基于条件高斯分布的未知输入与状态估计算法

针对未知输入同时存在于系统方程和测量方程的直接馈通线性随机系统, 提出了一种同时估计未知输入 和状态的算法. 首先, 通过将未知输入模型描述为有限方差的高斯分布, 利用条件高斯分布的性质, 推导出新的滤波 算法, 以同时得到未知输入估计和状态估计. 其次, 证明了当未知输入的方差趋于无穷大时, 本文提出的算法等价于 已有的递归三步滤波算法. 最后, 分析了本文算法的渐进稳定性条件, 结果表明, 与已有算法相比, 本文的算法适用 范围更广.     

Extension of unbiased minimum-variance input and state estimation for systems with unknown inputs

This paper extends the existing results on joint input and state estimation to systems with arbitrary unknown inputs. The objective is to derive an optimal filter in the general case where not only unknown inputs affect both the system state and the output, but also the direct feedthrough matrix has arbitrary rank. The paper extends both the results of Gillijns and De Moor [Gillijns, S., & De Moor, B. (2007b). Unbiased minimum-variance input and state estimation for linear discrete-time systems with direct feedthrough. Automatica, 43, 934–937] and Darouach, Zasadzinski, and Boutayeb [Darouach, M., Zasadzinski, M., & Boutayeb, M. (2003). Extension of minimum variance estimation for systems with unknown inputs. Automatica, 39, 867–876]. The resulting filter is an extension of the recursive three-step filter (ERTSF) and serves as a unified solution to the addressed unknown input filtering problem. The relationship between the ERTSF and the existing literature results is also addressed.     

线性离散随机系统输入和状态的多步估计方法及应用

具有未知输入的系统的状态估计问题已经在过去几十年里引起了相当的关注.本文对于线性离散随机系统提出了一种基于多步信息的输入和状态同步估计方法.首先,采用多步信息的最小方差方法来获得未知输入.由于引入了包含多个时间步骤的扩张状态和测量向量而计算多步信息,使估计结果与一步估计相比减少了对噪声的敏感性.其次,利用输入估计值和卡尔曼滤波估计过去和当前的状态.该方法在未知输入维数等于状态维数时仍然有良好的估计效果.数值仿真验证了提出的估计方法的有效性.最后,该方法应用于厌氧消化过程反应罐中的溶解甲烷和二氧化碳的浓度估计以验证方法的实用性.     

On the global optimality of unbiased minimum-variance state estimation for systems with unknown inputs

In this paper, a globally optimal filtering framework is developed for unbiased minimum-variance state estimation for systems with unknown inputs that affect both the system state and the output. The resulting optimal filters are globally optimal within the unbiased minimum-variance filtering over all linear unbiased estimators. Globally optimal state estimators with or without output and/or input transformations are derived. Through the global optimality evaluation of this research, the performance degradation of the filter proposed by Darouach, Zasadzinski, and Boutayeb [Darouach, M., Zasadzinski, M., & Boutayeb, M. (2003). Extension of minimum variance estimation for systems with unknown inputs. Automatica, 39, 867-876] is clearly illustrated and the global optimality of the filter proposed by Gillijns and De Moor [Gillijns, S., & De Moor, B. (2007b). Unbiased minimum-variance input and state estimation for linear discrete-time systems with direct feedthrough. Automatica, 43, 934-937] is further verified. The relationship with the existing literature results is addressed. A unified approach to design a specific globally optimal state estimator that is based on the desired form of the distribution matrix from the unknown input to the output is also presented. A simulation example is given to illustrate the proposed results.     

A framework for globally optimal state estimation for systems with unknown inputs (I): transformation approach

In this paper, a globally optimal state estimation is addressed in light of the conventional Luenberger observer‐type filter. This paper is the first part of a comprehensive extension of an original work by Hsieh, with the main aim being to develop a transformation‐based filtering framework for global unbiased minimum‐variance state estimation (GUMVSE) for systems with unknown inputs that affect both the system and the output. The main contributions of this paper are (i) a complete optimal solution for the GUMVSE is addressed, where both the globally optimal state filter and predictor are presented, and (ii) additional insights for implementing the globally optimal state filter are highlighted via the proposed decorrelation constraint. Compared with existing results, the proposed globally optimal filter has the most general filter form among all transformation‐based globally optimal filters in the sense that it does not use any specific unknown input transformation matrix in the derivation. A simulation example is given to illustrate the usefulness of the proposed results. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Unbiased minimum-variance input and state estimation for linear discrete-time systems

This paper addresses the problem of simultaneously estimating the state and the input of a linear discrete-time system. A recursive filter, optimal in the minimum-variance unbiased sense, is developed where the estimation of the state and the input are interconnected. The input estimate is obtained from the innovation by least-squares estimation and the state estimation problem is transformed into a standard Kalman filtering problem. Necessary and sufficient conditions for the existence of the filter are given and relations to earlier results are discussed.     

