scholarly journals Particle Filtering: A Priori Estimation of Observational Errors of a State-Space Model with Linear Observation Equation

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1445
Author(s):  
Rodi Lykou ◽  
George Tsaklidis
Keyword(s):  
State Space ◽  
Particle Filtering ◽  
A Priori ◽  
State Space Model ◽  
Computational Cost ◽  
The State ◽  
Observation Equation ◽  
Basic Algorithm ◽  
Space Model ◽  
Observational Errors

Observational errors of Particle Filtering are studied over the case of a state-space model with a linear observation equation. In this study, the observational errors are estimated prior to the upcoming observations. This action is added to the basic algorithm of the filter as a new step for the acquisition of the state estimations. This intervention is useful in the presence of missing data problems mainly, as well as sample tracking for impoverishment issues. It applies theory of Homogeneous and Non-Homogeneous closed Markov Systems to the study of particle distribution over the state domain and, thus, lays the foundations for the employment of stochastic control against impoverishment. A simulating example is quoted to demonstrate the effectiveness of the proposed method in comparison with existing ones, showing that the proposed method is able to combine satisfactory precision of results with a low computational cost and provide an example to achieve impoverishment prediction and tracking.

InSAR Adaptive Extended Kalman Filter Phase Unwrapping Algorithm

2013 ◽  
Vol 798-799 ◽  
pp. 493-496
Author(s):  
Hua Dong Hao ◽  
Ting Yi Bai ◽  
Guo Lin Liu
Keyword(s):  
Kalman Filter ◽  
State Space ◽  
Extended Kalman Filter ◽  
State Space Model ◽  
Model Error ◽  
Phase Unwrapping ◽  
The State ◽  
Observation Equation ◽  
Space Model ◽  
The One

Phase Unwrapping (PU) is the key step in the image processing for Interferometric Synthetic Aperture Radar (InSAR). In the Extended Kalman Filter (EKF) model of PU, due to the state space model is not taken into account the terrain factors, it is often resulted in unwrapping error delivery as the pixel to the next when the state changes rapidly in steep terrain. The observation equation is nonlinear and usually applied in PU through linear processing, requiring the system model and noise statistics known. But in fact the mathematical model or statistical noise is completely or partially unknown; the results have been inevitably lead to the declining of valuation accuracy and filter divergence. If directly applied in phase unwrapping, it is made impossible to retrieve surface deformation. In order to solve this problem and fully consider the terrain effect and model error, an adaptive EKF PU algorithm (AEKFPU) for InSAR is presented. On the one hand, it is achieved local adaptive estimation of image fringe frequency through 2D FFT and Chirp-Z Transform (CZT) joint method, by considering the impact of terrain factors on unwrapping results; On the one hand, the fading factor is calculated by innovation covariance and adaptively adjusted with the error covariance so as to suppress the memory length of the filter, compensating the effect of incomplete information on unwrapping. The experimental results are proved the proposed method is effective, it can be dealt with phase unwrapping and filtering simultaneously, and can be adaptively considered terrain factors in state space model and compensated for model error in observation equation model, ultimately improving the accuracy of phase unwrapping.

Modeling of CCLP in koryo extract production

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ji Chol ◽  
Ri Jun Il
Keyword(s):  
Process Control ◽  
Medical Care ◽  
State Space ◽  
State Space Model ◽  
The State ◽  
Space Model ◽  
Effective Components ◽  
Counter Current

Abstract The modeling of counter-current leaching plant (CCLP) in Koryo Extract Production is presented in this paper. Koryo medicine is a natural physic to be used for a diet and the medical care. The counter-current leaching method is mainly used for producing Koryo medicine. The purpose of the modeling in the previous works is to indicate the concentration distributions, and not to describe the model for the process control. In literature, there are no nearly the papers for modeling CCLP and especially not the presence of papers that have described the issue for extracting the effective components from the Koryo medicinal materials. First, this paper presents that CCLP can be shown like the equivalent process consisting of two tanks, where there is a shaking apparatus, respectively. It allows leachate to flow between two tanks. Then, this paper presents the principle model for CCLP and the state space model on based it. The accuracy of the model has been verified from experiments made at CCLP in the Koryo Extract Production at the Gang Gyi Koryo Manufacture Factory.

