基于变分贝叶斯估计方法的双尺度自适应Kalman滤波
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摘要
针对Kalman滤波在对敌目标估计应用中遇到的量测和过程噪声均未知且时变的情况,提出了一种利用变分贝叶斯估计的双尺度自适应滤波方法。解决了2个关键问题:一是针对量测和过程噪声协方差的共轭后验分布提出了相对转移概率指标,设计了启发式的自适应噪声估计窗口,实现了稳态精度和时变响应性能的综合提升,能适应敌方目标机动性高且统计特性变化快的特点;二是设计了在不同时间尺度上估计过程噪声和量测噪声的协方差方法,解决了在同一时间尺度上使协方差估计值发生严重偏差且增大滤波误差的问题。仿真表明,所提方法能快速跟踪目标状态噪声统计特性的变化并保证估计精度。
In consideration of the problem in applying Kalman filter when time varying noise covariance matric of measurement and process are neither known, a new adaptive filter was purposed by Variational Bayesian(VB) approach. This filter overcame two key problems as following: first, relative transfer probability was proposed as realizing to promote the performances of steady state precision and dynamic respond simultaneously, by designing the heuristic adaptive window for noise estimation, according to the conjugate posterior distribution of measurement and process noise; second, the serious offset of the estimation value of noise covariance matric under single time scale was notable reduced by designing the approach which estimated the covariance matric under double time scales. The simulations proved that this method could track the noise statistics feature quickly without losing estimation precision.
In consideration of the problem in applying Kalman filter when time varying noise covariance matric of measurement and process are neither known, a new adaptive filter was purposed by Variational Bayesian(VB) approach. This filter overcame two key problems as following: first, relative transfer probability was proposed as realizing to promote the performances of steady state precision and dynamic respond simultaneously, by designing the heuristic adaptive window for noise estimation, according to the conjugate posterior distribution of measurement and process noise; second, the serious offset of the estimation value of noise covariance matric under single time scale was notable reduced by designing the approach which estimated the covariance matric under double time scales. The simulations proved that this method could track the noise statistics feature quickly without losing estimation precision.
引文
[1] 袁美桂,严玉国,庞春雷,等.改进的自适应Kalman滤波在GPS/SINS中的应用[J].空军工程大学学报(自然科学版),2015,16(5):65-69.YUAN M G,YAN Y G,PANG C L,et al.The Application Improved Adaptive Kalman Filter to GPS/SINS[J].Journal of Air Force Engineering University(Natural Science Edition),2015,16(5):65-69.(in Chinese)
[2] 侯西倩,寇英信,李战武,等.高斯和估计Kalman滤波在多平台空战对抗评估数据预处理中的应用[J].空军工程大学学报(自然科学版),2015,16(3):25-29.HOU X Q,KOU Y X,LI Z W,et al.Pre-Processing of Multi-Platform Air Combat Rivalry Evaluation Based on Gaussian Sum Estimate Kalman Filter[J].Journal of Air Force Engineering University(Natural Science Edition),2015,16(3):25-29.(in Chinese)
[3] SAGE A P,HUS G W.Adaptive Filtering with Unknown Prior Statistics[C]//Joint Automatic Control Conference.[S.l.]:IEEE,1969:760-769.
[4] MAYBECK P.Stochastic Models,Estimation and Control(Volume 2)[M].New York:Academic Press,1982:128-135.
[5] JWO D J,CHO T S.A Practical Note on Evaluating Kalman Filter Performance Optimality and Degradation [J].Applied Mathematics and Computation,2007,193(2):482-505.
[6] JWO D J,WANG S H.Adaptive Fuzzy Strong Tracking Extended Kalman Filtering for GPS Navigation [J].IEEE Sensors Journal,2007,7(5):778-789.
[7] 赵琳,王小旭,孙明,等.基于极大后验估计和指数加权的自适应UKF滤波算法[J].自动化学报,2010,36(7):1007-1019.ZHAO L,WANG X X,SUN M,et al.Adaptive UKF Filtering Algorithm Based on Maximum a Posterior Estimation and Exponential Weighting[J].Acta Automatica Sinica,2010,36(7):1007-1019.(in Chinese)
[8] 王璐,李光春,乔相伟,等.基于极大似然准则和最大期望算法的自适应UKF算法[J].自动化学报,2012,38(7):1200-1210.WANG L,LI G C,QIAO X W ,et al.An Adaptive UKF Algorithm Based on Maximum Likelihood Principle and Expectation Maximization Algorithm [J].Acta Automatica Sinica,2012,38(7):1200-1210.(in Chinese)
[9] S?RKK? S,NUMMENMAA A.Recursive Noise Adaptive Kalman Filtering by Variational Bayesian Approximations[J].IEEE Transactions on Automatic Control,2009,54(3):596-600.
