Kalman filter (KF) can provide optimal solutions if the system dynamic and measurement models are correctly defined, and the noise statistics for the measurement and system are completely known. The conventional way of determining the covariance matrices of process noise and observation errors relies on analysis of empirical data from each sensor in a system, which is called KF tuning. In pract...

Many practical applications including speech and audio processing, signal processing, system identification, econometrics and time series analysis involve the problem of reconstructing a dynamic system model from data observed with noise in all variables. We consider an important class of dynamic single-input single-output nonlinear systems where the system model is polynomial in observations b...

Recently, a blind downlink channel estimator is proposed for long-code CDMA systems based on a covariance matching idea. By modeling long spreading codes as random codes and pre-computing some code-dependent quantities, the algorithm shows extremely low complexity. Due to inaccuracy of estimated data covariance from finite number of received data samples, its asymptotic performance depends on t...

In this article, the direction-of-arrival (DOA) estimation problem of wideband signal sources is studied. We pass the incident signals through a bank of narrowband filters to split the array outputs into several narrowband components. Then, a novel slice-sparse representation model of the joint narrowband array covariance data is proposed in the frequency domain to enforce joint sparsity in the...

We address the problem of estimation of covariance matrices expressible as a sum of Kronecker products (KPs). Our goal is to arrive at estimates of the KP component matrices within a maximum-likelihood (ML) framework. Since the exact solution of the ML cost function is non-tractable, we propose a covariance-matching (CM) approach, noting that the estimates obtained from covariance-matching coin...

This paper studies the problem of interacting multiple model (IMM) estimation for jump Markov linear systems with unknown measurement noise covariance. The system state and the unknown covariance are jointly estimated in the framework of Bayesian estimation, where the unknown covariance is modeled as a random matrix according to an inverse-Wishart distribution. For the IMM estimation with rando...