scholarly journals An Improved Unscented Kalman Filter for Discrete Nonlinear Systems with Random Parameters

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Yue Wang ◽  
Zhijian Qiu ◽  
Xiaomei Qu
Keyword(s):  
Nonlinear Systems ◽  
Unscented Kalman Filter ◽  
Taylor Series Expansion ◽  
Superior Performance ◽  
Random Parameters ◽  
Mobile Source ◽  
Unscented Transformation ◽  
Sensor Position ◽  
Discrete Nonlinear Systems ◽  
True Values

This paper investigates the nonlinear unscented Kalman filtering (UKF) problem for discrete nonlinear dynamic systems with random parameters. We develop an improved unscented transformation by incorporating the random parameters into the state vector to enlarge the number of sigma points. The theoretical analysis reveals that the approximated mean and covariance via the improved unscented transformation match the true values correctly up to the third order of Taylor series expansion. Based on the improved unscented transformation, an improved UKF method is proposed to expand the application of the UKF for nonlinear systems with random parameters. An application to the mobile source localization with time difference of arrival (TDOA) measurements and sensor position uncertainties is provided where the simulation results illustrate that the improved UKF method leads to a superior performance in comparison with the normal UKF method.

The Unscented Kalman Filter Estimators for High Dynamic Doppler Shift Environments

2012 ◽  
Vol 532-533 ◽  
pp. 1487-1491
Author(s):  
Kun Zhao ◽  
Ke Gang Pan ◽  
Ai Jun Liu ◽  
Dao Xing Guo
Keyword(s):  
Kalman Filter ◽  
Nonlinear Systems ◽  
Doppler Shift ◽  
Unscented Kalman Filter ◽  
The State ◽  
Extend Kalman Filter ◽  
Unscented Transformation ◽  
High Dynamic ◽  
Simulation Results ◽  
Dynamic Trajectory

The Extend Kalman Filter (EKF) is widely used in the tracking of high dynamic Doppler shift trajectories, but it has some flows when it is used to estimate the state of nonlinear systems. In this paper, we apply the Unscented Transformation (UT) based Unscented Kalman Filter (UKF) to the state estimation in the high dynamic Doppler environments. Two versions of the UKF estimators, augmented UKF estimator and nonaugemented UKF estimator are designed. To compare the performance of them, they are applied to tracking a common high dynamic trajectory, and simulation results declare that given different conditions, the performance of the estimators will be different.

scholarly journals Weighted Measurement Fusion Particle Filter for Nonlinear Systems with Correlated Noises

Sensors ◽  
2018 ◽  
Vol 18 (10) ◽  
pp. 3242 ◽  
Author(s):  
Ke Wei Zhang ◽  
Gang Hao ◽  
Shu Li Sun
Keyword(s):  
Nonlinear Systems ◽  
Particle Filter ◽  
Series Expansion ◽  
Taylor Series ◽  
Asymptotic Optimality ◽  
Taylor Series Expansion ◽  
Full Rank ◽  
Expansion Method ◽  
Least Square ◽  
Correlated Noises

The multi-sensor information fusion particle filter (PF) has been put forward for nonlinear systems with correlated noises. The proposed algorithm uses the Taylor series expansion method, which makes the nonlinear measurement functions have a linear relationship by the intermediary function. A weighted measurement fusion PF (WMF-PF) was put forward for systems with correlated noises by applying the full rank decomposition and the weighted least square theory. Compared with the augmented optimal centralized fusion particle filter (CF-PF), it could greatly reduce the amount of calculation. Moreover, it showed asymptotic optimality as the Taylor series expansion increased. The simulation examples illustrate the effectiveness and correctness of the proposed algorithm.

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