Progressive Bayesian methods formulate the Bayesian update as continuously pseudo-time probability density evolution to perform posterior state estimation.In this paper we derive a novel Gaussian nonlinear filter based on progressive Bayesian framework.A progressive Bayesian solution is firstly derived under linear Gaussian condition.It is proved that the moment evolution of the dynamic system determined by linear Gaussian solution possess the consistency with Kalman-Bucy filter for constant state estimation.For nonlinear system,by using first order Taylor expansion,an approximate solution is derived and the resultant progressive extended Kalman filter is presented.Simulation results demonstrate the superior performance of progressive extended Kalman filter over extended Kalman filter,moreover the performance degrading of nonlinear filtering caused by narrow shape likelihood is avoided.
[1] Geller D.Linear covariance techniques for orbital rendezvous analysis and autonomous onboard mission planning[J].AIAA Journal of Guidance,Control and Dynamics,2006,29(6):1404-1414.
[2] Steinbring J,Hanebeck U.Progressive Gaussian filtering using explicit likelihoods[A].IEEE International Conference on Information Fusion[C].Salamanca:IEEE,2014.1-8.
[3] Perea L,How J,Breger L,et al.Nonlinearity in sensor fusion:Divergence issues in EKF,modified truncated SOF,and UKF[A].AIAA Conference of Guidance,Navigation,and Control[C].South Carolina:IEEE,2007.3489-3499.
[4] Simon J,Jeffery U,Hugh D.A new method for the nonlinear transformation of means and covariances in filters and estimators[J].IEEE Trans on Auto control,2000,45(3):477-481.
[5] Arasaratnam I,Haykin S.Cubature Kalman filters[J].IEEE Trans on Auto Control,2009,56(6):1254-1269.
[6] Li X R,Jilkov V P.A survey of maneuvering target tracking,part VIc:approximate nonlinear density filtering in discrete time[J].Proceedings of SPIE-The International Society for Optical Engineering,2012,8393(1):2398-2415.
[7] Synder C,Bengtsson T,Bickel P,et al.Obstacles to high-dimensional particle filtering[J].Monthly Weather Review,2008,136(1):4629-4640.
[8] Daum F,Huang J.Nonlinear filters with particle flow induced by log-homotopy[A].Proceedings of SPIE,Signal and Data Processing[C].San Francisco,2009.9816-9825.
[9] Daum F.Coulomb's law particle flow for nonlinear filter[A].Proceedings of SPIE on Signal Processing and Sensor Fusion[C].San Diego,2011.3351-3362.
[10] 张宏欣,周穗华,冯士民.基于弱形式解的粒子流滤波器[J].控制与决策,2015,30(5):853-858. ZHANG Hong-xin,ZHOU sui-hua,FENG Shi-min.A weak solution based particle flow filter[J].Control & Decision,2015,30(5):853-858.(in Chinese)
[11] Daum F,Huang J.Exact particle flow for nonlinear filters:Seventeen dubious solutions to a first order linear underdetermined PDE[J].Circuits Systems & Computers,2010,45(2):64-71.
[12] Ding T,Coates M J.Implementation of the Daum-Huang exact-flow particle filter[A].Statistical Signal Processing Workshop (SSP)[C].San Diego:IEEE,2012.257-260.
[13] Daum F,Huang J.Particle flow with non-zero diffusion for nonlinear filters[A].Proceedings of SPIE on Signal Processing,Sensor Fusion,and Target Recognition[C].SPIE,2013.4335-4341.
[14] Bar-Shalom Y,XiaoRong Li.Estimation with Applications to Tracking and Navigation[M].New York:John Wiley&Sons,2005.50-54.
[15] Simon D.Optimal State Estimation[M].New York:John Wiley&Sons,2006.22-27.
[16] Bunch P,Godsill S.Approximations of the optimal importance density using Gaussian particle flow importance sampling[OL].http://arxiv.org/abs/1406.3183v3,2014-11-27.
2017, Vol. 45 
