Parameter and State Estimation Algorithm for a State Space Model with a One-unit State Delay
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Parameter and State Estimation Algorithm for a State Space Model with a One-unit State Delay Ya Gu · Xianling Lu · Ruifeng Ding
Received: 16 April 2012 / Revised: 22 February 2013 © Springer Science+Business Media New York 2013
Abstract This paper derives a state estimation based parameter identification algorithm for state space systems with a one-unit state delay. We derive the identification model of an observability canonical state space system with a one-unit state delay. The key is to replace the unknown states in the parameter estimation algorithm with their state estimates and to identify the parameters of the state space models. Finally, two illustrative examples are given to show the effectiveness of the proposed algorithm. Keywords Parameter estimation · State estimation · State space models · Time delay · Least squares
1 Introduction Recursive algorithms or iterative algorithms are often adopted in solving a matrix equation [3, 27, 34, 54, 55], such as Jacobi iteration, system modeling [31, 33, 43–45], filtering and control [47–49], and parameter estimation [29, 52, 53, 65, 66]. Kalman filtering is a typical recursive algorithm for state estimation that uses the available Y. Gu · X. Lu Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Jiangnan University, Wuxi 214122, P.R. China Y. Gu e-mail: [email protected] X. Lu e-mail: [email protected] R. Ding () School of Internet of Things Engineering, Jiangnan University, Wuxi 214122, P.R. China e-mail: [email protected]
Circuits Syst Signal Process
input-output data to estimate the states of dynamic systems [46]. State estimation of the state space model is of great significance in designing controllers based on state feedback. In the literature, Shi et al. presented sensor data scheduling for optimal state estimation with a communication energy constraint [50]. There exist a variety of parameter estimation methods for system modeling [21, 37, 39, 42, 51], e.g., recursive least squares methods for identifying equation error type models [1, 40, 56], auxiliary model identification methods for estimating the parameters of output error type models [60], and iterative identification methods for identifying systems with unknown noise terms in the information vectors [24]. McCusker et al. studied improved parameter estimation by using noise compensation in the time-scale domain [41]; Dua studied an artificial neural network approximation based decomposition approach for parameter estimation of ordinary differential equations [26]; Ding et al. presented an auxiliary model based multi-innovation stochastic gradient identification algorithm for estimating the parameters of systems with scarce measurements [23]; Liu et al. studied the multi-innovation extended stochastic gradient algorithm and its performance analysis [38]. Time-delay systems exist in industrial processes. The identification of time-delay systems is important for system control and system analysis, and has received much research attention in the area of control f
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