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.

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.

Identification of Stochastic System and Controller via Projection Filters

1996 ◽  
Vol 118 (2) ◽  
pp. 169-176 ◽  
Author(s):  
Hyun Chang Lee ◽  
Min-Hung Hsiao ◽  
Jen-Kuang Huang ◽  
Chung-Wen Chen
Keyword(s):  
Kalman Filter ◽  
State Space ◽  
Stochastic System ◽  
State Space Model ◽  
Open Loop ◽  
The State ◽  
Loop System ◽  
Test Facility ◽  
System Response ◽  
Space Model

A method based on projection filters is presented for identifying an open-loop stochastic system with an existing feedback controller. The projection filters are derived from the relationship between the state-space model and the AutoRegressive with eXogeneous input (ARX) model including the system, Kalman filter and controller. Two ARX models are identified from the control input, closed-loop system response and feedback signal using least-squares method. Markov parameters of the open-loop system, Kalman filter and controller are then calculated from the coefficients of the identified ARX models. Finally, the state-space model of the open-loop stochastic system and the gain matrices for the Kalman filter and controller are realized. The method is validated by simulations and test data from an unstable large-angle magnetic suspension test facility.

Bayesian monthly index for building activity based on mixed frequencies: the case of Chile

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Byron J. Idrovo-Aguirre ◽  
Javier E. Contreras-Reyes
Keyword(s):  
Kalman Filter ◽  
Bayesian Inference ◽  
State Space ◽  
State Space Model ◽  
Natural Extension ◽  
The State ◽  
Likelihood Method ◽  
Content Type ◽  
Space Model ◽  
Construction Activity

PurposeThis paper combines the objective information of six mixed-frequency partial-activity indicators with assumptions or beliefs (called priors) regarding the distribution of the parameters that approximate the state of the construction activity cycle. Thus, this paper uses Bayesian inference with Gibbs simulations and the Kalman filter to estimate the parameters of the state-space model, used to design the Imacon.Design/methodology/approachUnlike other economic sectors of similar importance in aggregate gross domestic product, such as mining and industry, the construction sector lacked a short-term measure that helps to identify its most recent performance.FindingsIndeed, because these priors are susceptible to changes, they provide flexibility to the original Imacon model, allowing for the assessment of risk scenarios and adaption to the greater relative volatility that characterizes the sector's activity.Originality/valueThe classic maximum likelihood method of estimating the monthly construction activity index (Imacon) is rigid to the incorporation of new measures of uncertainty, expectations or different volatility (risks) levels in the state of construction activity. In this context, this paper uses Bayesian inference with 10,000 Gibbs simulations and the Kalman filter to estimate the parameters of the state-space model, used to design the Imacon, inspired by the original works of Mariano and Murasawa (2003) and Kim and Nelson (1998). Thus, this paper consists of a natural extension of the classic method used by Tejada (2006) in the estimation of the old Imacon.

scholarly journals A Kalman particle filter for online parameter estimation with applications to affine models

2021 ◽  
Author(s):  
Jian He ◽  
Asma Khedher ◽  
Peter Spreij
Keyword(s):  
Kalman Filter ◽  
Particle Filter ◽  
State Space ◽  
Outer Layer ◽  
Posterior Distribution ◽  
State Space Model ◽  
The State ◽  
State Variables ◽  
Unknown Parameters ◽  
Space Model

AbstractIn this paper we address the problem of estimating the posterior distribution of the static parameters of a continuous-time state space model with discrete-time observations by an algorithm that combines the Kalman filter and a particle filter. The proposed algorithm is semi-recursive and has a two layer structure, in which the outer layer provides the estimation of the posterior distribution of the unknown parameters and the inner layer provides the estimation of the posterior distribution of the state variables. This algorithm has a similar structure as the so-called recursive nested particle filter, but unlike the latter filter, in which both layers use a particle filter, our algorithm introduces a dynamic kernel to sample the parameter particles in the outer layer to obtain a higher convergence speed. Moreover, this algorithm also implements the Kalman filter in the inner layer to reduce the computational time. This algorithm can also be used to estimate the parameters that suddenly change value. We prove that, for a state space model with a certain structure, the estimated posterior distribution of the unknown parameters and the state variables converge to the actual distribution in $$L^p$$ L p with rate of order $${\mathcal {O}}(N^{-\frac{1}{2}}+\varDelta ^{\frac{1}{2}})$$ O ( N - 1 2 + Δ 1 2 ) , where N is the number of particles for the parameters in the outer layer and $$\varDelta $$ Δ is the maximum time step between two consecutive observations. We present numerical results of the implementation of this algorithm, in particularly we implement this algorithm for affine interest models, possibly with stochastic volatility, although the algorithm can be applied to a much broader class of models.

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
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