[10] SMIDL V,QUINN A.The Variational Bayes Method in Signal Processing[M].New York:Springer,2006.
[11] SONG E,ZHU Y,ZHOU J,et al.Optimal Kalman Filtering Fusion with Cross-Correlated Sensor Noises[J].Automatica,2007,43(8):1450-1456.
[12] SUN J L,ZHOU J,GU X K.Variational Bayesian Two-Stage Kalman Filter for Systems with Unknown Inputs[J].Procedia Engineering,2012,29:2265-2273.
[13] GAO X,CHEN J,TAO D,et al.Multi-Sensor Centralized Fusion without Measurement Noise Covariance by Variational Bayesian Approximation[J].IEEE Transactions on Aerospace and Electronic Systems,2011,47(1),718-272.
[14] JOHNSTON L A,KRISHNAMURTHY V.An Improvement to the Interacting Multiple Model(IMM) Algorithm[J].IEEE Transactions on Signal Processing,2001,49(12):2909-2923.
[15] ANDERSON T W.An Introduction to Multivariate Statistical Analysis[M].3 ed.Stanford:Wiley Interscience,2004:251-285.
[2] 侯西倩,寇英信,李战武,等.高斯和估计Kalman滤波在多平台空战对抗评估数据预处理中的应用[J].空军工程大学学报(自然科学版),2015,16(3):25-29.HOU X Q,KOU Y X,LI Z W,et al.Pre-Processing of Multi-Platform Air Combat Rivalry Evaluation Based on Gaussian Sum Estimate Kalman Filter[J].Journal of Air Force Engineering University(Natural Science Edition),2015,16(3):25-29.(in Chinese)
[3] SAGE A P,HUS G W.Adaptive Filtering with Unknown Prior Statistics[C]//Joint Automatic Control Conference.[S.l.]:IEEE,1969:760-769.
[4] MAYBECK P.Stochastic Models,Estimation and Control(Volume 2)[M].New York:Academic Press,1982:128-135.
[5] JWO D J,CHO T S.A Practical Note on Evaluating Kalman Filter Performance Optimality and Degradation [J].Applied Mathematics and Computation,2007,193(2):482-505.
[6] JWO D J,WANG S H.Adaptive Fuzzy Strong Tracking Extended Kalman Filtering for GPS Navigation [J].IEEE Sensors Journal,2007,7(5):778-789.
[7] 赵琳,王小旭,孙明,等.基于极大后验估计和指数加权的自适应UKF滤波算法[J].自动化学报,2010,36(7):1007-1019.ZHAO L,WANG X X,SUN M,et al.Adaptive UKF Filtering Algorithm Based on Maximum a Posterior Estimation and Exponential Weighting[J].Acta Automatica Sinica,2010,36(7):1007-1019.(in Chinese)
[8] 王璐,李光春,乔相伟,等.基于极大似然准则和最大期望算法的自适应UKF算法[J].自动化学报,2012,38(7):1200-1210.WANG L,LI G C,QIAO X W ,et al.An Adaptive UKF Algorithm Based on Maximum Likelihood Principle and Expectation Maximization Algorithm [J].Acta Automatica Sinica,2012,38(7):1200-1210.(in Chinese)
[9] S?RKK? S,NUMMENMAA A.Recursive Noise Adaptive Kalman Filtering by Variational Bayesian Approximations[J].IEEE Transactions on Automatic Control,2009,54(3):596-600.
[10] SMIDL V,QUINN A.The Variational Bayes Method in Signal Processing[M].New York:Springer,2006.
[11] SONG E,ZHU Y,ZHOU J,et al.Optimal Kalman Filtering Fusion with Cross-Correlated Sensor Noises[J].Automatica,2007,43(8):1450-1456.
[12] SUN J L,ZHOU J,GU X K.Variational Bayesian Two-Stage Kalman Filter for Systems with Unknown Inputs[J].Procedia Engineering,2012,29:2265-2273.
[13] GAO X,CHEN J,TAO D,et al.Multi-Sensor Centralized Fusion without Measurement Noise Covariance by Variational Bayesian Approximation[J].IEEE Transactions on Aerospace and Electronic Systems,2011,47(1),718-272.
[14] JOHNSTON L A,KRISHNAMURTHY V.An Improvement to the Interacting Multiple Model(IMM) Algorithm[J].IEEE Transactions on Signal Processing,2001,49(12):2909-2923.
[15] ANDERSON T W.An Introduction to Multivariate Statistical Analysis[M].3 ed.Stanford:Wiley Interscience,2004:251-285.