Recursive parameter estimation methods and convergence analysis for a special class of nonlinear systems

This paper is concerned with the joint estimation of states and parameters of a special class of nonlinear systems, ie, bilinear systems. The key is to investigate new estimation methods for interactive state and parameter estimation of the considered system based on the interactive estimation theory. Because the system states are unknown, a bilinear state observer is established based on the Kalman filtering principle. Then, the unavailable states are updated by the state observer outputs recursively. Once the state estimates are obtained, the bilinear state observer–based hierarchical stochastic gradient algorithm is developed by using the gradient search. For the purpose of improving the convergence rate and the parameter estimation accuracy, a bilinear state observer–based hierarchical multi‐innovation stochastic gradient algorithm is proposed by expanding a scalar innovation to an innovation vector. The convergence analysis indicates that the parameter estimates can converge to their true values. The numerical example illustrates the effectiveness of the proposed algorithms.     

Joint state and multi-innovation parameter estimation for time-delay linear systems and its convergence based on the Kalman filtering

This paper studies the joint state and parameter estimation problem for a linear state space system with time-delay. A multi-innovation gradient algorithm is developed based on the Kalman filtering principle. To improve the convergence rate, a filtering based multi-innovation gradient algorithm is proposed by using the filtering technique. The analysis indicates that the parameter estimates given by the proposed algorithms converge to their true values under the persistent excitation conditions. A simulation example is given to confirm that the proposed algorithms are effective.     

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.     

Two‐stage auxiliary model gradient‐based iterative algorithm for the input nonlinear controlled autoregressive system with variable‐gain nonlinearity

This article focuses on the parameter estimation problem of the input nonlinear system where an input variable‐gain nonlinear block is followed by a linear controlled autoregressive subsystem. The variable‐gain nonlinearity is described analytical by using an appropriate switching function. According to the gradient search technique and the auxiliary model identification idea, an auxiliary model‐based stochastic gradient algorithm with a forgetting factor is presented. For the sake of improving the parameter estimation accuracy, an auxiliary model gradient‐based iterative algorithm is proposed by utilizing the iterative identification theory. To further optimize the performance of the algorithm, we decompose the identification model of the system into two submodels and derive a two‐stage auxiliary model gradient‐based iterative (2S‐AM‐GI) algorithm by using the hierarchical identification principle. The simulation results confirm the effectiveness of the proposed algorithms and show that the 2S‐AM‐GI algorithm has higher identification efficiency compared with the other two algorithms.     

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.     

电力系统状态估计多算法融合

为解决复杂电网大数据背景下单一算法难以满足状态估计要求的问题,提出一种电力系统状态估计多算法融合系统。基于数据融合思想,将加权最小二乘法、快速分解法、量测状态变换法与Sigmoid函数法相互融合实现电网状态估计,支持串行融合模式和并行融合模式。实验结果表明,融合算法使得估计结果保留了各自算法的优点,避免了单一算法的缺点,提高了状态估计的精度和效率。     

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

This paper extends previous work on joint input and state estimation to systems with direct feedthrough of the unknown input to the output. Using linear minimum-variance unbiased estimation, a recursive filter is derived where the estimation of the state and the input are interconnected. The derivation is based on the assumption that no prior knowledge about the dynamical evolution of the unknown input is available. The resulting filter has the structure of the Kalman filter, except that the true value of the input is replaced by an optimal estimate.     

On the application of a hybrid ellipsoidal-rectangular interval arithmetic algorithm to interval Kalman filtering for state estimation of uncertain systems

Modelling uncertainty is a key limitation to the applicability of the classical Kalman filter for state estimation of dynamic systems. For such systems with bounded modelling uncertainty, the interval Kalman filter (IKF) is a direct extension of the former to interval systems. However, its usage is not yet widespread owing to the over-conservatism of interval arithmetic bounds. In this paper, the IKF equations are adapted to use an ellipsoidal arithmetic that, in some cases, provides tighter bounds than direct, rectangular interval arithmetic. In order for the IKF to be useful, it must be able to provide reasonable enclosures under all circumstances. To this end, a hybrid ellipsoidal-rectangular enclosure algorithm is proposed, and its robustness is evidenced by its application to two characteristically different systems for which it provides stable estimate bounds, whereas the rectangular and ellipsoidal approaches fail to accomplish this in either one or the other case.     

Hierarchical Newton and least squares iterative estimation algorithm for dynamic systems by transfer functions based on the impulse responses

This paper develops a parameter estimation algorithm for linear continuous-time systems based on the hierarchical principle and the parameter decomposition strategy. Although the linear continuous-time system is a linear system, its output response is a highly nonlinear function with respect to the system parameters. In order to propose a direct estimation algorithm, a criterion function is constructed between the response output and the observation output by means of the discrete sampled data. Then a scheme by combining the Newton iteration and the least squares iteration is builded to minimise the criterion function and derive the parameter estimation algorithm. In light of the different features between the system parameters and the output function, two sub-algorithms are derived by using the parameter decomposition. In order to remove the associate terms between the two sub-algorithms, a Newton and least squares iterative algorithm is deduced to identify system parameters. Compared with the Newton iterative estimation algorithm without the parameter decomposition, the complexity of the hierarchical Newton and least squares iterative estimation algorithm is reduced because the dimension of the Hessian matrix is lessened after the parameter decomposition. The experimental results show that the proposed algorithm has good performance.     

