Adaptive Kalman Filter for Navigation Sensor Fusion

As a form of optimal estimator characterized by recursive evaluation, the Kalman filter (KF) (Bar-Shalom, et al, 2001; Brown and Hwang, 1997, Gelb, 1974; Grewal & Andrews, 2001) has been shown to be the filter that minimizes the variance of the estimation mean square error (MSE) and has been widely applied to the navigation sensor fusion. Nevertheless, in Kalman filter designs, the divergence due to modeling errors is critical. Utilization of the KF requires that all the plant dynamics and noise processes are completely known, and the noise process is zero mean white noise. If the input data does not reflect the real model, the KF estimates may not be reliable. The case that theoretical behavior of a filter and its actual behavior do not agree may lead to divergence problems. For example, if the Kalman filter is provided with information that the process behaves a certain way, whereas, in fact, it behaves a different way, the filter will continually intend to fit an incorrect process signal. Furthermore, when the measurement situation does not provide sufficient information to estimate all the state variables of the system, in other words, the estimation error covariance matrix becomes unrealistically small and the filter disregards the measurement. In various circumstances where there are uncertainties in the system model and noise description, and the assumptions on the statistics of disturbances are violated since in a number of practical situations, the availability of a precisely known model is unrealistic due to the fact that in the modelling step, some phenomena are disregarded and a way to take them into account is to consider a nominal model affected by uncertainty. The fact that KF highly depends on predefined system and measurement models forms a major drawback. If the theoretical behavior of the filter and its actual behavior do not agree, divergence problems tend to occur. The adaptive algorithm has been one of the approaches to prevent divergence problem of the Kalman filter when precise knowledge on the models are not available. To fulfil the requirement of achieving the filter optimality or to preventing divergence problem of Kalman filter, the so-called adaptive Kalman filter (AKF) approach (Ding, et al, 4