Abstract—This work considers the theory underlying a discrete-time quantum filter recently used in a quantum feedback experiment. It proves that this filter taking into account decoherence and measurement errors is optimal and stable. We present the general framework underlying this filter and show that it corresponds to a recursive expression of the least-square optimal estimation of the densi...

An adaptive extended Kalman filter is developed and investigated for a transient heat transfer problem in which a high heat flux spot source is applied on one side of a thin plate and ultrasonic pulse time of flight is measured between spatially separated transducers on the opposite side of the plate. The novel approach is based on the uncertainty in the state model covariance and leverages tre...

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 Kalman filter cannot be used with nonstationary state space models. To circumvent this difficulty, a conditional state space model and a new algorithm, calIed the conditional Kalman filter, can be used. The conditional state space model is obtained by first selecting adequately that part oof the initial state vector which has an unspecified distribution and then conditioning on O. Using the...

A nonlinear filter called the iterated modified gain extended Kalman filter (IMGEKF) is presented in this paper. This filter uses bearings only measurements to estimate the target state in passive target tracking scenario. This work combines the MGEKF and the iteration method. The filter utilizes the updated state to re-linearize the measurement equation. Then the proposed work is tested in a t...

Particle filters are becoming increasingly important and useful for state estimation in nonlinear systems. Many filter versions have been suggested, and several results on convergence of filter properties have been reported. However, apparently a result on the convergence of the state estimate itself has been lacking. This contribution describes a general framework for particle filters for stat...

Abstract In this paper, a real-time predictive filter is derived for nonlinear systems. The major advantage of this new filter over conventional filters is that it provides a method of determining optimal state estimates in the presence of significant error in the assumed (nominal) model. The new real-time nonlinear filter determines (“predicts”) the optimal model error trajectory so that the m...

The paper deals with the Kalman filtering in the factorized form. The target application area is the urban traffic control, which main controlled variable – queue length, expressing the optimality of a traffic network most adequately, can not be directly observed and has to be estimated. Additional problem is that some state variables are of a discrete-valued nature. Thus, estimation of mixed-t...

This paper deals with the state estimation of a strongly nonlinear system. In a noisy state space representation setting, Central Difference Kalman Filter, Ensemble Kalman Filter and Particle Filter are tested on a second order system. The choice of estimators parameters is then discussed, and their behaviour in relation to noise is studied, in order to compare estimation quality according to n...