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
The high-speed development of space defense technology demands a high state estimation capacity for spacecraft tracking methods.However,reentry flight is accompanied by complex flight environments,which brings to the ...The high-speed development of space defense technology demands a high state estimation capacity for spacecraft tracking methods.However,reentry flight is accompanied by complex flight environments,which brings to the uncertain,complex,and strongly coupled non-Gaussian detection noise.As a result,there are several intractable considerations on the problem of state estimation tasks corrupted by complex non-Gaussian outliers for non-linear dynamics systems in practical application.To address these issues,a new iterated rational quadratic(RQ)kernel high-order unscented Kalman filtering(IRQHUKF)algorithm via capturing the statistics to break through the limitations of the Gaussian assumption is proposed.Firstly,the characteristic analysis of the RQ kernel is investigated in detail,which is the first attempt to carry out an exploration of the heavy-tailed characteristic and the ability on capturing highorder moments of the RQ kernel.Subsequently,the RQ kernel method is first introduced into the UKF algorithm as an error optimization criterion,termed the iterated RQ kernel-UKF(RQ-UKF)algorithm by derived analytically,which not only retains the high-order moments propagation process but also enhances the approximation capacity in the non-Gaussian noise problem for its ability in capturing highorder moments and heavy-tailed characteristics.Meanwhile,to tackle the limitations of the Gaussian distribution assumption in the linearization process of the non-linear systems,the high-order Sigma Points(SP)as a subsidiary role in propagating the state high-order statistics is devised by the moments matching method to improve the RQ-UKF.Finally,to further improve the flexibility of the IRQ-HUKF algorithm in practical application,an adaptive kernel parameter is derived analytically grounded in the Kullback-Leibler divergence(KLD)method and parametric sensitivity analysis of the RQ kernel.The simulation results demonstrate that the novel IRQ-HUKF algorithm is more robust and outperforms the existing advanced UKF with respect to the kernel method in reentry vehicle tracking scenarios under various noise environments.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
The unscented Kalman filter(UKF)has four implementations in the additive noise case,according to whether the state is augmented with noise vectors and whether a new set of sigma points is redrawn from the predicted st...The unscented Kalman filter(UKF)has four implementations in the additive noise case,according to whether the state is augmented with noise vectors and whether a new set of sigma points is redrawn from the predicted state(which is so-called resampling)for the observation prediction.This paper concerns the differences of performances for those implementations,such as accuracy,adaptability,computational complexity,etc.The conditionally equivalent relationships between the augmented and non-augmented unscented transforms(UTs)are proved for several sampling strategies that are commonly used.Then,we find that the augmented and non-augmented UKFs have the same filter results with the additive measurement noise,but only have the same state predictions with the additive process noise.Resampling is not believed to be necessary in some researches.However,we find out that resampling can be helpful for an adaptive Kalman gain.This will improve the convergence and accuracy of the filter when the large scale state modeling bias or unknown maneuvers occur.Finally,some universal designing principles for a practical UKF are given as follows:1)for the additive observation noise case,it's better to use the non-augmented UKF;2)for the additive process noise case,when the small state modeling bias or maneuvers are involved,the non-resampling algorithms with state whether augmented or not are candidates for filters;3)the resampling and non-augmented algorithm is the only choice while the large state modeling bias or maneuvers are latent.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.
基金supported by the National Natural Science Foundation of China under Grant No.12072090.
文摘The high-speed development of space defense technology demands a high state estimation capacity for spacecraft tracking methods.However,reentry flight is accompanied by complex flight environments,which brings to the uncertain,complex,and strongly coupled non-Gaussian detection noise.As a result,there are several intractable considerations on the problem of state estimation tasks corrupted by complex non-Gaussian outliers for non-linear dynamics systems in practical application.To address these issues,a new iterated rational quadratic(RQ)kernel high-order unscented Kalman filtering(IRQHUKF)algorithm via capturing the statistics to break through the limitations of the Gaussian assumption is proposed.Firstly,the characteristic analysis of the RQ kernel is investigated in detail,which is the first attempt to carry out an exploration of the heavy-tailed characteristic and the ability on capturing highorder moments of the RQ kernel.Subsequently,the RQ kernel method is first introduced into the UKF algorithm as an error optimization criterion,termed the iterated RQ kernel-UKF(RQ-UKF)algorithm by derived analytically,which not only retains the high-order moments propagation process but also enhances the approximation capacity in the non-Gaussian noise problem for its ability in capturing highorder moments and heavy-tailed characteristics.Meanwhile,to tackle the limitations of the Gaussian distribution assumption in the linearization process of the non-linear systems,the high-order Sigma Points(SP)as a subsidiary role in propagating the state high-order statistics is devised by the moments matching method to improve the RQ-UKF.Finally,to further improve the flexibility of the IRQ-HUKF algorithm in practical application,an adaptive kernel parameter is derived analytically grounded in the Kullback-Leibler divergence(KLD)method and parametric sensitivity analysis of the RQ kernel.The simulation results demonstrate that the novel IRQ-HUKF algorithm is more robust and outperforms the existing advanced UKF with respect to the kernel method in reentry vehicle tracking scenarios under various noise environments.
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.
基金supported by the National Defense Pre-Research Foundation of China(Grant No 9140A21010908KG0162)CAST Foundation(Grant No 2009-HT-GFKD)
文摘The unscented Kalman filter(UKF)has four implementations in the additive noise case,according to whether the state is augmented with noise vectors and whether a new set of sigma points is redrawn from the predicted state(which is so-called resampling)for the observation prediction.This paper concerns the differences of performances for those implementations,such as accuracy,adaptability,computational complexity,etc.The conditionally equivalent relationships between the augmented and non-augmented unscented transforms(UTs)are proved for several sampling strategies that are commonly used.Then,we find that the augmented and non-augmented UKFs have the same filter results with the additive measurement noise,but only have the same state predictions with the additive process noise.Resampling is not believed to be necessary in some researches.However,we find out that resampling can be helpful for an adaptive Kalman gain.This will improve the convergence and accuracy of the filter when the large scale state modeling bias or unknown maneuvers occur.Finally,some universal designing principles for a practical UKF are given as follows:1)for the additive observation noise case,it's better to use the non-augmented UKF;2)for the additive process noise case,when the small state modeling bias or maneuvers are involved,the non-resampling algorithms with state whether augmented or not are candidates for filters;3)the resampling and non-augmented algorithm is the only choice while the large state modeling bias or maneuvers are latent.
