Damián Marelli

On identification of FIR systems having quantized output data

In this paper, we present a novel algorithm for estimating the parameters of a linear system when the observed output signal is quantized. This question has relevance to many areas including sensor networks and telecommunications. The algorithms described here have closed form solutions for the SISO case. However, for the MIMO case, a set of pre-computed scenarios is used to reduce the computational complexity of EM type algorithms that are typically deployed for this kind of problem. Comparisons are made with other algorithms that have been previously described in the literature as well as with the implementation of algorithms based on the Quasi-Newton method.

Identification of ARMA models using intermittent and quantized output observations

This paper studies system identification of ARMA models whose outputs are subject to finite-level quantization and random packet dropouts. Using the maximum likelihood criterion, we propose a recursive identification algorithm, which we show to be strongly consistent and asymptotically normal. We also propose a simple adaptive quantization scheme, which asymptotically achieves the minimum parameter estimation error covariance. The joint effect of finite-level quantization and random packet dropouts on identification accuracy are exactly quantified. The theoretical results are verified by simulations.

Distributed weighted least-squares estimation with fast convergence for large-scale systems

We propose a distributed method for weighted least squares estimation. Our method is suitable for large-scale systems, in which each node only estimates a subset of the unknown parameters. As opposed to other works, our goal is to maximize the convergence speed of the distributed algorithm. To this end, we propose a distributed method for estimating the optimal value of certain scaling parameter on which this speed depends. To further speed the convergence, we use a simple preconditioning method, and we bound the difference between the resulting speed, and the fastest theoretically achievable using preconditioning. We include numerical experiments to illustrate the performance of the proposed method.

Kalman Filtering With Intermittent Observations: On the Boundedness of the Expected Error Covariance

This paper addresses the stability of a Kalman filter when measurements are intermittently available due to constraints in the communication channel between the sensor and the estimator. We give a necessary condition and a sufficient condition, with a trivial gap between them, for the boundedness of the expected value of the estimation error covariance. These conditions are more general than the existing ones in the sense that they only require the state matrix of the system to be diagonalizable and the sequence of packet losses to be a stationary finite order Markov process. Hence, we extend the class of systems for which these conditions are known in two directions, namely, by including degenerate systems, and by considering network models more general than i.i.d. and Gilbert-Elliott. We show that these conditions recover known results from the literature when evaluated for non-degenerate systems under the assumption of i.i.d. or Gilbert-Elliott packet loss models.

Linear LMS Compensation for Timing Mismatch in Time-Interleaved ADCs

The time-interleaved architecture permits the implementation of high-frequency analog-to-digital converters (ADCs) by multiplexing the output of several time-shifted low-frequency ADCs. An issue in the design of a time-interleaved ADC is the compensation of timing mismatch, which is the difference between the ideal and real sampling instants. In this paper, we propose a compensation method that, as opposite to existing approaches, does not assume that the input signal is band limited but assumes instead that it has a stationary known power spectrum. The compensation is then designed in a statistically optimal sense. This largely reduces the compensation order required to achieve a given reconstruction accuracy. Also, under the band-limited assumption, the proposed method achieves perfect reconstruction if no constraints are imposed on the order of the compensation. Simulation results show that a rough estimate of the input spectrum can be used without much performance loss, showing that an accurate knowledge of the input spectrum is not necessarily required.

A Continuous-Time Linear System Identification Method for Slowly Sampled Data

Both direct and indirect methods exist for identifying continuous-time linear systems. A direct method estimates continuous-time input and output signals from their samples and then use them to obtain a continuous-time model, whereas an indirect method estimates a discrete-time model first. Both methods rely on fast sampling to ensure good accuracy. In this paper, we propose a more direct method where a continuous-time linear model is directly fitted to the available samples. This method produces an exact model asymptotically, modulo some possible aliasing ambiguity, even when the sampling rate is relatively slow. We also state conditions under which the aliasing ambiguity can be resolved, and we provide experiments showing that the proposed method is a valid option when a slow sampling frequency must be used but a large number of samples is available.

Statistical properties of the error covariance in a Kalman filter with random measurement losses

In this paper we study statistical properties of the error covariance matrix of a Kalman filter, when it is subject to random measurement losses. We introduce a sequence of tighter upper bounds for the asymptotic expected error covariance (EEC). This sequence starts with a given upper bound in the literature and converges to the actual asymptotic EEC. Although we have not yet shown the monotonic convergence of this whole sequence, monotonic convergent subsequences are identified. The feature of these subsequences is that a tighter upper bound is guaranteed if more computation is allowed. An iterative algorithm is provided for computing each of these upper bounds. A byproduct of this paper is a more compact proof for a known necessary condition on the measurement arrival probability for the asymptotic EEC to be finite. A similar analysis leads to a necessary condition on the measurement arrival probability for the error covariance to have a finite asymptotic variance.

Kalman filtering with intermittent observations: Bounds on the error covariance distribution

When measurements are subject to random losses, the covariance of the estimation error of a state estimator becomes a random variable. In this paper we present bounds on the cumulative distribution function of the covariance of the estimation error for a discrete time linear system. We also show that the bounds can be arbitrarily tight if sufficient computational power is available. Numerical simulations show that the proposed method provides tighter bounds than the ones available in the literature.

Performance analysis for subband identification

The so-called subband identification method has been introduced recently as an alternative method for identification of finite-impulse response systems with large tap sizes. It is known that this method can be more numerically efficient than the classical system identification method. However, no results are available to quantify its advantages. This paper offers a rigorous study of the performance of the subband method. More precisely, we aim to compare the performance of the subband identification method with the classical (fullband) identification method. The comparison is done in terms of the asymptotic residual error, asymptotic convergence rate, and computational cost when the identification is carried out using the prediction error method, and the optimization is done using the least-squares method. It is shown that by properly choosing the filterbanks, the number of parameters in each subband, the number of subbands, and the downsampling factor, the two identification methods can have compatible asymptotic residual errors and convergence rate. However, for applications where a high order model is required, the subband method is more numerically efficient. We study two types of subband identification schemes: one using critical sampling and another one using oversampling. The former is simpler to use and easier to understand, whereas the latter involves more design problems but offers further computational savings.

On Pole-Zero Model Estimation Methods Minimizing a Logarithmic Criterion for Speech Analysis

A speech production model consists of a linear, slowly time-varying filter. Pole-zero models are required for a good representation of certain types of speech sounds, like nasals and laterals. From a perceptual point of view, designing them by minimizing a logarithmic criterion appears as a very suitable approach. The most accurate available results are obtained by using Newton-like search algorithms to optimize pole and zero positions, or the coefficients of a decomposition into quadratic factors. In this paper, we propose to optimize the numerator and denominator coefficients instead. Experimental results show that this is the computationally most efficient approach, especially when the optimization criterion considers a psychoacoustical frequency scale. To illustrate its applicability in speech processing, we used the proposed method for formant and anti-formant tracking as well as speech resynthesis.