A Prediction-error-method tailored for model based predictive control is presented. The prediction-error method studied are based on predictions using the Kalman filter and Kalman predictors for a linear discrete-time stochastic state space model. The linear discrete-time stochastic state space model is realized from a continuous-discrete-time linear stochastic system specified using transfer f...

A new sequential data assimilation method is discussed. It is based on forecasting the error statistics using Monte Carlo methods, a better alternative than solving the traditional and computationally extremely demanding approximate error covariance equation used in the extended Kalman filter. The unbounded error growth found in the extended Kalman filter, which is caused by an overly simplifie...

Conventional spherical simplex-radial cubature Kalman filter (SSRCKF) for maneuvering target tracking may decline in accuracy and even diverge when a target makes abrupt state changes. To overcome this problem, a novel algorithm named strong tracking spherical simplex-radial cubature Kalman filter (STSSRCKF) is proposed in this paper. The proposed algorithm uses the spherical simplex-radial (SS...

In this paper propose a denoising method for reducing noise in digital images. An efficient RaoBlackwellized Particle Filter (RBPF) with maximum likelihood Estimation approach is used for improving the learning stage of the image structural model and guiding the particles to the most appropriate direction. It increases the efficiency of particle transitions. The proposal distribution is compute...

A solution to the state estimation problem of systems with unmeasurable non-zero mean inputs/disturbances, which do not satisfy the disturbance decoupling conditions, is given using the Kalman filtering and Bayesian estimation theory. The proposed estimation algorithm, named Supervisory Kalman Filter (SKF), consists of a Kalman filter with an extra update step which is inspired by the particle ...

The extended Kalman filter (EKF) is one of the most widely used methods for state estimation with communication and aerospace applications based on its apparent simplicity and tractability (Shi et al., 2002; Bolognani et al., 2003; Wu et al., 2004). However, for an EKF to guarantee satisfactory performance, the system model should be known exactly. Unknown external disturbances may result in th...

Formal code certification is a rigorous approach to demonstrate software quality. Its basicidea is to require that code producers provide formal certificates, or proofs, that their codesatisfies certain quality properties. In this paper, we focus on certifying software developed forstate estimation of dynamic systems, which is an important problem found in spacecraft, aircraft,g...

We consider non-linear state space models in high-dimensional situations, where the two common tools for state space models both have difficulties. The Kalman filter variants are seriously biased due to non-Gaussianity and the particle filter suffers from the “curse of dimensionality”. Inspired by a regression perspective on the Kalman filter, a novel approach is developed by combining the Kalm...

State estimation theory is one of the best mathematical approaches to analyze variants in the states of the system or process. The state of the system is defined by a set of variables that provide a complete representation of the internal condition at any given instant of time. Filtering of Random processes is referred to as Estimation, and is a well-defined statistical technique. There are two...

The two step filter is applied to process intersatellite radar measurements to determine the motion of one satellite relative to another in close elliptical orbits. This filter breaks a nonlinear estimation problem into two state vectors. The “first step” state is chosen so as to have a linear measurement equation. This is nonlinearly related to the “second step” state which describes the dynam...