中心差分卡尔曼平滑器

针对一类非线性离散系统的状态平滑问题, 本文设计了一种中心差分卡尔曼平滑器(CDKS). 文中基于最小方差估计准则, 详细推导了非线性系统的状态最优平滑递推公式, 并采用中心差分变换来近似计算状态的后验均值和协方差. 相比于传统中心差分卡尔曼滤波器(CDKF), 所设计的CDKS算法有效提高了非线性状态的估计精度, 拓展了中心差分变换的应用范围. 仿真实例验证了所提出平滑器的可行性和有效性.     

离散随机线性系统最优滤波,预报和平滑估计的一种统一方法

基于射影理论及新息分析方法，讨论离散随机线性系统最优化状态估计问题。提出了一种统一处理最优滤波、预报和平滑估计的的新方法，证明了新算法的渐近稳定性。     

一种新的固定点容积Rauch-Tung-Striebel平滑算法

针对在目标跟踪实际应用中对于观测时间区间的某个固定时刻估计值精度的要求,提出了一种运用于非线性模型中的目标跟踪算法--固定点容积Rauch-Tung-Striebel平滑。该算法将高斯最优平滑中固定点平滑策略与传统的运用于非线性状态空间模型的容积Rauch-Tung-Striebel平滑相结合,有效地提高了固定点估计值的精度。仿真结果验证了新算法的有效性。     

线性广义系统的最优和鲁棒满阶平滑器

对于线性离散随机广义系统,利用增广状态方法将平滑器问题转化为增广状态的滤波器问题.基于极大似然线性估计准则,提出了最优的满阶平滑器,其中增广状态滤波器的误差方差阵满足广义Riccati方程.当线性离散广义系统的过程噪声和观测噪声的方差不确定时,基于极大极小鲁棒设计原理和最优满阶平滑算法,得到了鲁棒满阶平滑器.应用动态误差方差分析方法证明了其鲁棒性,即鲁棒平滑误差方差阵存在一个上界方差矩阵.数值仿真例子验证了其有效性和正确性.     

广义系统Wiener状态滤波新算法

应用时域上的现代时间序列分析方法，基于ARMA新息模型和白噪声估计理论，由一种新的非递推最优状态估值器的递推变形，提出了广义系统Wiener状态滤波的一种新算法，它可统一处理滤波、平滑和预报问题，且具有渐近稳定性。同某些算法相比，它避免了求解Riccati方程和Diophantine方程，且避免了计算伪逆，因而减小了计算负担。仿真例子说明了其有效性。     

时变系统的统一和通用的最优噪声估值器

对于带相邻及同一时刻相关噪声的时变系统,基于Kalman滤波理论提出了统一和通用的最优噪声估值器,包括观测噪声估值器和输入噪声估值器,提出了统一和通用的固定点和固定区间的最优噪声平滑器,它们为解决状态和信号估计问题提供了新的工具.一个仿真算例说明了其有效性.     

快速次优固定区间Wiener平滑器算法

为了克服带相关噪声控制系统的最优固定区间Kalman平滑算法要求较大计算负担的缺点,应用Kalman滤波方法,基于CARMA新息模型,由稳态最优Kalman平滑器导出了带相关噪声控制系统的最优固定区间Wiener递推状态平滑器,它带有系数阵指数衰减到零的高阶多项式矩阵.用截断系数矩阵近似为零的项的方法提出了相应的快速次优固定区间Wiener平滑算法.它显著地减少了计算负担,便于实时应用,还给出了截断误差公式和选择截断指标的公式.仿真例子说明了快速平滑算法的有效性.     

高速列车非线性模型的极大似然辨识

提出高速列车非线性模型的极大似然(Maximum likelihood, ML)辨识方法,适合于高速列车在非高斯噪声干扰下的非线性模型的参数估计.首先,构建了描述高速列车单质点力学行为的随机离散非线性状态空间模型,并将高速列车参数的极大似然(ML)估计问题转化为期望极大(Expectation maximization, EM)的优化问题; 然后,给出高速列车状态估计的粒子滤波器和粒子平滑器的设计方法,据此构造列车的条件数学期望,并给出最大化该数学期望的梯度搜索方法,进而得到列车参数的辨识算法,分析了算法的收敛速度; 最后,进行了高速列车阻力系数估计的数值对比实验. 结果表明, 所提出的辨识方法的有效性.     

固定区间Kalman平滑新算法

用现代时间序列分析方法,基于ＡＲＭＡ新息模型和白噪声估值器,提出了一种正向固定区间稳态Ｋａｌｍａｎ平滑新算法和两种反向固定区间稳态Ｋａｌｍａｎ平滑新算法,并给出了保证算法最优性的最优初值公式。算法简单,便于实时应用。仿真例子说明了它们的有效性。     

一般相关噪声下线性系统固定延迟平滑算法

针对机动目标跟踪中固定延迟平滑估计算法的精度问题,当具有一般相关过程噪声和量测噪声时,提出了离散线性系统最优固定延迟平滑估计算法.该算法通过将延迟区间内全部量测进行集中式扩维.并对误差传递进行分析,从而精确地给出了误差间的相关性.在线性无偏最小方差意义下对系统状态进行递推估计,新算法在噪声的高斯分布假设下是最优的.仿真实验结果表明了该算法的有效性.     