故障系统的状态估计

本文讨论故障系统的状态估计问题.文中给出了在故障检测滤波器误差方程基础上,利用未知输入观测器或逆系统算法,根据输出误差估计状态误差,从而得到故障系统状态的估计方法.文中还给出了一个数字仿真例子.     

Unbiased minimum-variance state estimation for linear systems with unknown input

The problem of state estimation for a linear system with unknown input, which affects both the system and the output, is discussed in this paper. A recursive optimal filter with global optimality in the sense of unbiased minimum variance over all linear unbiased estimators, is provided. The necessary and sufficient condition for the convergence and stability is also given, which is milder than existing approaches.     

Linear filtering for bilinear stochastic differential systems with unknown inputs

Investigates the problem of state estimation for bilinear stochastic multivariable differential systems in the presence of an additional disturbance, whose statistics are completely unknown.. A linear filter is proposed, based on a suitable decomposition of the state of the bilinear system into two components. The first one is a computable function of the observations while the second component is estimated via a suitable linear filtering algorithm. No a priori information on the disturbance is required for the filter implementation. The proposed filter is robust with respect to the unknown input, in that the covariance of the estimation error is not affected by such input. Numerical simulations show the effectiveness of the proposed filter.     

Robust state estimation for uncertain linear systems with deterministic input signals

In this paper, we investigate state estimations of a dynamical system in which not only process and measurement noise, but also parameter uncertainties and deterministic input signals are involved. The sensitivity penalization based robust state estimation is extended to uncertain linear systems with deterministic input signals and parametric uncertainties which may nonlinearly affect a state-space plant model. The form of the derived robust estimator is similar to that of the well-known Kalman filter with a comparable computational complexity. Under a few weak assumptions, it is proved that though the derived state estimator is biased, the bound of estimation errors is finite and the covariance matrix of estimation errors is bounded. Numerical simulations show that the obtained robust filter has relatively nice estimation performances.     

状态和参数联合估计方法及其在飞行试验中的应用

本文提出了一种有效的状态和参数的联合估计方法.针对参数估计结果有偏或发散的问 题,本文给出了一种参数向量可控性模型,并由此模型得到了噪声相关的一种状态和参数的估 计方法.运用状态和参数联合估计的新方法进行飞行状态和测量仪器的误差估计,仿真和实 际飞行数据处理的结果表明;本文提出的方法可以给出飞行状态和仪器误差估计的满意结果, 比普通推广Kalman滤波方法更有效.     

Simultaneous state and input estimation of hybrid systems with unknown inputs

This paper addresses the problem of the simultaneous state and input estimation for hybrid systems when subject to input disturbances. The proposed algorithm is based on the moving horizon estimation (MHE) method and uses mixed logical dynamical (MLD) systems as equivalent representations of piecewise affine (PWA) systems. So far the MHE method has been successfully applied for the state estimation of linear, hybrid, and nonlinear systems. The proposed extension of the MHE algorithm enables the estimation of unknown inputs, or disturbances, acting on the hybrid system. The new algorithm is shown to improve the convergence characteristics of the MHE method by reducing the delay of convergent estimates, while assuring convergence for every possible sequence of input disturbances. To ensure convergence the system is required to be incrementally input observable, which is an extension to the classical incremental observability property.     

量子态估计简介及其在超导电路电动力学系统中的应用

量子态估计是量子计算以及量子调控的基础,一般分为量子态层析,即对未知量子态(或过程的初态)进行估计,以及量子滤波,即对量子态进行实时的估计.本文首先介绍了近年来量子态层析技术新的进展,内容包括极大似然方法,压缩感知方法和线性回归方法,并分析了它们的适用范围及各自的优缺点.进一步,基于量子计算的成熟载体超导电路电动力学系统,介绍了基于连续弱测量对量子态进行实时估计的贝叶斯方法,并分析了贝叶斯估计的适用情形.进一步,通过仿真实现了量子贝叶斯估计,可以很容易发现贝叶斯方法能够精确地实时追踪量子态的演化.     

