scholarly journals A Stochastic Covariance Shrinkage Approach to Particle Rejuvenation in the Ensemble Transform Particle Filter

2021 ◽  
Author(s):  
Andrey A. Popov ◽  
Amit N. Subrahmanya ◽  
Adrian Sandu
Keyword(s):  
Particle Filter ◽  
State Space ◽  
Importance Sampling ◽  
Numerical Experiments ◽  
High Probability ◽  
Prior Information ◽  
The State ◽  
Transport Particle ◽  
Ensemble Transform ◽  
Number Of Particles

Abstract. Rejuvenation in particle filters is necessary to prevent the collapse of the weights when the number of particles is insufficient to sample the high probability regions of the state space. Rejuvenation is often implemented in a heuristic manner by the addition of stochastic samples that widen the support of the ensemble. This work aims at improving canonical rejuvenation methodology by the introduction of additional prior information obtained from climatological samples; the dynamical particles used for importance sampling are augmented with samples obtained from stochastic covariance shrinkage. The ensemble transport particle filter, and its second order variant, are extended with the proposed rejuvenation approach. Numerical experiments show that modified filters significantly improve the analyses for low dynamical ensemble sizes.

scholarly journals Accelerating Stratified Sampling SGD by Reconstructing Strata

2020 ◽  
Author(s):  
Weijie Liu ◽  
Hui Qian ◽  
Chao Zhang ◽  
Zebang Shen ◽  
Jiahao Xie ◽  
...  
Keyword(s):  
Theoretical Analysis ◽  
Convergence Rate ◽  
Numerical Experiments ◽  
High Probability ◽  
State Of The Art ◽  
Sampling Strategy ◽  
The State ◽  
Stratified Sampling

In this paper, a novel stratified sampling strategy is designed to accelerate the mini-batch SGD. We derive a new iteration-dependent surrogate which bound the stochastic variance from above. To keep the strata minimizing this surrogate with high probability, a stochastic stratifying algorithm is adopted in an adaptive manner, that is, in each iteration, strata are reconstructed only if an easily verifiable condition is met. Based on this novel sampling strategy, we propose an accelerated mini-batch SGD algorithm named SGD-RS. Our theoretical analysis shows that the convergence rate of SGD-RS is superior to the state-of-the-art. Numerical experiments corroborate our theory and demonstrate that SGD-RS achieves at least 3.48-times speed-ups compared to vanilla minibatch SGD.

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.

Particle Filter with Constraints for Articulated Upper Body Tracking

2010 ◽  
Vol 439-440 ◽  
pp. 971-976
Author(s):  
Qiong Liu ◽  
Guang Zheng Peng
Keyword(s):  
Particle Filter ◽  
Likelihood Function ◽  
Depth Map ◽  
The State ◽  
Upper Body ◽  
Body Model ◽  
Body Tracking ◽  
Human Pose ◽  
Human Body Tracking ◽  
Number Of Particles

For sophisticated background, a human body tracking algorithm using particle filter based on a 3D articulated body model is introduced. First, a high-fidelity biomechanical upper body model, which is accurate for representing varies complicated human poses and simple to be developed, has been built. Then sequences of images are obtained by using a stereo camera. After calibration, verification and background subtraction, depth map, foreground silhouette, arms skeleton are chosen to construct the likelihood function. The state vectors describing the human pose are computed by fitting the articulated body model to observed person using particle filter. In order to reduce the computational complexity and the number of particles, constraints are employed to restrict the state parameters. Experimental results show that the proposed algorithm can track human upper body with different poses, different person under different illumination conditions fast and accurately.

PHM of Leadfree Interconnects Using Resistance Spectroscopy Based Particle Filter Models for Shock and Vibration Environments

2011 ◽  
Author(s):  
Pradeep Lall ◽  
Ryan Lowe ◽  
Kai Goebel
Keyword(s):  
Particle Filter ◽  
State Space ◽  
Feature Vector ◽  
Health Management ◽  
Residual Life ◽  
The State ◽  
Remaining Useful Life ◽  
Damage Initiation ◽  
State Variable ◽  
Useful Life

