Optimal linear filter design for systems with correlation in the measurement matrices and noises: recursive algorithm and applications

This paper addresses the optimal least-squares linear estimation problem for a class of discrete-time stochastic systems with random parameter matrices and correlated additive noises. The system presents the following main features: (1) one-step correlated and cross-correlated random parameter matrices in the observation equation are assumed; (2) the process and measurement noises are one-step autocorrelated and two-step cross-correlated. Using an innovation approach and these correlation assumptions, a recursive algorithm with a simple computational procedure is derived for the optimal linear filter. As a significant application of the proposed results, the optimal recursive filtering problem in multi-sensor systems with missing measurements and random delays can be addressed. Numerical simulation examples are used to demonstrate the feasibility of the proposed filtering algorithm, which is also compared with other filters that have been proposed.     

Sliding-mode and proportional-derivative-type motion control with radial basis function neural network based estimators for wheeled vehicles

An obstacle avoidance problem of rear-steered wheeled vehicles in consideration of the presence of uncertainties is addressed. Modelling errors and additional uncertainties are taken into consideration. Controller designs for driving and steering motors are designed. A proportional-derivative-type driving motor controller and a sliding-mode steering controller combined with radial basis function neural network (RBFNN) based estimators are proposed. The convergence properties of the RBFNN-based estimators are proven by the Stone–Weierstrass theorem. The stability of the proposed control law is proven using Lyapunov stability analysis. The obstacle avoidance strategy utilising the sliding surface adjustment to an existing navigation method is presented. It is concluded that the driving velocity and steering-angle performances of the proposed control system are satisfactory.     

A distributed solution to the network reconstruction problem

It has been recently shown in Ren et al. (2010) that by collecting noise-contaminated time series generated by a coupled-oscillator system at each node of a network, it is possible to robustly reconstruct its topology, i.e. determine the graph Laplacian. Restricting ourselves to linear consensus dynamics over undirected communication networks, in this paper we introduce a new dynamic average consensus least-squares algorithm to locally estimate these time series at each node, thus making the reconstruction process fully distributed and more easily applicable in the real world. We also propose a novel efficient method for separating the off-diagonal entries of the reconstructed Laplacian, and examine several concepts related to the trace of the dynamic correlation matrix of the coupled single integrators, which is a distinctive element of our network reconstruction method. The theory is illustrated with examples from computer, power and transportation systems.     

FAULT DIAGNOSIS OF HYDRAULIC SERVO SYSTEM USING THE UNSCENTED KALMAN FILTER

Fault occurrence can be embodied by the physical parameter variations of the hydraulic servo system. Faults can, therefore, be diagnosed according to the model coefficient variations of the hydraulic servo system. This paper proposes an approach for fault diagnosis based on the unscented Kalman filter (UKF) with a mathematical model of the hydraulic servo system. The mathematical model is established using the dynamic equations of the hydraulic servo system. Based on the fault mechanism analysis results, several important system model parameters that can separately represent different faults in different components of the hydraulic servo system are chosen. Discrete state space equations are derived from the dynamic equations. The UKF algorithm is used to estimate the important system model parameters of the hydraulic servo system by utilizing the discretized state space model. According to the variations of these model parameters, the fault modes and locations of the hydraulic servo system can be diagnosed and isolated. Two types of faults, namely, abrupt fault in servovalve gain and slow wear fault in hydraulic cylinder piston, which cannot be directly detected from the system output, are introduced individually to the hydraulic servo system in this work. By comparing with the extended Kalman Filter, three different experimental cases are used to validate the effectiveness of the UKF for hydraulic servo system fault diagnosis.     

