A deterministic least squares estimation theory of linear time-invariant systems is presented. It is demonstrated that the well-known Kalman filtering results can be obtained for purely deterministic systems with impulsive noises entering into every measurement. Applying known results from singular optimal control theory, the Kalman filtering results are extended to cases where some or all meas...

Kalman filtering is introduced as a rational means for developing a monitoring strategy for concrete structures. The mathematics and utility of linear Kalman filters are presented briefly, and the use of linear filters is demonstrated for Fickian diffusion. The nonlinear extended Kalman filter is introduced and its utility in estimating a transport parameter is demonstrated. The concrete servic...

The GPS/INS integration system estimates the navigation errors as well as internal sensor errors through the use of a Kalman filter. The tight integration processing mode uses the GPS range and range-rate measurements in a nonlinear Kalman filter. Extended Kalman filtering (EKF) has been discussed in many publications dealing with GPS/INS integration. The recently developed sigma-point Kalman f...

This paper addresses the problem of tracking extended objects. Examples of extended objects are ships and a convoy of vehicles. Such kind of objects have particularities which pose challenges in front of methods considering the extended object as a single point. Measurements of the object extent can be used for estimating size parameters of the object, whose shape is modeled by an ellipse. This...