Stability of the Kalman filter with stochastic time-varying parameters

2002 ◽  
Author(s):  
V. Solo
Keyword(s):  
Kalman Filter ◽  
Time Varying ◽  
Varying Parameters ◽  
Time Varying Parameters ◽  
Stochastic Time

STATISTICAL LEARNING WITH TIME-VARYING PARAMETERS

2003 ◽  
Vol 7 (1) ◽  
pp. 119-139 ◽  
Author(s):  
Bruce McGough
Keyword(s):  
Stochastic Process ◽  
Kalman Filter ◽  
Statistical Learning ◽  
Rational Expectations ◽  
Stability Parameter ◽  
Time Varying ◽  
Rational Expectations Equilibrium ◽  
Varying Parameters ◽  
Time Varying Parameters ◽  
The Stability

In their landmark paper, Bray and Savin note that the constant-parameters model used by their agents to form expectations is misspecified and that, using standard econometric techniques, agents may be able to determine the time-varying nature of the model's parameters. Here, we consider the same type of model as employed by Bray and Savin except that our agents form expectations using a perceived model with parameters that vary with time. We assume agents use the Kalman filter to form estimates of these time-varying parameters. We find that, under certain restrictions on the structure of the stochastic process and on the value of the stability parameter, the model will converge to its rational expectations equilibrium. Further, the restrictions on the stability parameter required for convergence are identical to those found by Bray and Savin.

Identification of Linear Time-Varying Systems

2010 ◽  
pp. 221-237
Author(s):  
Vinayak G. Asutkar ◽  
Balasaheb M. Patre
Keyword(s):  
Kalman Filter ◽  
Physical Situation ◽  
Time Varying ◽  
Varying Parameters ◽  
System Parameters ◽  
Optimal Estimator ◽  
Time Varying Parameters ◽  
Time Varying Systems ◽  
Filter Approach ◽  
Kalman Filter Method

This chapter deals with identification of time-varying systems using Kalman filter approach. Most physical systems exhibit some degree of time-varying behaviour for many reasons. These systems cannot effectively be modelled using time invariant models. A time-varying autoregressive with exogenous input (TVARX) model is good to model these time-varying systems. The Kalman filter approach is a superior way to estimate the system parameters. This approach can track the time-varying parameters and is suitable for recursive estimation. It works well even when there are abrupt changes in the system parameters. Kalman filter is known to be an optimal estimator even when there is significant noise. In the proposed approach, for the purpose of simulation, we employ first order TVARX model and its parameters are estimated using recursive Kalman filter method. The system parameters are varied in continuous and abruptly changing manner to reveal the physical situation. To show the efficacy of the proposed approach, the time-varying parameters are estimated for different noise conditions. The performance is evaluated by calculating error performance measures. The results are found to be satisfactory with reasonable accuracy for noisy conditions even for fast changing parameters. The numerical examples illustrate efficacy of the proposed Kalman filter based approach for identification of time-varying systems.

scholarly journals Online Identification of Time-Variant Structural Parameters Under Unknown Inputs Basing On Extended Kalman Filter

2021 ◽  
Author(s):  
Xiaoxiong Zhang ◽  
Jia He ◽  
Xugang Hua ◽  
Zhengqing Chen ◽  
Ou Yang
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Structural Parameters ◽  
Optimization Procedure ◽  
Unbiased Estimation ◽  
Time Varying ◽  
Time Step ◽  
Varying Parameters ◽  
Unknown Inputs ◽  
Time Varying Parameters

Abstract To date, a number of parameter identification methods have been developed for the purpose of structural health monitoring and vibration control. Among them, the extended Kalman filter (EKF) series methods are attractive in view of the efficient unbiased estimation in recursive manner. However, most of these methods are performed on the premise that the parameters are time-invariant and/or the loadings are known. To circumvent the aforementioned limitations, an online EKF with unknown input (OEKF-UI) approach is proposed in this paper for the identification of time-varying parameters and the unknown excitation. A revised observation equation is obtained with the aid of projection matrix. To capture the changes of structural parameters in real-time, an online tracking matrix (OTM) associated with the time-varying parameters is introduced and determined via an optimization procedure. Then, based on the principle of EKF, the recursive solution of structural states including the time-variant parameters can be analytically derived. Finally, using the estimated structural states, the unknown inputs are identified by means of least-squares estimation (LSE) at the same time-step. The effectiveness of the proposed approach is validated via linear and nonlinear numerical examples with the consideration of parameters being varied abruptly.

Synchronization of Chaotic Systems with Uncertain Time-Varying Parameters

2015 ◽  
Vol 9 (6) ◽  
pp. 568
Author(s):  
Ahmad Al-Jarrah ◽  
Mohammad Ababneh ◽  
Suleiman Bani Hani ◽  
Khalid Al-Widyan
Keyword(s):  
Chaotic Systems ◽  
Time Varying ◽  
Varying Parameters ◽  
Time Varying Parameters ◽  
Uncertain Time
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