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
A new approach of smoothing the white noise for nonlinear stochastic system was proposed. Through presenting the Gaussian approximation about the white noise posterior smoothing probability density fimction, an optima...A new approach of smoothing the white noise for nonlinear stochastic system was proposed. Through presenting the Gaussian approximation about the white noise posterior smoothing probability density fimction, an optimal and unifying white noise smoothing framework was firstly derived on the basis of the existing state smoother. The proposed framework was only formal in the sense that it rarely could be directly used in practice since the model nonlinearity resulted in the intractability and infeasibility of analytically computing the smoothing gain. For this reason, a suboptimal and practical white noise smoother, which is called the unscented white noise smoother （UWNS）, was further developed by applying unscented transformation to numerically approximate the smoothing gain. Simulation results show the superior performance of the proposed UWNS approach as compared to the existing extended white noise smoother （EWNS） based on the first-order linearization.展开更多
The effect of signal modulating noise in bistable stochastic resonance systems was studied theoretically and experimentally. A mathematical analysis was made on the bistable stochastic resonance model with small syste...The effect of signal modulating noise in bistable stochastic resonance systems was studied theoretically and experimentally. A mathematical analysis was made on the bistable stochastic resonance model with small system parameters. An analogue circuit was designed to perform the effect. The effect of signal modulating noise was shown in the analog simulation experiment. The analog experiment was conducted for two sinusoidal signals with different frequencies. The results show that there are a sinusoidal component corresponding to the input sinusoidal signal and a noise component presented as a Wiener process corresponding to the input white noise in the system output. By properly selecting system parameters, the effect of signal modulating noise can be manifested in the system output.展开更多
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Projects(61203234,61135001,61075029,61074179) supported by the National Natural Science Foundation of ChinaProject(20110491692) supported by the Postdoctoral Science Foundation of China
文摘A new approach of smoothing the white noise for nonlinear stochastic system was proposed. Through presenting the Gaussian approximation about the white noise posterior smoothing probability density fimction, an optimal and unifying white noise smoothing framework was firstly derived on the basis of the existing state smoother. The proposed framework was only formal in the sense that it rarely could be directly used in practice since the model nonlinearity resulted in the intractability and infeasibility of analytically computing the smoothing gain. For this reason, a suboptimal and practical white noise smoother, which is called the unscented white noise smoother （UWNS）, was further developed by applying unscented transformation to numerically approximate the smoothing gain. Simulation results show the superior performance of the proposed UWNS approach as compared to the existing extended white noise smoother （EWNS） based on the first-order linearization.
基金Project (10276032) supportedjointly by the National Natural Science Foundation of China and by the Science Foundationof China Academy of Engineering Physics NSAFproject(2005038228) supported by Postdoctoral Science Foundation of China projectsupported by the Postdoctoral Science Foundation of Central South University(2005)
文摘The effect of signal modulating noise in bistable stochastic resonance systems was studied theoretically and experimentally. A mathematical analysis was made on the bistable stochastic resonance model with small system parameters. An analogue circuit was designed to perform the effect. The effect of signal modulating noise was shown in the analog simulation experiment. The analog experiment was conducted for two sinusoidal signals with different frequencies. The results show that there are a sinusoidal component corresponding to the input sinusoidal signal and a noise component presented as a Wiener process corresponding to the input white noise in the system output. By properly selecting system parameters, the effect of signal modulating noise can be manifested in the system output.
