Robust Kalman filtering for nonlinear multivariable stochastic systems in the presence of non-Gaussian noise

2015 ◽  
Vol 26 (3) ◽  
pp. 445-460 ◽  
Author(s):  
Vladimir Stojanovic ◽  
Novak Nedic
Keyword(s):  
Kalman Filtering ◽  
Gaussian Noise ◽  
Stochastic Systems ◽  
Non Gaussian

scholarly journals An OGI model for personalized estimation of glucose and insulin concentration in plasma

2021 ◽  
Vol 18 (6) ◽  
pp. 8499-8523
Author(s):  
Weijie Wang ◽  
◽  
Shaoping Wang ◽  
Yixuan Geng ◽  
Yajing Qiao ◽  
...  
Keyword(s):  
Kalman Filtering ◽  
Gaussian Noise ◽  
Particle Filtering ◽  
In Silico ◽  
Insulin Concentration ◽  
Model Parameters ◽  
Bayesian Filtering ◽  
Extended Kalman Filtering ◽  
External Disturbances ◽  
Non Gaussian

<abstract><p>Plasma glucose concentration (PGC) and plasma insulin concentration (PIC) are two essential metrics for diabetic regulation, but difficult to be measured directly. Often, PGC and PIC are estimated from continuous glucose monitoring and insulin delivery data. Nevertheless, the inter-individual variability and external disturbance (e.g. carbohydrate intake) bring challenges for accurate estimations. This study is to estimate PGC and PIC adaptively by identifying personalized parameters and external disturbances. An observable glucose-insulin (OGI) dynamic model is established to describe insulin absorption, glucose regulation, and glucose transport. The model parameters and disturbances can be extended to observable state variables and be identified dynamically by Bayesian filtering estimators. Two basic Gaussian noise based Bayesian filtering estimators, extended Kalman filtering (EKF) and unscented Kalman filtering (UKF), are implemented. Recognizing the prevalence of non-Gaussian noise, in this study, two new filtering estimators: particle filtering with Gaussian noise (PFG), and particle filtering with mixed non-Gaussian noise (PFM) are designed and implemented. The proposed OGI model in conjunction with the estimators is evaluated using the data from 30 in-silico subjects and 10 human participants. For in-silico subjects, the OGI with PFM estimator has the ability to estimate PIC and PGC adaptively, achieving RMSE of PIC $ 9.49\pm3.81 $ mU/L, and PGC $ 0.89\pm0.19 $ mmol/L. For human, the OGI with PFM has the promise to identify disturbances ($ 95.46\%\pm0.65\% $ accurate rate of meal identification). OGI model provides a way to fully personalize the parameters and external disturbances in real time, and has potential clinical utility for artificial pancreas.</p></abstract>

scholarly journals The synchronization of coupled stochastic systems driven by symmetric α-stable process and Brownian motion

Filomat ◽  
2018 ◽  
Vol 32 (6) ◽  
pp. 2219-2245
Author(s):  
Shahad Al-Azzawi ◽  
Jicheng Liu ◽  
Xianming Liu
Keyword(s):  
Dynamical System ◽  
Mathematical Model ◽  
Brownian Motion ◽  
Gaussian Noise ◽  
Stochastic Systems ◽  
Stable Process ◽  
Symmetric Stable Process ◽  
And Brownian Motion ◽  
Coupled Dynamical System ◽  
Non Gaussian

The synchronization of stochastic differential equations (SDEs) driven by symmetric ?-stable process and Brownian Motion is investigated in pathwise sense. This coupled dynamical system is a new mathematical model, where one of the systems is driven by Gaussian noise, another one is driven by non- Gaussian noise. In this paper, we prove that the synchronization still persists for this coupled dynamical system. Examples and simulations are given.

scholarly journals Sequential parameter estimation for stochastic systems

2003 ◽  
Vol 10 (3) ◽  
pp. 253-259 ◽  
Author(s):  
G. A. Kivman
Keyword(s):  
Kalman Filtering ◽  
Ensemble Kalman Filter ◽  
Stochastic Systems ◽  
Lorenz System ◽  
Initial Conditions ◽  
Model Parameters ◽  
Forecast Errors ◽  
Importance Resampling ◽  
Non Gaussian

Abstract. The quality of the prediction of dynamical system evolution is determined by the accuracy to which initial conditions and forcing are known. Availability of future observations permits reducing the effects of errors in assessment the external model parameters by means of a filtering algorithm. Usually, uncertainties in specifying internal model parameters describing the inner system dynamics are neglected. Since they are characterized by strongly non-Gaussian distributions (parameters are positive, as a rule), traditional Kalman filtering schemes are badly suited to reducing the contribution of this type of uncertainties to the forecast errors. An extension of the Sequential Importance Resampling filter (SIR) is proposed to this aim. The filter is verified against the Ensemble Kalman filter (EnKF) in application to the stochastic Lorenz system. It is shown that the SIR is capable of estimating the system parameters and to predict the evolution of the system with a remarkably better accuracy than the EnKF. This highlights a severe drawback of any Kalman filtering scheme: due to utilizing only first two statistical moments in the analysis step it is unable to deal with probability density functions badly approximated by the normal distribution.

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