Adaptive parameter estimation for a general dynamical system with unknown states

This paper is concerned with the design of a state filter for a time‐delay state‐space system with unknown parameters from noisy observation information. The key is to investigate new identification algorithms for interactive state and parameter estimation of the considered system. Firstly, an observability canonical state‐space model is derived from the original model by linear transformation for the purpose of simplifying the model structure. Secondly, a direct state filter is formulated by minimizing the state estimation error covariance matrix on the basis of the Kalman filtering principle. Thirdly, once the unknown states are estimated, a state filter–based recursive least squares algorithm is proposed for parameter estimation using the least squares principle. Then, a state filter–based hierarchical least squares algorithm is derived by decomposing the original system into several subsystems for improving the computational efficiency. Finally, the numerical examples illustrate the effectiveness and robustness of the proposed algorithms.     

Systematic physics constrained parameter estimation of stochastic differential equations

A systematic Bayesian framework is developed for physics constrained parameter inference of stochastic differential equations (SDE) from partial observations. Physical constraints are derived for stochastic climate models but are applicable for many fluid systems. A condition is derived for global stability of stochastic climate models based on energy conservation. Stochastic climate models are globally stable when a quadratic form, which is related to the cubic nonlinear operator, is negative definite. A new algorithm for the efficient sampling of such negative definite matrices is developed and also for imputing unobserved data which improve the accuracy of the parameter estimates. The performance of this framework is evaluated on two conceptual climate models.     

考虑约束参数切换的小蜂窝LTE移动负载自适应均衡

针对因用户设备移动性和小区覆盖率造成的网络负载周期性不平衡问题,引入小蜂窝网络以支持高数据率服务和密集部署,提出一种自适应网络负载状态并考虑负载估计的小蜂窝网络移动性负载平衡算法。该算法根据过载单元和相邻单元调整进行参数切换,其资源利用取决于信号质量和所连接用户设备在长期演进网络(LTE)中的流量需求,并定义资源块利用率作为单元负载的度量,根据网络负载情况使用自适应阈值来确定过载单元。为避免性能振荡,考虑移动负载对网络的影响,进行负载均衡过程设计。最后通过系统级仿真评价了该算法在不同环境下的性能,仿真结果表明,该算法在网络间提供了更均衡的负载(即小区间的标准差较小),比以前的算法具有更高的网络吞吐量。     

Adaptive divided difference filtering for simultaneous state and parameter estimation

A novel adaptive version of the divided difference filter (DDF) applicable to non-linear systems with a linear output equation is presented in this work. In order to make the filter robust to modeling errors, upper bounds on the state covariance matrix are derived. The parameters of this upper bound are then estimated using a combination of offline tuning and online optimization with a linear matrix inequality (LMI) constraint, which ensures that the predicted output error covariance is larger than the observed output error covariance. The resulting sub-optimal, high-gain filter is applied to the problem of joint state and parameter estimation. Simulation results demonstrate the superior performance of the proposed filter as compared to the standard DDF.     

Adaptive estimation for a linear system with interrupted observation

This short paper is concerned with the Bayesian estimation problem for a linear system with the interrupted observation mechanism that is expressed in terms of the stationary two-state Markov chain with unknown transition probabilities. Derived is the approximate minimum variance adaptive estimator algorithm coupled with the estimation of the unknown transition probabilities.     

Adaptive receding horizon predictive control for constrained discrete-time linear systems with parameter uncertainties

This paper proposes a discrete-time model predictive control (MPC) scheme combined with an adaptive mechanism. To this end, first, an adaptive parameter estimation algorithm suitable for MPC is proposed, which uses the available input and output signals to estimate the unknown system parameters. It enables the prediction of a monotonically decreasing worst-case estimation error bound over the prediction horizon of MPC. These distinctive features allow for future model improvement to be explicitly considered in MPC. Thus, a less conservative adaptive-type MPC controller can be developed based on the proposed estimation method. Second, we show how the discrete-time adaptive-type state-feedback MPC controller is constructed by combining the on-line parameter estimation scheme with a modified robust MPC method based on the comparison model. The developed MPC controller guarantees feasibility and stability of the closed-loop system theoretically in the presence of input and state constraints. A numerical example is given to demonstrate its effectiveness.     