Modified UBB-based input estimation method for nonlinear manoeuvring target tracking problem

The input detection and estimation methods in the manoeuvring target tracking (MTT) application need algorithms for manoeuvring detection and covariance resetting. This algorithm causes an improper delay in target states tracking. In this paper, for solving this problem, unknown but bounded approach for uncertainties modelling is used and a different state space model is developed. In this model, target acceleration is treated as an augmented state in the corresponding state equation. By using interval mathematics, the linearisation error is bounded by an ellipsoidal set and considered in the model development. In augmented state equations, the MTT problem converted to non-manoeuvring target tracking problem. Therefore, the set membership filter is rearranged and used for simultaneous target state and manoeuvre estimation. Furthermore, estimated convex set boundedness is analysed and an upper bound for the estimation error is calculated. The theoretical development of the proposed method is verified with numerical simulations, which contain examples of tracking various manoeuvring targets. The simulation result of the proposed method is compared with traditional input estimation methods. The comparison shows the acceptable performance of the proposed method in the simultaneous estimation of the target acceleration and state vector for the manoeuvring and non-manoeuvring scenarios.     

基于带输入估计变维滤波的多传感器信息融合

带输入估计变维滤波利用最小二乘法对系统未知输入进行估计,同时对机动运行开始时刻给出估计,从而有效地克服了输入估计算法和变维滤波各自在系统模型单一和机动运行开始时刻估计不精确方面的缺陷。考虑到多传感器信息融合系统可给出比单传感器更为精确的结果,基于带输入估计变维滤波,将系统状态融合和确定性输入融合相结合,提出了一种多传感器带输入估计变维滤波融合算法。系统仿真结果表明,该算法可以有效地提高估计精度,适用于机动目标跟踪。     

A note on interval observer design for unknown input estimation

This paper addresses the problem of interval observer design for unknown input estimation in linear time-invariant systems. Although the problem of unknown input estimation has been widely studied in the literature, the design of joint state and unknown input observers has not been considered within a set-membership context. While conventional interval observers could be used to propagate with some additional conservatism, unknown inputs by considering them as disturbances, the proposed approach allows their estimation. Under the assumption that the measurement noise and the disturbances are bounded, lower and upper bounds for the unmeasured state and unknown inputs are computed. Numerical simulations are presented to show the efficiency of the proposed approach.     

Robust discrete‐time nonlinear sliding mode state estimation of uncertain nonlinear systems

In this paper, we propose a discrete‐time nonlinear sliding mode observer for state and unknown input estimations of a class of single‐input/single‐output nonlinear uncertain systems. The uncertainties are characterized by a state‐dependent vector and a scalar disturbance/unknown input. The discrete‐time model is derived through Taylor series expansion together with nonlinear state transformation. A design methodology that combines the discrete‐time sliding mode (DSM) and a nonlinear observer design is adopted, and a strategy is developed to guarantee the convergence of the estimation error to a bound within the specified boundary layer. A relation between sliding mode gain and boundary layer is established for the existence of DSM, and the estimation is made robust to external disturbances and uncertainties. The unknown input or disturbance can also be estimated through the sliding mode. The conditions for the asymptotical stability of the estimation error are analysed. Application to a bioreactor is given and the simulation results demonstrate the effectiveness of the proposed scheme. Copyright © 2006 John Wiley & Sons, Ltd.     

基于自适应Kalman滤波的合成孔径声纳运动估计

合成孔径声纳姿态、位移测量系统一般包括：惯性测量单元（IMU），差分DGPS，声多普勒计程仪DVL，深度传感器等。通常情况下，惯性测量单元（IMU）必须与DVL或DGPS进行数据融合，才能减小发散现象，提高导航精度。合成孔径声纳基阵安装在拖体上，由水面舰船利用拖缆拖曳航行，其运动受海流扰动及拖船机动的影响，未知的机动输入估计及海流的估计是必须要考虑的，这是合成孔径声纳基阵运动估计的比较特殊的地方。传统的Kalman滤波器不能直接应用于合成孔径声纳姿态、运动估计。因此，采用自适应Kalman滤波算法来处理合成孔径声纳姿态、运动估计问题。数值仿真表明，该方法较好地解决了合成孔径声纳姿态、运动估计问题。