Based on the principle of statistical linear regression, a set of n ＋ 2 sigma points instead of 2n ＋ 1 sigma points used in the unscented Kalman filter （UKF）, is constructed to approximate the system state. And fi...Based on the principle of statistical linear regression, a set of n ＋ 2 sigma points instead of 2n ＋ 1 sigma points used in the unscented Kalman filter （UKF）, is constructed to approximate the system state. And filter accuracy is second order. Real-time of modified UKF is improved. In order to describe accurately the maneuvering target, the ＂current＂ statistical model is used. And the equation of acceleration error covariance is modified at every sample time of the filter. The modified adaptive UKF is presented for estimating the position, velocity and acceleration of maneuvering target. Monte Carlo simulations show the modified adaptive UKF acquires good performance for tracking position of maneuvering target. The modified adaptive UKF has better computational efficiency than UKF.展开更多
New sigma point filtering algorithms, including the unscented Kalman filter （UKF） and the divided difference filter （DDF）, are designed to solve the nonlinear filtering problem under the condition of correlated no...New sigma point filtering algorithms, including the unscented Kalman filter （UKF） and the divided difference filter （DDF）, are designed to solve the nonlinear filtering problem under the condition of correlated noises. Based on the minimum mean square error estimation theory, the nonlinear optimal predictive and correction recursive formulas under the hypothesis that the input noise is correlated with the measurement noise are derived and can be described in a unified framework. Then, UKF and DDF with correlated noises are proposed on the basis of approximation of the posterior mean and covariance in the unified framework by using unscented transformation and second order Stirling＇s interpolation. The proposed UKF and DDF with correlated noises break through the limitation that input noise and measurement noise must be assumed to be uneorrelated in standard UKF and DDF. Two simulation examples show the effectiveness and feasibility of new algorithms for dealing with nonlinear filtering issue with correlated noises.展开更多
Recently there have been researches about new efficient nonlinear filtering techniques in which the nonlinear filters generalize elegantly to nonlinear systems without the burdensome lineafization steps. Thus, truncat...Recently there have been researches about new efficient nonlinear filtering techniques in which the nonlinear filters generalize elegantly to nonlinear systems without the burdensome lineafization steps. Thus, truncation errors due to linearization can be compensated. These filters include the unscented Kalman filter （UKF）, the central difference filter （CDF） and the divided difference filter （DDF）, and they are also called Sigma Point Filters （SPFs） in a unified way. For higher order approximation of the nonlinear function. Ito and Xiong introduced an algorithm called the Gauss Hermite Filter, which is revisited in [5]. The Gauss Hermite Filter gives better approximation at the expense of higher computation burden, although it＇s less than the particle filter. The Gauss Hermite Filter is used as introduced in [5] with additional pruning step by adding threshold for the weights to reduce the quadrature points.展开更多
基金the National Natural Science Foundation of China (413090503)
文摘Based on the principle of statistical linear regression, a set of n ＋ 2 sigma points instead of 2n ＋ 1 sigma points used in the unscented Kalman filter （UKF）, is constructed to approximate the system state. And filter accuracy is second order. Real-time of modified UKF is improved. In order to describe accurately the maneuvering target, the ＂current＂ statistical model is used. And the equation of acceleration error covariance is modified at every sample time of the filter. The modified adaptive UKF is presented for estimating the position, velocity and acceleration of maneuvering target. Monte Carlo simulations show the modified adaptive UKF acquires good performance for tracking position of maneuvering target. The modified adaptive UKF has better computational efficiency than UKF.
基金Projects(61135001, 61075029, 61074155) supported by the National Natural Science Foundation of ChinaProject(20110491690) supported by the Postdocteral Science Foundation of China
文摘New sigma point filtering algorithms, including the unscented Kalman filter （UKF） and the divided difference filter （DDF）, are designed to solve the nonlinear filtering problem under the condition of correlated noises. Based on the minimum mean square error estimation theory, the nonlinear optimal predictive and correction recursive formulas under the hypothesis that the input noise is correlated with the measurement noise are derived and can be described in a unified framework. Then, UKF and DDF with correlated noises are proposed on the basis of approximation of the posterior mean and covariance in the unified framework by using unscented transformation and second order Stirling＇s interpolation. The proposed UKF and DDF with correlated noises break through the limitation that input noise and measurement noise must be assumed to be uneorrelated in standard UKF and DDF. Two simulation examples show the effectiveness and feasibility of new algorithms for dealing with nonlinear filtering issue with correlated noises.
文摘Recently there have been researches about new efficient nonlinear filtering techniques in which the nonlinear filters generalize elegantly to nonlinear systems without the burdensome lineafization steps. Thus, truncation errors due to linearization can be compensated. These filters include the unscented Kalman filter （UKF）, the central difference filter （CDF） and the divided difference filter （DDF）, and they are also called Sigma Point Filters （SPFs） in a unified way. For higher order approximation of the nonlinear function. Ito and Xiong introduced an algorithm called the Gauss Hermite Filter, which is revisited in [5]. The Gauss Hermite Filter gives better approximation at the expense of higher computation burden, although it＇s less than the particle filter. The Gauss Hermite Filter is used as introduced in [5] with additional pruning step by adding threshold for the weights to reduce the quadrature points.
