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...

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 ...

One method to account for parameters errors in the Kalman filter is to ‘consider’ their effect in the so-called Schmidt-Kalman filter. This paper addresses issues that arise when implementing a consider Kalman filter as a real-time, recursive algorithm. A favorite implementation of the Kalman filter as an onboard navigation subsystem is the UDU formulation. A new way to implement a UDU Schmidt-...

This paper presents a novel approach for estimating the ego-motion of a vehicle in dynamic and unknown environments using tightly-coupled inertial and visual sensors. To improve the accuracy and robustness, we exploit the combination of point and line features to aid navigation. The mathematical framework is based on trifocal geometry among image triplets, which is simple and unified for point ...

The Kalman filter is the optimal minimum-variance state estimator for linear dynamic systems with Gaussian noise. In addition, the Kalman filter is the optimal linear state estimator for linear dynamic systems with non-Gaussian noise. For nonlinear systems various modifications of the Kalman filter (e.g., the extended Kalman filter, the unscented Kalman filter, and the particle filter) have bee...

The Kalman filter is the minimum-variance state estimator for linear dynamic systems with Gaussian noise. Even if the noise is non-Gaussian, the Kalman filter is best linear estimator. For nonlinear systems it is not possible, in general, to derive the optimal state estimator in closed form, but various modifications of the Kalman filter can be used to estimate the state. These modifications in...

The Kalman filter is used in this paper as a framework for space time data analysis. Using Kalman filtering it is possible to include physically based simulation models into the data analysis procedure. Attention is concentrated on the development of fast filter algorithms to make Kalman filtering feasible for high dimensional space time models. The ensemble Kalman filter and the reduced rank s...