A constrained recursive pseudo-linear regression scheme for on-line parameter estimation in adaptive control

In adaptive control of systems with poles close to the unit circle, application of the recursive estimation techniques can lead to excursions of the poles of the identified model outside the unit circle even when the process is open loop stable. These excursions can be of two types. The poles of the deterministic component of the model can drift outside unit circle even when the process has no unstable modes. Alternatively, the poles and/or zeros of the unmeasured disturbance (noise) model can drift outside the unit circle. In either case, the identified model is not suitable for on-line controller adaptation. In this work, a novel constrained recursive formulation is proposed for on-line parameter estimation based on the pseudo-linear regression (PLR) approach. The efficacy of the proposed approach is demonstrated by conducting experimental studies on a benchmark laboratory scale heater-mixer setup. The analysis of the open and closed loop experimental results reveals that the proposed constrained parameter estimation scheme provides a systematic and computationally attractive approach to ensure that the identified model parameters are restricted to the feasible region.     

一种新的线性系统模型参数估计方法

分析了使用区间分析进行参数估计的原因,由此在未知但有界（UBB）误差假设下,提出了线性系统模型参数估计的区间分析方法,同时,对Matlab区间算法工具箱INTLAB进行了简介,并将INTLAB应用于使用所提算法的算例中。通过数值算例,将此算法与Fogel椭球算法和最小二乘算法进行了比较,算例结果表明了所提算法的有效性和可行性。     

Continuous-time constrained least-squares algorithms for recursive parameter estimation of stochastic linear systems by a stabilized output-error method

Discrete-time least-squares algorithms for recursive parameter estimation have continuous-time counterparts, which minimize a quadratic functional. The continuous-time algorithms can also include (in)equality constraints. Asymptotic convergence is demonstrated by means of Lyapunov methods. The constrained algorithms are applied in a stabilized output-error configuration for parameter estimation in stochastic linear systems.     

Adaptive nonlinear observer for state and unknown parameter estimation in noisy systems

This paper proposes a novel adaptive observer for Lipschitz nonlinear systems and dissipative nonlinear systems in the presence of disturbances and sensor noise. The observer is based on an H_∞ observer that can estimate both the system states and unknown parameters by minimising a cost function consisting of the sum of the square integrals of the estimation errors in the states and unknown parameters. The paper presents necessary and sufficient conditions for the existence of the observer, and the equations for determining observer gains are formulated as linear matrix inequalities (LMIs) that can be solved offline using commercially available LMI solvers. The observer design has also been extended to the case of time-varying unknown parameters. The use of the observer is demonstrated through illustrative examples and the performance is compared with extended Kalman filtering. Compared to previous results on nonlinear observers, the proposed observer is more computationally efficient, and guarantees state and parameter estimation for two very broad classes of nonlinear systems (Lipschitz and dissipative nonlinear systems) in the presence of input disturbances and sensor noise. In addition, the proposed observer does not require online computation of the observer gain.     

Modified stochastic gradient parameter estimation algorithms for a nonlinear two-variable difference system

This paper proposes a stochastic gradient algorithm and two modified stochastic gradient algorithms for a nonlinear two-variable difference system. The output and the input of a two-variable parameter system depend on time and on spatial coordinates. A stochastic gradient algorithm is introduced to estimate the unknown parameters. In order to increase the convergence rate but not to increase the computational effort, two modified stochastic gradient algorithms are also proposed. The simulation results indicate that the proposed methods are effective.     

Nonlinear state estimation for rigid-body motion with low-pass sensors

In this paper, we consider the state estimation problem for the nonlinear kinematic equations of a rigid body observed under low-pass sensors. The problem is motivated from a walking robot application where inclinometers and gyros are the sensors used. We show that a non-local high gain observer exists for the nonlinear rigid-body kinematic equations and that it under a small angle assumption is possible to use one inclinometer only to estimate two angles.     

An algorithm for steady-state system optimization and parameter estimation

In this paper an algorithm is described which uses a steady-state mode! to determine the optimum operating point of a process. The model, which is not required to be an accurate representation of the real process, contains parameters to be estimated and the algorithm involves an iterative procedure between the two problems of system optimization and parameter estimation. Lagrangian analysis is employed to account for the interaction between the two problems, resulting in a procedure which may be regarded as a modified two-step approach in which the optimization objective index includes an extra term. The extra term contains a comparison between model and real process output derivatives and ensures that the optimal steady-state operating condition is achieved in spite of model inaccuracies.

The algorithm is shown to perform satisfactorily in a digital simulation study concerned with determining food flow rate and temperature controller set points to maximize the net rate of return from an exothermic chemical reactor using a simplified non-linear model for system optimization and parameter estimation. The simulation is employed to investigate the convergence properties of the algorithm and to study the effects of measurement errors.     

