Jiahe Xu

UKF design and stability for nonlinear stochastic systems with correlated noises

Based on the standard unscented Kalman filter (UKF), the modified UKF is presented for nonlinear stochastic systems with correlated noises. The modified UKF consists of the prediction equations and the measurement equations, and holds the sigma points chosen by unscented transformation (UT). The stability of the modified UKF for the nonlinear stochastic system with correlated noises is analyzed. It is proved that under certain conditions, the estimation error of the UKF remains bounded. These results are verified by using Matlab simulations on two numerical example systems.

Two-stage Unscented Kalman Filter for nonlinear systems in the presence of unknown random bias

The two-stage unscented Kalman filter (TUKF) is proposed to consider the nonlinear system in the presence of unknown random bias in a number of practical situations. The adaptive fading UKF is designed by using the forgetting factor to compensate the effects of incomplete information. The TUKF to estimate unknown random bias is designed by using the adaptive fading UKF. This filter can be used for nonlinear systems with unknown random bias on the assumption that the stochastic information of a random bias is incomplete. The stability of the TUKF is analyzed and ensured under certain conditions. The performance of the TUKF is verified by using MATLAB simulation on the high-update rate wheel mobile robot (WMR).

Stochastic stability of the continuous-time unscented Kalman filter

The performance of the modified unscented Kalman-Bucy filter (UKBF) for the nonlinear stochastic continuous-time system is investigated. The error behavior of the UKBF is analyzed. It is proved that the estimation error remains bounded if the system satisfies a detectability condition and both the initial estimation error and the disturbing noise terms are small enough. Furthermore, it is shown that the design of noise covariance matrix plays an important role in improving the stability of the algorithm. Moreover, some selected cases with both bounded and unbounded estimation error are demonstrated by numerical simulations.

Comparison of centralized multi-sensor measurement and state fusion methods with ensemble Kalman filter for process fault diagnosis

This paper investigates the application of centralized multi-sensor data fusion (CMSDF) technique to enhance the process fault detection. The ensemble Kalman filter (EnKF) is used to estimate the process faults of the simulated high-update rate Wheel Mobile Robot (WMR) benchmark. Currently there exist two commonly used centralized multi-sensor data fusion methods for Kalman filter including centralized measurement fusion and centralized state-vector fusion. The measurement fusion methods directly fuse observations or sensor measurements to obtain a weighted or combined measurement and then use a single Kalman filter to obtain the final state estimate based upon the fused measurement. Whereas state-vector fusion methods use a group of local Kalman filters to obtain individual sensor based state estimates which are then fused to obtain an improved joint state estimate. The simulation results are shown for single, double, triple and quadruple faults detection and diagnosis.

Optimal nonlinear estimation for aircraft flight control in wind shear

The continue-time unscented Kalman filter (UKF) is developed to estimate the state of a jet transport aircraft. The UKF is based on the nonlinear longitudinal aircraft equations of motion, and it is designed to provide estimates of horizontal and vertical atmospheric wind inputs. The optimal state and disturbance estimates are incorporated in feedback control laws based on the slow- and fast-time-scale subsystems of the aircraft nonlinear inverse dynamics. The UKF produces accurate estimates, and the resultant flight trajectories are very similar to those obtained with perfect state feedback. The UKF is sensitive to uncertainty in the dynamic model, but much of the lost performance can be restored by treating the uncertainty as a random disturbance input.

Unscented Kalman-Bucy filtering for nonlinear continuous-time systems with multiple delayed measurements

The unscented Kalman-Bucy filter (UKBF) is developed to nonlinear continuous-time systems with multiple delayed measurements. An explicit and simpler solution to the unscented Kalman-Bucy filtering problem is presented for such systems. The approach applied is the reorganized innovation analysis. The obtained UKBF is given in terms of Riccati differential equations. A numerical example is given to demonstrate the proposed approach.

The unscented Kalman filtering in extended noise environments

This paper introduces an extended environment for the unscented Kalman filtering that considers also the presence of additive noise on input observations in order to solve the problem of optimal estimation of noise-corrupted input and output sequences. This environment includes as sub-cases both errors-in-variables filtering and unscented Kalman filtering. The unscented Kalman filtering to the presence of additive noise on input observations is considered, and is used to solve the problem of optimal estimation of noise-corrupted input and output sequences. A Monte Carlo simulation shows that the performance of the unscented Kalman filtering technique leads to the expected minimal variance estimates.

Extended target tracking for high resolution sensor based ensemble Kalman filters

The ensemble Kalman filter (EnKF) is developed to extended target tracking problem for high resolution sensors. The ensemble Kalman filter is based on an ellipsoidal model, which is proposed to exploit sensor measurement of target extent. The ellipsoidal model can provide extra information to enhance tracking accuracy, data association performance, and target identification. In contrast to the most commonly used extended Kalman filter (EKF), the EnKF provide more accurate and reliable estimation performance, due to the presence of high nonlinearity of the model. Correspondingly, the EnKF has lower computational complexity than the EKF. The EnKF is sensitive to uncertainty in the dynamic model, but much of the lost performance can be restored by treating the uncertainty as a random disturbance input. The developed EnKF algorithm on extended target tracking problem is validated and evaluated by computer simulations.

Notice of Violation of IEEE Publication Principles Extended target tracking using an IMM based nonlinear Kalman filters

The unscented Kalman filter (UKF) and ensemble Kalman filter (EnKF) are developed to extended target tracking problem for high resolution sensors. The nonlinear Kalman filters are based on an ellipsoidal model, which is proposed to exploit sensor measurement of target extent. The ellipsoidal model can provide extra information to enhance tracking accuracy, data association performance, and target identification. In contrast to the most commonly used extended Kalman filter (EKF), the UKF and EnKF provide more accurate and reliable estimation performance, due to the presence of high nonlinearity of the model. Correspondingly, the EnKF has lower computational complexity than the UKF. An interacting multiple model (IMM) technique is combined with the filters to adapt the target maneuver and motion mode switching problem which is vital for nonlinear filtering. The developed IMM-UKF and IMM-EnKF algorithms on extended target tracking problem are validated and evaluated by computer simulations.

Sensor fusion of delay and non-delay signal using unscented Kalman filter with moving covariance

This paper describes the design of unscented Kalman filter (UKF) to implement fusion of the delay and non-delay data for nonlinear discrete-time system in order to achieve the excellent dynamic response. We proposed a fusion method with UKF that only needs to update the stored covariance between two different time instants, instead of classical method, which is re-performing Kalman operation at every step from the time of measured delay signal to current time. To solve the fusion method, the measurement update equations of UKF algorithm is slightly modified in order to discuss and analysis the proposed fusion method clearly. With less computational cost comparing to the classical method and the uniformity of the computation in every iteration, the UKF is superior to extended Kalman filter (EKF) and offer much advantage in terms of estimation performance, which is verified by using MATLAB simulation on the high-update rate Wheel Mobile Robot (WMR).