In the classical Kalman-Bucy filter and in the subsequent literature so far, it has been assumed that the initial value of the signal process is independent of both the noise of the signal and of the noise of the observations. The purpose of this paper is to prove a filtering equation for a linear system where the (normally distributed) initial value X0 of the signal process Xt has a given corr...

This note is devoted to deriving the measurement update of the geometric extended Kalman filter using the multiplicative extended Kalman filtering approach, resulting in the attitude estimator referred as geometric multiplicative extended Kalman filter. The equivalence of the derived geometric multiplicative extended Kalman filter and geometric extended Kalman filter is also demonstrated in thi...

In this paper, a mechanism is designed for integration of inertial navigation system information (INS) and global positioning system information (GPS). In this type of system a series of mathematical and filtering algorithms with Tightly Coupled techniques with several objectives such as application of integrated navigation algorithms, precise calculation of flying object position, speed and at...

An approach, based on a distributed delay, is presented to handle wide-band noise processes. This approach is closely related with the semigroups of right translation and allows a reduction of a wide-band noise driven linear system to a white noise driven linear system. This reduction is applied to the Kalman-Bucy filtering in order to modify it to a wideband noise driven linear system.

A fuzzy Kalman filter algorithm is developed for target tracking applications and its performance evaluated using several numerical examples. The approach is relatively novel. A comparison with Kalman filter and an adaptive tuning algorithm is carried out. The applicability and usefulness of fuzzy logic in data fusion is also demonstrated. The performance of both the extended Kalman filter and ...

We revisit in-sample asymptotic analysis extensively used in the realized volatility literature. show that there are gains to be made estimating current from considering realizations prior periods. The weighting schemes also relate Kalman-Bucy filters, although our approach is non-Gaussian and model-free. derive theoretical results for a broad class of processes pertaining volatility, higher mo...