A New Derivation of the Cubature Kalman Filters

This paper investigates the cubature Kalman filtering (CKF) for nonlinear dynamic systems. This third‐degree rule based filter employs a spherical‐radial cubature rule to numerically compute the integrals encountered in nonlinear filtering problems, thereby removing the requirements of explicitly computing the Jacobians. The cubature rule, however, requires computing the intractable integrals over a high‐dimensional spherical region for multidimensional applications. Moreover, the cubature formula that has been used to construct the spherical cubature formula has some demerits, most notably its inconvenient properties in computation and low estimation accuracy. Aimed at these issues, a general class of CKFs that uses only cubature rules is derived in this paper. It can be shown that the conventional CKF is a special case of the proposed algorithm. The paper also includes higher‐degree CKFs, especially two representative types of the fifth‐degree CKFs. Performance of the proposed algorithms is demonstrated via two target tracking problems. The experimental results, presented herein, illustrate the superior performance of higher‐degree CKFs to conventional nonlinear filters.     

Adaptive Lipschitz Observer Design for a Mammalian Model

This paper deals with observer designs for a proposed mathematical model of circadian rhythms which exist in almost every living organism. A 7th order model for mammalian circadian rhythms which captures the main dynamic features is considered in this paper. A recent result of one‐sided Lipschitz observer design in the literature is applied to this mammalian model to show a possibility of reducing measurements for circadian models in system biology. The mammalian model presented may contain an uncertainty parameter. An adaptive design of the Lipschitz observer is then applied to deal with this case. Besides detailed designs of both observers, detailed analysis is also performed for nonlinear functions in the mammalian model to show that the Lipschitz observers can indeed be applied. Several simulation studies of the proposed observers are carried out with the results shown in this paper.     

基于多渐消因子强跟踪UKF 和约束AR模型的故障估计与预测

针对非线性系统中不可观测故障参数估计和预测问题, 提出一种基于多重渐消因子强跟踪无迹卡尔曼滤波(MSTUKF) 的状态和参数联合估计法, 通过引入多重渐消因子增强了对变化函数未知的故障参数的跟踪能力. 对于得到的故障参数估计值, 利用递推最小二乘法更新约束AR预测模型, 从而实现故障参数的在线估计与预测. 仿真结果表明, MSTUKF方法在故障参数估计精度上优于UKF 和单渐消因子强跟踪UKF, 约束AR模型的预测精度高于无约束条件下的预测精度.

     

Development of soft sensor by incorporating the delayed infrequent and irregular measurements

Originated from challenging industrial applications, this paper addresses a soft sensor development problem for linear systems with two types of measurements. One is fast, regular and delay-free measurements. The other is infrequent, irregular measurements with time-varying delays. The approach to be taken is based on the Kalman filter and data fusion technique, avoiding running the full augmented state Kalman filter, and leading to a considerably lower implementation cost. Although it is suboptimal, the loss in performance is minor compared to the optimal filter. Two simulation examples demonstrate the advantages of the proposed approach. An industrial soft sensor application example is also used to demonstrate its practicality.     

旋转变压器信号的标定与解调

针对检波后信号存在直流偏置、幅值不等和相位偏移等问题,采用梯度估计算法,对检波后的包络信号进行离线标定;并设计了基于状态观测器的旋转变压器-数字转换(RDC)算法,对标定后的包络信号进行解调.试验结果表明,梯度估计算法收敛速度快,估计精度高.与反正切法相比,所设计的RDC算法不需通过数值差分即可获得角速度信息,干扰抑制能力强,角位置和角速度估计精度高.     

Online stiffness estimation for robotic tasks with force observers

In this paper we propose an online stiffness estimation technique for robotic tasks based only on force data, therefore, not requiring contact position information. This allows estimations to be obtained in robotic tasks involving interactions with unstructured and unknown environments where geometrical data is unavailable or unreliable. Our technique – the Candidate Observer Based Algorithm (COBA) – uses two force observers, configured with different candidate stiffnesses, to estimate online the actual target object stiffness. COBA is embedded in a force control architecture with computed torque in the task space. The theoretical presentation of the algorithm, as well as simulation tests and experimental results with a lightweight robot arm are also presented.