Outlier detection in the state space model

1994 ◽  
Vol 20 (2) ◽  
pp. 143-148 ◽  
Author(s):  
Siddhartha Chib ◽  
Ram C. Tiwari
Keyword(s):  
State Space ◽  
Outlier Detection ◽  
State Space Model ◽  
The State ◽  
Space Model

Establishment of State Variable Model of Aeroengine with Improved Least Square Fitting

2010 ◽  
Vol 40-41 ◽  
pp. 27-33 ◽  
Author(s):  
Yi Hui Lin ◽  
Hai Bo Zhang
Keyword(s):  
Differential Equations ◽  
State Space ◽  
State Space Model ◽  
Model Fitting ◽  
The State ◽  
Least Square ◽  
Variable Model ◽  
Space Model ◽  
Fitting Method ◽  
Linear Differential

The method of state space model fitting is carried out by using the linear relation of the variable of the differential equations and separating the steady process and instant process to eliminate the steady errors course by instant errors. The improved fitting method is without solving the linear differential equations or using any iterative methods. The coefficient of the state space model can be solve simply using matrix operation under the premise of high accuracy, so it has a higher computational efficiency than former least square method. And this method can also be used with other fitting method. Finally, to illustrate the validity and accuracy of the improved method, a small perturbation state space model of a certain turboshaft engine model has been established by this method, and the simulation result between state space model and nonlinear model was also compared. Also, the state space model could be applied to fault diagnosis and control system design for aeroengines.

scholarly journals A Stochastic and State Space Model for Tumour Growth and Applications

2009 ◽  
Vol 10 (2) ◽  
pp. 117-138 ◽  
Author(s):  
Wai-Yuan Tan ◽  
Weiming Ke ◽  
G. Webb
Keyword(s):  
State Space ◽  
Stochastic System ◽  
Tumour Growth ◽  
Deterministic Model ◽  
State Space Model ◽  
Tumour Cells ◽  
The State ◽  
System Model ◽  
State Variables ◽  
Space Model

We develop a state space model documenting Gompertz behaviour of tumour growth. The state space model consists of two sub-models: a stochastic system model that is an extension of the deterministic model proposed by Gyllenberg and Webb (1991), and an observation model that is a statistical model based on data for the total number of tumour cells over time. In the stochastic system model we derive through stochastic equations the probability distributions of the numbers of different types of tumour cells. Combining with the statistic model, we use these distribution results to develop a generalized Bayesian method and a Gibbs sampling procedure to estimate the unknown parameters and to predict the state variables (number of tumour cells). We apply these models and methods to real data and to computer simulated data to illustrate the usefulness of the models, the methods, and the procedures.

scholarly journals A review of Bayesian state-space modelling of capture–recapture–recovery data

2012 ◽  
Vol 2 (2) ◽  
pp. 190-204 ◽  
Author(s):  
Ruth King
Keyword(s):  
State Space ◽  
State Space Model ◽  
Model Fitting ◽  
The State ◽  
State Space Models ◽  
Observation Error ◽  
Space Model ◽  
System Process ◽  
Observation Process ◽  
Capture Recapture

Traditionally, state-space models are fitted to data where there is uncertainty in the observation or measurement of the system. State-space models are partitioned into an underlying system process describing the transitions of the true states of the system over time and the observation process linking the observations of the system to the true states. Open population capture–recapture–recovery data can be modelled in this framework by regarding the system process as the state of each individual observed within the study in terms of being alive or dead, and the observation process the recapture and/or recovery process. The traditional observation error of a state-space model is incorporated via the recapture/recovery probabilities being less than unity. The models can be fitted using a Bayesian data augmentation approach and in standard BUGS packages. Applying this state-space framework to such data permits additional complexities including individual heterogeneity to be fitted to the data at very little additional programming effort. We consider the efficiency of the state-space model fitting approach by considering a random effects model for capture–recapture data relating to dippers and compare different Bayesian model-fitting algorithms within WinBUGS.

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