scholarly journals Adaptation of the mathematical apparatus of the Markov chain theory for the probabilistic analysis of recurrent estimation of image inter-frame geometric deformations

2019 ◽  
pp. 103-108
Author(s):  
G L Safina ◽  
A G Tashlinskii ◽  
M G Tsaryov
Keyword(s):  
Transition Probabilities ◽  
A Priori ◽  
Recurrent Algorithm ◽  
Image Deformation ◽  
Estimated Parameters ◽  
Markov Chain Theory ◽  
The Matrix ◽  
One Step ◽  
The One ◽  
Inter Frame

The paper is devoted to the analysis of the possibilities of using Markov chains for analyzing the accuracy of stochastic gradient relay estimation of image geometric deformations. One of the ways to reduce computational costs is to discretize the domain of studied parameters. This approach allows to choose the dimension of transition probabilities matrix a priori. However, such a matrix has a rather complicated structure. It does not significantly reduce the number of computations. A modification of the transition probabilities matrix is proposed, it’s dimension does not depend on the dimension of estimated parameters vector. In this case, the obtained relations determine a recurrent algorithm for calculating the matrix at the estimation iterations. For the one-step transitions matrix, the calculated expressions for the probabilities of image deformation parameters estimates drift are given.

WTLS-Bayes Filter-based Relative Pose Estimation for Space Non-cooperative Unknown Target Without a Priori Knowledge

2021 ◽  
Author(s):  
CHENGGUANG ZHU ◽  
zhongpai Gao ◽  
Jiankang Zhao ◽  
Haihui Long ◽  
Chuanqi Liu
Keyword(s):  
Pose Estimation ◽  
A Priori ◽  
Convergence Time ◽  
Estimation Accuracy ◽  
A Priori Knowledge ◽  
One Step ◽  
Relative Pose ◽  
The One ◽  
Negative Factors ◽  
Priori Knowledge

Abstract The relative pose estimation of a space noncooperative target is an attractive yet challenging task due to the complexity of the target background and illumination, and the lack of a priori knowledge. Unfortunately, these negative factors have a grave impact on the estimation accuracy and the robustness of filter algorithms. In response, this paper proposes a novel filter algorithm to estimate the relative pose to improve the robustness based on a stereovision system. First, to obtain a coarse relative pose, the weighted total least squares (WTLS) algorithm is adopted to estimate the relative pose based on several feature points. The resulting relative pose is fed into the subsequent filter scheme as observation quantities. Second, the classic Bayes filter is exploited to estimate the relative state except for moment-of-inertia ratios. Additionally, the one-step prediction results are used as feedback for WTLS initialization. The proposed algorithm successfully eliminates the dependency on continuous tracking of several fixed points. Finally, comparison experiments demonstrate that the proposed algorithm presents a better performance in terms of robustness and convergence time.

Perturbation theory for unbounded Markov reward processes with applications to queueing

1988 ◽  
Vol 20 (01) ◽  
pp. 99-111 ◽  
Author(s):  
Nico M. Van Dijk
Keyword(s):  
Transition Probabilities ◽  
Arrival Rate ◽  
Average Reward ◽  
Reward Function ◽  
One Step ◽  
Reward Process ◽  
Markov Reward ◽  
Step Transition ◽  
The One ◽  
Queueing Processes

Consider a perturbation in the one-step transition probabilities and rewards of a discrete-time Markov reward process with an unbounded one-step reward function. A perturbation estimate is derived for the finite horizon and average reward function. Results from [3] are hereby extended to the unbounded case. The analysis is illustrated for one- and two-dimensional queueing processes by an M/M/1-queue and an overflow queueing model with an error bound in the arrival rate.

scholarly journals Transient analysis of a queue with queue-length dependent MAP and its application to SS7 network

1999 ◽  
Vol 12 (4) ◽  
pp. 371-392
Author(s):  
Bong Dae Choi ◽  
Sung Ho Choi ◽  
Dan Keun Sung ◽  
Tae-Hee Lee ◽  
Kyu-Seog Song
Keyword(s):  
Congestion Control ◽  
Queue Length ◽  
Transient Analysis ◽  
Transition Probabilities ◽  
Transient Behavior ◽  
Complex Model ◽  
Arrival Process ◽  
One Step ◽  
Step Transition ◽  
The One

We analyze the transient behavior of a Markovian arrival queue with congestion control based on a double of thresholds, where the arrival process is a queue-length dependent Markovian arrival process. We consider Markov chain embedded at arrival epochs and derive the one-step transition probabilities. From these results, we obtain the mean delay and the loss probability of the nth arrival packet. Before we study this complex model, first we give a transient analysis of an MAP/M/1 queueing system without congestion control at arrival epochs. We apply our result to a signaling system No. 7 network with a congestion control based on thresholds.