Cone-bounded nonlinearities and mean-square bounds—Smoothing and prediction

Mean-square performance bounds are derived for smoothing and prediction problems associated with the broad class of nonlinear dynamic systems which, when modeled by Ito differential equations, contain drift (·dt) coefficients which are, to within a uniformly Lipschitz residual, jointly linear in the system state and externally applied control. Included in this paper are lower bounds on the error covariance attainable by any smoother or any predictor, including the optimum, and upper bounds on the performance of some simple, implementable predictors reminiscent of the designs which are optimal in the linear case. The lower bounds on smoothing and prediction performance are established using measure-transformation techniques to relate a version of the nonlinear problem to its linearization. The upper bound on prediction performance is constructed by a direct analysis of the estimation error. All the bounds hold for correlated system and observation noises. All are rigorously derived and independent of control or control law. In each case, the computational effort is comparable to that for the corresponding optimum linear smoothing or prediction problem. The bounds converge with vanishing nonlinearity (vanishing Lipschitz constants) to the known optimum performance for the limiting linear system. Consequently, the bounds are asymptotically tight and the simple designs studied are asymptotically optimal with vanishing nonlinearity.     

On stable, forward, filtering and fixed-lag smoothing in a class of systems with time delays

The problem of optimal estimation (filtering and fixed-lag smoothing) for linear continuous time systems containing multiple time delays can be considerably simplified in the absence of state excitation noise. The optimal filter and fixed-lag smoother can be computed forward in time and are asymptotically stable.     

Particle Smoother for Nonlinear Systems With One‐Step Randomly Delayed Measurements

In this paper, a new particle smoother based on forward filtering backward simulation is developed to solve the nonlinear and non‐Gaussian smoothing problem when measurements are randomly delayed by one sampling time. The heart of the proposed particle smoother is computation of delayed posterior filtering density based on stochastic sampling approach, whose particles and corresponding weights are updated in Bayesian estimation framework by considering the one‐step randomly delayed measurement model. The superior performance of the proposed particle smoother as compared with existing methods is illustrated in a numerical example concerning univariate non‐stationary growth model.     

采用分段RTS的CPHD平滑算法

针对多目标跟踪中的固定间隔平滑问题,将势概率假设密度（CPHD）滤波器和RTS平滑器相结合,提出了RTS的势概率假设密度滤波平滑算法。考虑到在平滑过程中存在较大的输出延迟问题,采用分段思想,提出了分段RTS的势概率假设密度滤波平滑算法。对需要平滑的估计值进行分段;采用匈牙利算法进行航迹-估计关联;对关联后的估计值逐段进行RTS平滑。实验结果表明,与CPHD滤波结果相比,分段RTS的势概率假设密度滤波平滑算法能够更加精确地估计目标状态,并且可以有效避免直接应用RTS平滑造成的实时性欠佳问题。     

目标跟踪系统自校正解耦融合Wiener平滑器

针对带未知模型参数和噪声的多传感器目标跟踪系统,为了解决信号的平滑问题,分别利用系统辨识及相关方法得到未知模型参数和噪声方差的局部估值,并对这些局部估值求平均值作为它们的融合估值。然后将具有高可靠性的在线融合估值代入到基于现代时间序列的最优解耦融合Wiener平滑器中即可得自校正解耦融合,使自校正融合Wiener平滑器收敛于相应的最优融合Wiener平滑器,并具有渐近最优性。从而证明自校正平滑器能够很好地解决未知模型参数和噪声统计系统的平滑问题。最后利用Matlab软件仿真验证了该自校正解耦融合Wiener平滑器算法的有效性。     

A new finite-time linear smoothing filter

A new time-invariant linear smoothing filter is derived for finite data records. The message generating process is assumed to be represented by constant state equations driven by stationary white noise. The smoothing filter transfer function matrix is obtained by solving the finite-time Wiener-Hopf equation in the ε-domain. The filter has the property that it produces an optimal state estimate [xcirc](T₁ |T) at the end of a fixed interval of length [0, T], At other times within the interval the filtor acts as a fixed-lag smoother and gives a sub-optimal state estimate [xcirc](t ₁|t). At times t< T the filter has a fixed memory length. The more conventional optimal time-varying smoother may also be calculated using the expression for the time-invariant smoother impulse response matrix. The major advantage of the time-invariant smoother lies in the ease of implementation. The stability of these smoothing filters is discussed and examples are given of the calculation procedure.     

Generalized fixed-interval smoothers for discrete-time systems

The generalized fixed-interval smoothing problem involves predictive information concerning the final state in addition to a priori information concerning the initial state. Forwards and backwards Markovian models which incorporate the predictive and a priori information, respectively, are constructed by simply using the standard smoothing formulae. The generalized backward- or forward-pass fixed-interval smoothing algorithm and two-filter smoothing algorithm are described in a unified manner. It is then shown that the generalized smoothers include as special cases almost all existing smoothers, e.g., Rauch–Tung–Striebel smoother, Mayne–Fraser two-filter smoother, Wall–Willsky–Sandell two-filter smoother and Desai–Weinert–Yusypchuk smoother. Simulation examples are included to illustrate the characteristics of the present fixed-interval smoothers.     

A Polynomial Approach to Bias Aware Fixed-Lag Smoothing Problem

In the present technical note, a solution to the problem of fixed-lag smoothing of SISO systems in presence of a dynamical bias is presented in a polynomial framework. The bias aware smoothing problem is solved in three steps, namely, the design of the general structure of the smoother, the estimation of the dynamical bias by means of a deconvolution technique and, then, the combination of the previous results to obtain the bias aware fixed-lag smoother. Applied to an example, this approach shows its efficiency.