一维自适应Kalman滤波的一种最优算法
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摘要
<正>1 引言 Kalman滤波是一种用于对含有随机摄动的动态系统的最优状态估值过程。更准确地讲,Kalman滤波器是一种从受噪声干扰的观测信号中,对被观测系统的状态进行统计估值的方法,这种估值是以线性、无偏、最小方差为准则的递推估值。它被广泛地应用于空间技术、雷达、导航、通信、工业自动化、气象和地震预报、生物医学工程等领域。 虽然Kalman滤波有许多成功的应用,但是从实用角度上看它仍有一些不足。众所周知,对于一个系统模型我们往往缺少对其真正特征的认识,即系统模型中常常含有未知的参数,而这一点将严重影响滤波器的工作。
This study aims at the Kalman filter for one-dimension time-invariant stochastic system in which system noise variance Q and observation variance R are unknown. According to the optimal criterion of Kalman filter, an optimal adaptive Kalman filter algorithm is given by means of the minimun of a constructed function. Finally, the convergence of filter is proved.
This study aims at the Kalman filter for one-dimension time-invariant stochastic system in which system noise variance Q and observation variance R are unknown. According to the optimal criterion of Kalman filter, an optimal adaptive Kalman filter algorithm is given by means of the minimun of a constructed function. Finally, the convergence of filter is proved.
引文
1 Astrom,K.J.and Eykhoff,P., System identification—a Survey,Automatica,7(1971),12—162.
2 Chen,G.and Chui,C.K.,A modified'adaptive Kalman filter for real-time applications,IEEE Trans.Aero.Elec.Syst.,28(1991),126—133.
3 Chin,L.,Advances in adaptive filtering,in Advances in Control Systems Theory and Applications,15,ed.by C.T.Leondes (Academic Press,New York),1979.
4 Jazwinski,A.H.,Adaptive filtering,Automatica,5(1969),475—485.
5 Mehra,R.K.,On the identification of variances and adaptive kalman filtering,IEEE Trans.Auto.Con—tr.,AC—15,1970.
6 Mehra,R.K.,Approaches to adaptive filtering,IEEE Trans.Auto.Contr.,AC—17,(1972).
7 Stengel,R.F.,Stochastic Optimal Control,Theory and Application (Wiley,Newyork),1986
8 Chui,C.K.and Chen,G.,Kalman Filtering with Real—Time Application,Springer—Verlag,Berlin Heidelberg,New York,199l
9 Xia,Q.J.,Rao,M.,Ying,Y.Q.and Shen,X.M.,Adaptive fading Kalman filter with an application,Automatica,30,1333—1338,1994
10 Deyst,J.J.and Prince,C.F.,Conditions for asymptotic stability of the discrete minimum-variance linear estimator.IEEE Trans.Automatic Control,AC—13(1968),702—705.
11 Sorenson,H.W.and Sacks,J.E.,Recursive fading memory filtering,Information Sciences,3(1971),10l—119.
2 Chen,G.and Chui,C.K.,A modified'adaptive Kalman filter for real-time applications,IEEE Trans.Aero.Elec.Syst.,28(1991),126—133.
3 Chin,L.,Advances in adaptive filtering,in Advances in Control Systems Theory and Applications,15,ed.by C.T.Leondes (Academic Press,New York),1979.
4 Jazwinski,A.H.,Adaptive filtering,Automatica,5(1969),475—485.
5 Mehra,R.K.,On the identification of variances and adaptive kalman filtering,IEEE Trans.Auto.Con—tr.,AC—15,1970.
6 Mehra,R.K.,Approaches to adaptive filtering,IEEE Trans.Auto.Contr.,AC—17,(1972).
7 Stengel,R.F.,Stochastic Optimal Control,Theory and Application (Wiley,Newyork),1986
8 Chui,C.K.and Chen,G.,Kalman Filtering with Real—Time Application,Springer—Verlag,Berlin Heidelberg,New York,199l
9 Xia,Q.J.,Rao,M.,Ying,Y.Q.and Shen,X.M.,Adaptive fading Kalman filter with an application,Automatica,30,1333—1338,1994
10 Deyst,J.J.and Prince,C.F.,Conditions for asymptotic stability of the discrete minimum-variance linear estimator.IEEE Trans.Automatic Control,AC—13(1968),702—705.
11 Sorenson,H.W.and Sacks,J.E.,Recursive fading memory filtering,Information Sciences,3(1971),10l—119.
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