不确定Chua电路系统的固定时间自适应参数估计

针对具有未知参数的不确定Chua电路系统, 本文提出了一种基于Volterra积分算子的固定时间自适应参数 估计算法. 在仅有输出信号的已知的情况下, 该算法能够保证参数的估计值在一个不依赖于初始误差的固定时间内 收敛到参数的真实值. 通过在Volterra积分算子中巧妙的选取核函数, 使其满足在τ = 0和τ = t时核函数及其导数为 零, 从而能够有效消除系统初始值的影响, 同时避免了对系统输出导数的计算. 最后, 仿真结果验证了所提算法的有 效性.     

行人导航系统中航迹推算参数估计方法的研究

将GPS/DR组合导航技术应用到行人导航系统中。利用加速度计对行人步态进行判别,将神经网络用于行人步幅信息的标定。同时利用电子罗盘实现方位角的测量,并结合加速度计信息进行倾斜角度的误差补偿。现场测试结果表明,本文提出的DR参数估计方法不但提高参数估计的精度,而且能够满足行人导航定位的要求。     

Bayes cost of parameter estimation for a quantum system interacting with an environment

Quantum Information Processing - The Bayes cost of parameter estimation is studied for a quantum system which is influenced by an external environment, where the cost function is assumed to be a...     

基于粒子滤波的非线性系统静态参数估计方法*

针对基于滤波方法的最大似然参数估计步长序列过于单一,算法收敛缓慢并很容易收敛于局部最优解的问题,提出了基于似然权值的在线EM参数估计算法(LWOEM)。通过粒子滤波方法实时估计系统的状态值变化,结合最大似然方法计算静态参数的点估计,然后通过计算更新参数的似然值来动态更新步长序列.与在线EM参数估计算法(OEM)的实验结果比较,表明该算法具有更好的适应性和收敛效果。     

Newton-like algorithm for integrated system optimization and parameter estimation technique

The problem of obtaining the correct optimal steady-state operation of an industrial process, despite the deficiencies in its available mathematical model, is addressed in the paper. The control method considered is the integrated system optimization and parameter estimation (ISOPE) technique, and a new algorithm, of Newton-like type, is presented in the paper for this technique. The algorithm is derived for the augmented version of the ISOPE technique and hence it is also applicable for non-convex problems. The algorithm does not require more measurement information than the previous simple relaxation-type algorithms. It is convergent in one iteration for the case of a linear process and quadratic performance function. A local convergence analysis is provided for the general non-linear case. Simulation results are also given, and comparison with the relaxation type algorithm is presented, indicating the superiority of the new approach for the examples considered     

Fast parametric imaging algorithm for dual-input biomedical system parameter estimation

Medical parametric imaging with dynamic positron emission tomography (PET) plays an increasingly potential role in modern biomedical research and clinical diagnosis. The key issue in parametric imaging is to estimate parameters based on sampled data at the pixel-by-pixel level from certain dynamic processes described by valid mathematical models. Classic nonlinear least squares (NLS) algorithm requires a "good" initial guess and the computational time-complexity is high, which is impractical for image-wide parameter estimation. Although a variety of fast parametric imaging techniques have been developed, most of them focus on single input systems, which do not provide an optimal solution for dual-input biomedical system parameter estimation, which is the case of liver metabolism. In this study, a dual-input-generalized linear least squares (D-I-GLLS) algorithm was proposed to identify the model parameters including the parameter in the dual-input function. Monte Carlo simulation was conducted to examine this novel fast algorithm. The results of the quantitative analysis suggested that the proposed technique could provide comparable reliability of the parameter estimation with NLS fitting and accurately identify the parameter in the dual-input function. This method may be potentially applicable to other dual-input biomedical system parameter estimation as well.     

On an algorithm for combined system optimisation and parameter estimation

The paper is concerned with the determination of optimum steady-state operation of industrial plant where the optimisation is performed using a mathematical model with parameters whose values are estimated by comparing model and real plant measurements. The two associated problems of system optimisation and model parameter estimation are discussed and an algorithm is examined whose purpose is to accomplish the correct steady-state optimum operating condition on the real plant in spite of inaccuracies in the structure of the mathematical model. The aim of the paper is to investigate the performance of the algorithm which is accomplished through a theoretical analysis of its application to a linear process, where the optimisation is performed using a quadratic performance index and a mathematical model of incorrect structure. Particular emphasis is given to the stability and convergence properties of the algorithm and to the effect of real process measurement errors. Simulation results are also presented illustrating the effectiveness of the technique when applied to nonlinear optimisation problems including a study concerned with determining optimum controller set points to maximise the net rate of return from a chemical reactor plant.