基于辅助模型和数据滤波的伪线性回归系统参数估计方法

针对伪线性输出误差回归系统的辨识模型新息信息向量存在不可测变量的问题,首先通过构造一个辅助模型,用辅助模型的输出代替未知中间变量,推导得到的基于辅助模型的递推最小二乘参数估计算法计算量较大,但算法的辨识效果不佳。进一步采用估计的噪声模型对系统观测数据进行滤波,使用滤波后的数据进行参数估计,从而推导提出了基于数据滤波的递推最小二乘参数估计算法。仿真结果表明,所提算法能够有效估计伪线性回归线性输出误差系统的参数。     

含有迟滞Hammerstein系统的非光滑卡尔曼状态估计

迟滞特性具有非光滑、多值映射等复杂特性.如果迟滞环节的末端还存在一个线性子系统,导致迟滞的输出信号不可测,使得整个系统的状态估计工作成为很大的难题,常规的估计方法无法直接应用到这类系统中.本文提出一种新的非光滑卡尔曼滤波器,描述了Hammerstein系统的状态空间方程.据此构造了能够随系统工作区间变化而自动切换的非光滑滤波器.最后通过仿真和实验,比较了非光滑卡尔曼滤波器和传统的卡尔曼滤波器的状态估计效果,比较结果表明非光滑卡尔曼滤波器对于带迟滞的Hammerstein系统状态变量的估计的准确性要优于传统的卡尔曼滤波器.     

Robust state estimation for a class of uncertain time-delay systems

This paper considers a robust state estimation problem for a class of uncertain time-delay systems. In this problem, the noise and uncertainty are modelled deterministically via an integral quadratic constraint. The robust state estimation problem involves constructing the set of all possible states at the current time consistent with given output measurements and the integral quadratic constraint. This set is found to be an ellipsoid which is constructed via a linear state estimator.     

A separated bias identification and state estimation algorithm for nonlinear systems

A computational algorithm for the identification of biases in discrete-time, nonlinear, stochastic systems is derived by extending the separate bias estimation results for linear systems to the extended Kalman filter formulation. The merits of the approach are illustrated by identifying instrument biases using a terminal configured vehicle simulation.     

空间连接系统分布式递推状态估计

针对空间连接系统, 提出一种分布式递推状态估计算法, 并给出算法收敛的充分必要条件. 该分布式估计器由一系列子估计器组成, 每个子估计器只利用本地子系统和相邻子系统的输出测量值估计本地子系统的状态. 与集总式Kalman 滤波相比, 在牺牲少量估计精度的情况下, 所提出算法大幅降低了计算复杂度和数据传输压力.     

Frequency‐shifting‐based algebraic approach to stable on‐line parameter identification and state estimation of multirotor UAV

In this paper, a frequency‐shifting‐based (FSB) algebraic approach to stable on‐line parameter identification and state estimation is proposed. The proposed simultaneous parameter identification and state estimation algebraic approach are applied to multirotor adaptive‐like tracking control assuming that only position measurement is available. The proposed algebraic approach provides very fast convergence towards true values of system parameters and states, without transients that depend on initial conditions and without peaking phenomenon which is characteristics of high‐gain observers. The efficiency of the proposed algorithm is illustrated by a simulation example.     

Decomposition‐based multiinnovation gradient identification algorithms for a special bilinear system based on its input‐output representation

This article considers the parameter estimation for a special bilinear system with colored noise. Its input‐output representation is derived by eliminating the state variables in the bilinear system. Based on the input‐output representation of the bilinear system, a multiinnovation generalized extended stochastic gradient (MI‐GESG) algorithm is proposed by using the multiinnovation identification theory. Furthermore, a decomposition‐based multiinnovation (ie, hierarchical multiinnovation) generalized extended stochastic gradient identification (H‐MI‐GESG) algorithm is derived to enhance the parameter estimation accuracy by using the hierarchical identification principle, and a GESG algorithm is presented for comparison. Compared with the existing identification algorithms for the bilinear system, the proposed MI‐GESG and H‐MI‐GESG algorithms can generate more accurate parameter estimation. Finally, a simulation example is provided to verify the effectiveness of the proposed algorithms.     

改进的迭代收缩阈值算法及其在量子状态估计中的应用

本文将含有稀疏干扰的量子状态估计问题,转化为考虑量子状态的约束条件下,分别求解密度矩阵的核范数,以及稀疏干扰l1范数的两个子问题的优化问题.针对迭代收缩阈值算法(ISTA)所存在的收敛速度慢的问题,通过在两个子问题的迭代估计中,引入一个加速算子,对当前值与前一次值之差进行进一步的补偿,来提高算法的迭代速度(FISTA).并将FISTA算法应用于求解含有稀疏干扰的量子状态估计中.针对5个量子位的状态估计的仿真实验,将FISTA分别与ISTA、交替方向乘子法(ADMM)、不动点方程的ADMM算法(FP–ADMM),以及非精确的ADMM算法(I–ADMM)4种优化算法进行性能对比.实验结果表明, FISTA算法具有更加优越的收敛速度,并且能够得到更小的量子状态估计误差.     

Reduced‐order state estimation for linear time‐varying systems

We consider reduced‐order and subspace state estimators for linear discrete‐time systems with possibly time‐varying dynamics. The reduced‐order and subspace estimators are obtained using a finite‐horizon minimization approach, and thus do not require the solution of algebraic Lyapunov or Riccati equations. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

基于自适应迭代学习算法的一类非线性系统故障检测与估计

针对迭代学习算法在非线性系统故障检测与估计过程中存在估计误差较大和收敛速度较慢等不足的问题,提出了一种基于龙格–库塔故障估计观测器模型的自适应迭代学习算法,有效降低了故障估计误差;并引入H∞性能指标,提高了故障估计观测器的收敛速度.该算法首先设计故障检测观测器对故障进行检测,然后设计故障估计观测器,并将自适应算法与迭代学习策略相结合,使得估计故障逐渐逼近真实故障,从而实现对非线性系统中多种常见故障的精确检测与估计.最后,通过机械臂旋转关节驱动电机的执行器故障仿真验证了所提算法的有效性.