Nonlinear State Estimation Using Aggregate Modeling

2007 ◽  
Author(s):  
Kiriakos Kiriakidis ◽  
Matthew Feemster ◽  
Richard T. O’Brien
Keyword(s):  
State Estimation ◽  
Estimation Error ◽  
The State ◽  
Linear Feedback ◽  
Aggregate Model ◽  
Nonlinear State Estimation ◽  
Aggregate Modeling ◽  
Error Dynamics ◽  
The Stability ◽  
Nonlinear State

The paper addresses the state estimation problem for a general class of nonlinear systems. Using an expansion of nonlinear drift dynamics in terms of an aggregate model, the authors analyze the stability of the estimation error equation. Although the treatment is limited to linear feedback, the method results in quadratically stable error dynamics inside a large subset of the state space. The authors tested and verified the proposed approach on the nonlinear dynamics of the rotary pendulum.

scholarly journals Research on Projection Filtering Method Based on Projection Symmetric Interval and Its Application in Underwater Navigation

Symmetry ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1715
Author(s):  
Lijuan Chen ◽  
Zihao Zhang ◽  
Yapeng Zhang ◽  
Xiaoshuang Xiong ◽  
Fei Fan ◽  
...  
Keyword(s):  
State Estimation ◽  
Probability Density ◽  
Basis Function ◽  
Prior Probability ◽  
The State ◽  
Estimation Problem ◽  
Nonlinear State Estimation ◽  
Non Gaussian ◽  
Projection Filtering ◽  
Nonlinear State

For non-linear systems (NLSs), the state estimation problem is an essential and important problem. This paper deals with the nonlinear state estimation problems in nonlinear and non-Gaussian systems. Recently, the Bayesian filter designer based on the Bayesian principle has been widely applied to the state estimation problem in NLSs. However, we assume that the state estimation models are nonlinear and non-Gaussian, applying traditional, typical nonlinear filtering methods, and there is no precise result for the system state estimation problem. Therefore, the larger the estimation error, the lower the estimation accuracy. To perfect the imperfections, a projection filtering method (PFM) based on the Bayesian estimation approach is applied to estimate the state. First, this paper constructs its projection symmetric interval to select the basis function. Second, the prior probability density of NLSs can be projected into the basis function space, and the prior probability density solution can be solved by using the Fokker–Planck Equation (FPE). According to the Bayes formula, the proposed estimator utilizes the basis function in projected space to iteratively calculate the posterior probability density; thus, it avoids calculating the partial differential equation. By taking two illustrative examples, it is also compared with the traditional UKF and PF algorithm, and the numerical experiment results show the feasibility and effectiveness of the novel nonlinear state estimation filter algorithm.

Estimation of Plasma Insulin Using Nonlinear Filtering

2007 ◽  
Author(s):  
Kiriakos Kiriakidis ◽  
Richard O’Brien
Keyword(s):  
Nonlinear Filtering ◽  
Plasma Insulin ◽  
Estimation Error ◽  
Nonlinear Filter ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Aggregate Model ◽  
Aggregate Modeling ◽  
The Stability

The glucose-insulin dynamics as captured by the standard (Bergman) model are both nonlinear and time-varying. To develop an insulin estimator (or filter), the authors use an aggregate model expansion of the nonlinear dynamics while treating the time-varying component of the model as an exogenous input. The aggregate model allows for the design of a particular nonlinear filter (or observer) that uses a weighted summation of constant feedback gains and admits a straightforward implementation. Furthermore, the aggregate modeling approach enables the stability analysis of the estimation error equation through linear matrix inequalities. The aggregate model insulin filter is compared with an existing insulin filter through numerical simulation.

A Strong Tracking Cubature Kalman Filter for Nonlinear Estimation

2013 ◽  
Vol 313-314 ◽  
pp. 1115-1119
Author(s):  
Yong Qi Wang ◽  
Feng Yang ◽  
Yan Liang ◽  
Quan Pan
Keyword(s):  
Kalman Filter ◽  
State Estimation ◽  
Scaling Factor ◽  
Estimation Accuracy ◽  
Nonlinear State Estimation ◽  
Cubature Kalman Filter ◽  
Novel Method ◽  
Simulation Results ◽  
Tracking Filter ◽  
Nonlinear State

In this paper, a novel method based on cubature Kalman filter (CKF) and strong tracking filter (STF) has been proposed for nonlinear state estimation problem. The proposed method is named as strong tracking cubature Kalman filter (STCKF). In the STCKF, a scaling factor derived from STF is added and it can be tuned online to adjust the filtering gain accordingly. Simulation results indicate STCKF outperforms over EKF and CKF in state estimation accuracy.

Observer-Based Fault Diagnosis of Satellite Systems Subject to Time-Varying Thruster Faults

2006 ◽  
Vol 129 (3) ◽  
pp. 352-356 ◽  
Author(s):  
Wen Chen ◽  
Mehrdad Saif
Keyword(s):  
Fault Diagnosis ◽  
Estimation Error ◽  
Fault Estimation ◽  
Time Varying ◽  
Satellite Systems ◽  
Adaptive Observers ◽  
Error Dynamics ◽  
The Stability ◽  
Estimation Of Time ◽  
Identification Strategy

This paper presents a novel fault diagnosis approach in satellite systems for identifying time-varying thruster faults. To overcome the difficulty in identifying time-varying thruster faults by adaptive observers, an iterative learning observer (ILO) is designed to achieve estimation of time-varying faults. The proposed ILO-based fault-identification strategy uses a learning mechanism to perform fault estimation instead of using integrators that are commonly used in classical adaptive observers. The stability of estimation-error dynamics is established and proved. An illustrative example clearly shows that time-varying thruster faults can be accurately identified.

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