This paper presents the second part of a study aiming at the error state selection in Kalman filters applied to the stationary self-alignment and calibration (SSAC) problem of strapdown inertial navigation systems (SINS). The observability properties of the system are systematically investigated, and the number of unobservable modes is established. Through the analytical manipulation of the ful...

GPS/INS integrated system is very subject to uncertainties due to exogenous disturbances, device damage, and inaccurate sensor noise statistics. Conventional Kalman filer has no robustness to address system uncertainties which may corrupt filter performance and even cause filter divergence. Based on the INS error dynamic equation, a robust Kalman filter is analyzed and applied in loosely couple...

This work studies the effect of using Monte Carlo based methods to estimate high-dimensional systems. Recent focus in the geosciences has been on representing the atmospheric state using a probability density function, and, for extremely high-dimensional systems, various sample based Kalman filter techniques have been developed to address the problem of real-time assimilation of system informat...

The Global Positioning System (GPS) is a satellite-based navigation system that provides a user with the proper equipment access to useful and accurate positioning information anywhere on the globe. The well-known Kalman filter (Gelb, 1974; Brown & Hwang, 1997; Axelrad & Brown, 1996) provides optimal (minimum mean square error) estimate of the system state vector, and has been widely applied to...

Accuracy of inertial navigation system (INS) is limited by inertial sensors imperfections. Before using inertial sensors signals in the data fusion algorithm, noise removal method should be performed, in which, wavelet decomposition method is used. In this method the raw data is decomposed into high and low frequency data sets. In this study, wavelet multi-level resolution analysis (WMRA) techn...

The possible methodologies to handle the uncertain parameter are reviewed. The core idea of the desensitized Kalman filter is introduced. A new cost function consisting of a posterior covariance trace and trace of a weighted norm of the state error sensitivities matrix is minimizing to obtain a well-known analytical gain matrix, which is different from the gain of the desensitized Kalman filter...

Recurrent neural networks (RNNs) trained with gradient-based algorithms such as real-time recurrent learning or back-propagation through time have a drawback of slow convergence rate. These algorithms also need the derivative calculation through the error back-propagation process. In this paper, a derivative-free Kalman filter, so called the unscented Kalman filter (UKF), for training a fully c...

For the mobile robot Simultaneous Localization and Mapping (SLAM),a new algorithm is proposed, and named Adaptive Iterated Square-Root Cubature Kalman Filter based SLAM algorithm (AISRCKF-SLAM). The main contribution of the algorithm is that the numerical integration method based on cubature rule is directly used to calculate the SLAM posterior probability density. To improve innovation covaria...