Electronic assemblies have been monitored using state-space vectors from resistance spectroscopy, phase-sensitive detection and particle filtering (PF) to quantify damage initiation, progression and remaining useful life of the electronic assembly. A prognostication health management (PHM) methodology has been presented for electronic components subjected to mechanical shock and vibration. The presented methodology is an advancement of the state-of-art, which presently focuses on reactive failure detection and provides limited or no insight into the system reliability and residual life. Previously damage initiation, damage progression, and residual life in the pre-failure space has been correlated with micro-structural damage based proxies, feature vectors based on time, spectral and joint time-frequency characteristics of electronics [Lall2004a-d, 2005a-b, 2006a-f, 2007a-e, 2008a-f]. Precise resistance measurements based on the resistance spectroscopy method have been used to monitor interconnects for damage and prognosticate failure [Lall 2009a,b, 2010a,b, Constable 1992, 2001]. In this paper, the effectiveness of the proposed particle filter and resistance spectroscopy based approach in a prognostic health management (PHM) framework has been demonstrated for electronics. The measured state variable has been related to the underlying damage state using non-linear finite element analysis. The particle filter has been used to estimate the state variable, rate of change of the state variable, acceleration of the state variable and construct a feature vector. The estimated state-space parameters have been used to extrapolate the feature vector into the future and predict the time-to-failure at which the feature vector will cross the failure threshold. Remaining useful life has been calculated based on the evolution of the state space feature vector. Standard prognostic health management metrics were used to quantify the performance of the algorithm against the actual remaining useful life. Application to part replacement decisions for ultra-high reliability system has been demonstrated. Using the technique described in the paper the appropriate time to reorder a replacement part could be monitored, and defended statistically. Robustness of the prognostication algorithm has been quantified using standard performance evaluation metrics.

scholarly journals Open Markov Chains: Cumulant Dynamics, Fluctuations and Correlations

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 256
Author(s):  
Raúl Salgado-García
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
State Space ◽  
Generating Function ◽  
Moment Generating Function ◽  
The State ◽  
Interacting Particles ◽  
The Moment ◽  
Dependent Correlation ◽  
Number Of Particles

In this work we propose a model for open Markov chains that can be interpreted as a system of non-interacting particles evolving according to the rules of a Markov chain. The number of particles in the system is not constant, because we allow the particles to arrive or leave the state space according to prescribed protocols. We describe this system by looking at the population of particles on every state by establishing the rules of time-evolution of the distribution of particles. We show that it is possible to describe the distribution of particles over the state space through the corresponding moment generating function. This description is given through the dynamics ruling the behavior of such a moment generating function and we prove that the system is able to attain the stationarity under some conditions. We also show that it is possible to describe the dynamics of the two first cumulants of the distribution of particles, which in some way is a simpler technique to obtain useful information of the open Markov chain for practical purposes. Finally we also study the behavior of the time-dependent correlation functions of the number of particles present in the system. We give some simple examples of open chains that either, can be fully described through the moment generating function or partially described through the exact solution of the cumulant dynamics.

First passage time for the state of exact chemical equilibrium

1980 ◽  
Vol 45 (3) ◽  
pp. 777-782 ◽  
Author(s):  
Milan Šolc
Keyword(s):  
Chemical Equilibrium ◽  
First Passage Time ◽  
Passage Time ◽  
The State ◽  
Recurrence Time ◽  
First Passage ◽  
First Order ◽  
The Mean ◽  
Passage Times ◽  
Number Of Particles

The establishment of chemical equilibrium in a system with a reversible first order reaction is characterized in terms of the distribution of first passage times for the state of exact chemical equilibrium. The mean first passage time of this state is a linear function of the logarithm of the total number of particles in the system. The equilibrium fluctuations of composition in the system are characterized by the distribution of the recurrence times for the state of exact chemical equilibrium. The mean recurrence time is inversely proportional to the square root of the total number of particles in the system.

scholarly journals Unscented Particle Filter Algorithm Based on Divide-and-Conquer Sampling for Target Tracking

Sensors ◽  
2021 ◽  
Vol 21 (6) ◽  
pp. 2236
Author(s):  
Sichun Du ◽  
Qing Deng
Keyword(s):  
Particle Filter ◽  
State Space ◽  
Adaptive Filtering ◽  
Divide And Conquer ◽  
Particle Swarm Algorithm ◽  
Tracking Accuracy ◽  
Filtering Algorithm ◽  
Maneuvering Target ◽  
Unscented Particle Filter ◽  
Particle Filter Algorithm

Unscented particle filter (UPF) struggles to completely cover the target state space when handling the maneuvering target tracing problem, and the tracking performance can be affected by the low sample diversity and algorithm redundancy. In order to solve this problem, the method of divide-and-conquer sampling is applied to the UPF tracking algorithm. By decomposing the state space, the descending dimension processing of the target maneuver is realized. When dealing with the maneuvering target, particles are sampled separately in each subspace, which directly prevents particles from degeneracy. Experiments and a comparative analysis were carried out to comprehensively analyze the performance of the divide-and-conquer sampling unscented particle filter (DCS-UPF). The simulation result demonstrates that the proposed algorithm can improve the diversity of particles and obtain higher tracking accuracy in less time than the particle swarm algorithm and intelligent adaptive filtering algorithm. This algorithm can be used in complex maneuvering conditions.

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.

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