Equation (1) is called the measurement equation. It relates the measured observable variables that provide information on αt. We use Zt ∈ M (pt ×m) to denote the matrix of factor loadings. The Ht ∈M (pt × pt) matrix is the variance-covariance matrix of the measurement noise vector, εt. Equation (2) is called the transition equation. We use Gt ∈ M (m×m) to denote the matrix of factor coefficient...

Contraction theory entails a theoretical framework in which convergence of a nonlinear system can be analysed differentially in an appropriate contraction metric. This paper is concerned with utilizing stochastic contraction theory to conclude on exponential convergence of the Unscented Kalman-Bucy Filter. The underlying process and measurement models of interest are Itô-type stochastic differe...

Model-based joint uncertainty decoding (JUD) has recently achieved promising results by integrating the front-end uncertainty into the back-end decoding by estimating JUD transforms in a mathematically consistent framework. There are different ways of estimating the JUD transforms resulting in different JUD methods. This paper gives an overview of the estimation techniques existing in the liter...

By monitoring the future process status via information prediction, process fault prognosis is able to give an early alarm and therefore prevent faults, when the faults are still in their early stages. A fuzzy-adaptive unscented Kalman filter (FAUKF)-based predictor is proposed to improve the tracking and forecasting capability for process fault prognosis. The predictor combines the strong trac...

Since Bayesian network (BN) was introduced in the field of artificial intelligence in 1980s, a number of inference algorithms have been developed for probabilistic reasoning. However, when continuous variables are present in Bayesian networks, their dependence relationships could be nonlinear and their probability distributions could be arbitrary. So far no efficient inference algorithm could d...

The Unscented Transform (UT) approximates the result of applying a specified nonlinear transformation to a given mean and covariance estimate. The UT works by constructing a set of points, referred to as sigma points, which has the same known statistics, e.g., first and second and possibly higher moments, as the given estimate. The given nonlinear transformation is applied to the set, and the u...

A method is introduced for determination of a vector network analyzer’s calibration residual errors for measurement of the reflection coefficient. The method utilizes unscented Kalman filtering and spline interpolation time domain techniques. All three residual errors are calculated by processing the measured reflection coefficient of a single verification device, such as an air line terminated...

The basic problem in Target tracking is to estimate the trajectory of a object from noise corrupted measurements and hence becoming very important field of research as it has wider applications in defense as well as civilian applications. Kalman filter is generally used for such applications. When the process and measurements are non linear extensions of Kalman filters like Extended Kalman Filt...

This work develops an algorithm to initialize an Unscented Kalman Filter using a Particle Filter for applications with initial non-Gaussian probability density functions. The method is applied to estimating the position of a road vehicle along a one-mile test track using terrain-based localization where the pitch response of the vehicle is compared to a premeasured pitch map of the test track. ...