Almost estimators are designed for the white observation noise. In the estimation problems, rather than the white observation noise, there might be actual cases where the observation noise is modeled by the colored no...Almost estimators are designed for the white observation noise. In the estimation problems, rather than the white observation noise, there might be actual cases where the observation noise is modeled by the colored noise process. This paper examines to design a new estimation technique of recursive least-squares (RLS) Wiener fixed-point smoother and filter for colored observation noise in linear discrete-time wide-sense stationary stochastic systems. The observation y(k) is given as the sum of the signal z(k)=Hx(k) and the colored observation noise vc(k). The RLS Wiener estimators explicitly require the following information: 1) the system matrix for the state vector x(k);2) the observation matrix H;3) the variance of the state vector x(k);4) the system matrix for the colored observation noise vc(k);5) the variance of the colored observation noise;6) the input noise variance in the state equation for the colored observation noise.展开更多
A square-root version of the divided difference Rauch-Tung-Striebel (RTS) smoother is proposed in this paper. The square-root variant essentially propagates the square roots of the covariance matrices and can consiste...A square-root version of the divided difference Rauch-Tung-Striebel (RTS) smoother is proposed in this paper. The square-root variant essentially propagates the square roots of the covariance matrices and can consistently improve the numerical stability because all the resulting covariance matrices are guaranteed to stay positive semi-definite. Furthermore, the square-root form ensures reliable implementation in an embedded system with fixed or limited precision although it is algebraically equivalent to the standard form. The new smoothing algorithm is tested in a challenging two-dimensional maneuvering target tracking problem with unknown and time-varying turn rate, and its performance is compared with that of other de-facto standard filters and smoothers. The simulation results indicate that the proposed RTS smoother markedly outperforms the associated filters and gives slightly smaller error than an unscented-based RTS smoother.展开更多
文摘Almost estimators are designed for the white observation noise. In the estimation problems, rather than the white observation noise, there might be actual cases where the observation noise is modeled by the colored noise process. This paper examines to design a new estimation technique of recursive least-squares (RLS) Wiener fixed-point smoother and filter for colored observation noise in linear discrete-time wide-sense stationary stochastic systems. The observation y(k) is given as the sum of the signal z(k)=Hx(k) and the colored observation noise vc(k). The RLS Wiener estimators explicitly require the following information: 1) the system matrix for the state vector x(k);2) the observation matrix H;3) the variance of the state vector x(k);4) the system matrix for the colored observation noise vc(k);5) the variance of the colored observation noise;6) the input noise variance in the state equation for the colored observation noise.
基金the Fundamental Research Fund of Northwestern Polytechnical University( Grant No. JC20120210,JC20110238)
文摘A square-root version of the divided difference Rauch-Tung-Striebel (RTS) smoother is proposed in this paper. The square-root variant essentially propagates the square roots of the covariance matrices and can consistently improve the numerical stability because all the resulting covariance matrices are guaranteed to stay positive semi-definite. Furthermore, the square-root form ensures reliable implementation in an embedded system with fixed or limited precision although it is algebraically equivalent to the standard form. The new smoothing algorithm is tested in a challenging two-dimensional maneuvering target tracking problem with unknown and time-varying turn rate, and its performance is compared with that of other de-facto standard filters and smoothers. The simulation results indicate that the proposed RTS smoother markedly outperforms the associated filters and gives slightly smaller error than an unscented-based RTS smoother.
