For a zero mean, proper, complex random vector x, the Hermitian covariance Exx is a complete second-order characterization. However, if the vector x is improper, it is correlated with its complex conjugate, meaning Exx 6= 0. This improper or complementary covariance must be accounted for in a complete second-order characterization. The improper covariance has been exploited for widely linear (W...

The Kalman Filter (KF) is pervasively used to control a vast array of consumer, health and defense products. By grouping sets of symmetric state variables, the Relational Kalman Filter (RKF) enables us to scale the exact KF for large-scale dynamic systems. In this paper, we provide a parameter learning algorithm for RKF, and a regrouping algorithm that prevents the degeneration of the relationa...

The increased power of small computers makes the use of parameter estimation methods attractive. Such methods have a number of uses in analytical chemistry. When valid models are available, many methods work well, but when models used in the estimation are in error, most methods fail. Methods based on the Kalman filter, a linear recursive estimator, may be modified to perform parameter estimati...

Noise reduction in speech signals is a growing area that encountered several applications like communication channel transmission, automatic speech recognition, telephony and hearing aids, among others. This paper introduces a technique for noise reduction in speech signals that combines both Discrete-time Kalman filtering and Wavelet transforms. While filtering provides noise reduction, Wavele...

This paper develops the impulse control approach to the observation process in Kalman-like filtering problems, which is based on impulsive model-ing of the transition matrix in an observation equation. The impulse control generates the jumps of the estimate variance from its current position down to zero and, as a result, enables us to obtain the filtering equations for the Kalman estimate with...

In conventional distributed Kalman filtering, employing diffusion strategies, each node transmits its state estimate to all its direct neighbors in each iteration. In this paper we propose a partial diffusion Kalman filter (PDKF) for state estimation of linear dynamic systems. In the PDKF algorithm every node (agent) is allowed to share only a subset of its intermediate estimate vectors at each...

We consider robust recursive filtering in the case of a linear, finite-dimensional and timediscrete state-space model with Euclidean state space. Insisting on recursivity for computational reasons, we come up with a new procedure, the rLS-filter, using a Huberized correction-step in the Kalman-filter recursions. Simulation results for ideal and contaminated data indicate that this procedure ach...

The paper analyzes two important issues in the design of multi-robot systems: (i) motion planning with the use of distributed algorithms, (ii) sensor fusion with the use of Extended Kalman or Particle Filtering. First, distributed gradient for motion planning of a multi-robot system is examined. The dynamic model of the multi-robot system is derived and its convergence to the desirable position...

This paper deals with the problem of speech enhancement when a corrupted speech signal with an additive Gaussian white noise is the only information available for processing. Speech enhancement aims to improve speech quality by using various algorithms. The objective of enhancement is improvement in intelligibility and/or overall perceptual quality of degraded speech signal using audio signal p...