

Frequency domain Volterra filters in terms of distributions

The Fourier transform of the output of a Volterra filter is given in terms of Schwartz distributions. This theory is developed in order to handle input signals that do not possess a Fourier transform in the usual sense. To illustrate this, the authors apply the result to the case of a sinusoidal input and to the case of a sampled and periodized signal.<<ETX>>

Examples of Output-only Modal Identification Using Compressive Sensing Techniques

In this paper, we make use of compressive sensing-based techniques in the context of output-only modal identification. Two power spectral density estimators are defined and applied to real-data experiments, finally their performances are illustrated. Our methods do not require high energy-consumer optimization algorithms, signals are converted into a very simple, and easy-to-process representation (compressed and highly quantized) which preserves information, reconstruction is therefore unnecessary. These savings are relevant for modal identification with wireless sensor networks, which have high power consumption and lifetime (autonomy) con- straints. doi: 10.12783/SHM2015/162

Revisiting the estimation of the mean using order statistics

Abstract This paper deals with the problem of estimating expected values using Order Statistics of a small sample. Estimators using a linear combination of Order Statistics, are compared to usual linear estimators. It is shown that while the use of Order Statistics improves the estimation of white sequences, linear estimators are sometimes more effective for colored sequences. Thus, a new estimator based on both the variates and their Order Statistics is developed. It is shown that this new estimator performs at least as well as Order Statistics estimators, and at least as well as linear estimators. An adaptive scheme of these estimators is then given and applied to estimate a binary noisy signal.