State Estimation Based on Unscented Kalman Filter for Burgers’ Equation

Controlling the flow of fluids is a challenging problem that arises in many fields. Burgers’ equation is a fundamental equation for several flow phenomena such as traffic, shock waves, and turbulence. The optimal feedback control method, so-called model predictive control, has been proposed for Burgers’ equation. However, the model predictive control method is inapplicable to systems whose all state variables are not exactly known. In practical point of view, it is unusual that all the state variables of systems are exactly known, because the state variables of systems are measured through output sensors and limited parts of them can be only available. In fact, it is usual that flow velocities of fluid systems cannot be measured for all spatial domains. Hence, any practical feedback controller for fluid systems must incorporate some type of state estimator. To apply the model predictive control to the fluid systems described by Burgers’ equation, it is needed to establish a state estimation method for Burgers’ equation with limited measurable state variables. To this purpose, we apply unscented Kalman filter for estimating the state variables of fluid systems described by Burgers’ equation. The objective of this study is to establish a state estimation method based on unscented Kalman filter for Burgers’ equation. The effectiveness of the proposed method is verified by numerical simulations.

Relative Navigation with Laser-Based Intermittent Measurement for Formation Flying Satellites

This study presents a precise relative navigational method for satellites flying in formation using laser-based intermittent measurement data. The measurement data for the relative navigation between two satellites consist of a relative distance measured by a laser instrument and relative attitude angles measured by attitude determination. The relative navigation solutions are estimated by both the Extended Kalman filter (EKF) and unscented Kalman filter (UKF). The solutions estimated by the EKF may become inaccurate or even diverge as measurement outage time gets longer because the EKF utilizes a linearization approach. However, this study shows that the UKF with the appropriate scaling parameters provides a stable and accurate relative navigation solutions despite the long measurement outage time and large initial error as compared to the relative navigation solutions of the EKF. Various navigation results have been analyzed by adjusting the scaling parameters of the UKF.

The Enhancement of Target Localization Using Ship-Borne Electro-Optical Stabilized Platform

Electro-optical (EO) stabilized platforms have been widely used for surveillance and reconnaissance on various types of vehicles, from surface ships to unmanned air vehicles (UAVs). EO stabilized platforms usually consist of an assembly of structure, bearings, and motors called gimbals in which a gyroscope is installed. EO elements such as a CCD camera and IR camera, are mounted to a gimbal, which has a range of motion in elevation and azimuth and can designate and track a target. In addition, a laser range finder (LRF) can be added to the gimbal in order to acquire the precise slant range from the platform to the target. Recently, a versatile functionality of target localization is needed in order to cooperate with the weapon systems that are mounted on the same platform. The target information, such as its location or velocity, needed to be more accurate. The accuracy of the target information depends on diverse component errors and alignment errors of each component. Specially, the type of moving platform can affect the accuracy of the target information. In the case of flying platforms, or UAVs, the target location error can be increased with altitude so it is important to measure altitude as precisely as possible. In the case of surface ships, target location error can be increased with obliqueness of the elevation angle of the gimbal since the altitude of the EO stabilized platform is supposed to be relatively low. The farther the slant ranges from the surface ship to the target, the more extreme the obliqueness of the elevation angle. This can hamper the precise acquisition of the target information. So far, there have been many studies on EO stabilized platforms of flying vehicles. However, few researchers have focused on ship-borne EO stabilized platforms of the surface ship. In this paper, we deal with a target localization method when an EO stabilized platform is located on the mast of a surface ship. Especially, we need to overcome the limitation caused by the obliqueness of the elevation angle of the gimbal. We introduce a well-known approach for target localization using Unscented Kalman Filter (UKF) and present the problem definition showing the above-mentioned limitation. Finally, we want to show the effectiveness of the approach that will be demonstrated through computer simulations.

A New Version of Unscented Kalman Filter

This paper presents a new algorithm which yields a nonlinear state estimator called iterated unscented Kalman filter. This state estimator makes use of both statistical and analytical linearization techniques in different parts of the filtering process. It outperforms the other three nonlinear state estimators: unscented Kalman filter (UKF), extended Kalman filter (EKF) and iterated extended Kalman filter (IEKF) when there is severe nonlinearity in system equation and less nonlinearity in measurement equation. The algorithm performance has been verified by illustrating some simulation results.