The departure process from the GI/G/1 Queue

1969 ◽  
Vol 6 (3) ◽  
pp. 704-707 ◽  
Author(s):  
Thomas L. Vlach ◽  
Ralph L. Disney
Keyword(s):  
Markov Chain ◽  
Markov Process ◽  
Transition Probabilities ◽  
Two Dimensional ◽  
Departure Process ◽  
Dimensional State Space ◽  
Semi Markov Process ◽  
One Step ◽  
Step Transition ◽  
The One

The departure process from the GI/G/1 queue is shown to be a semi-Markov process imbedded at departure points with a two-dimensional state space. Transition probabilities for this process are defined and derived from the distributions of the arrival and service processes. The one step transition probabilities and a stationary distribution are obtained for the imbedded two-dimensional Markov chain.

Perturbation theory for unbounded Markov reward processes with applications to queueing

1988 ◽  
Vol 20 (1) ◽  
pp. 99-111 ◽  
Author(s):  
Nico M. Van Dijk
Keyword(s):  
Transition Probabilities ◽  
Arrival Rate ◽  
Average Reward ◽  
Reward Function ◽  
One Step ◽  
Reward Process ◽  
Markov Reward ◽  
Step Transition ◽  
The One ◽  
Queueing Processes

Consider a perturbation in the one-step transition probabilities and rewards of a discrete-time Markov reward process with an unbounded one-step reward function. A perturbation estimate is derived for the finite horizon and average reward function. Results from [3] are hereby extended to the unbounded case. The analysis is illustrated for one- and two-dimensional queueing processes by an M/M/1-queue and an overflow queueing model with an error bound in the arrival rate.

Parameter values of ARMA models minimising the one-step-ahead prediction error when the true system is not in the model set

1983 ◽  
Vol 20 (2) ◽  
pp. 405-408 ◽  
Author(s):  
Paul Kabaila
Keyword(s):  
Prediction Error ◽  
A Priori ◽  
Arma Model ◽  
Model Parameters ◽  
Arma Models ◽  
One Step ◽  
Model Set ◽  
The One ◽  
Parameter Values ◽  
True System

In This paper we answer the following question. Is there any a priori reason for supposing that there is no more than one set of ARMA model parameters minimising the one-step-ahead prediction error when the true system is not in the model set?

On a characterization property of finite irreducible Markov chains

1970 ◽  
Vol 7 (3) ◽  
pp. 771-775
Author(s):  
I. V. Basawa
Keyword(s):  
Transition Matrix ◽  
Transition Probabilities ◽  
Homogeneous Markov Chain ◽  
Finite State ◽  
One Step ◽  
Characterization Property ◽  
Step Transition ◽  
The One ◽  
Image Position ◽  
Finite State Space

Let {Xk}, k = 1, 2, ··· be a sequence of random variables forming a homogeneous Markov chain on a finite state-space, S = {1, 2, ···, s}. Xk could be thought of as the state at time k of some physical system for which are the (one-step) transition probabilities. It is assumed that all the states are inter-communicating, so that the transition matrix P = ((pij)) is irreducible.

Estimating Derivatives Via Poisson's Equation

1991 ◽  
Vol 5 (4) ◽  
pp. 415-428 ◽  
Author(s):  
Bennett L. Fox ◽  
Paul Glasserman
Keyword(s):  
Markov Chain ◽  
Conditional Expectation ◽  
Transition Probabilities ◽  
Ratio Method ◽  
Absorbing Set ◽  
Reward Function ◽  
Poisson Equations ◽  
One Step ◽  
The One ◽  
Likelihood Ratio Method

Let x(j) be the expected reward accumulated up to hitting an absorbing set in a Markov chain, starting from state j. Suppose the transition probabilities and the one-step reward function depend on a parameter, and denote by y(j) the derivative of x(j) with respect to that parameter. We estimate y(0) starting from the respective Poisson equations that x = [x(0),x(l),…] and y = [y(0),y(l),…] satisfy. Relative to a likelihood-ratio-method (LRM) estimator, our estimator generally has (much) smaller variance; in a certain sense, it is a conditional expectation of that estimator given x. Unlike LRM, however, we have to estimate certain components of x. Our method has broader scope than LRM: we can estimate sensitivity to opening arcs.

An indication of the asymptotic nature of the mendelian Markov process

1968 ◽  
Vol 5 (02) ◽  
pp. 350-356 ◽  
Author(s):  
R. G. Khazanie
Keyword(s):  
Markov Process ◽  
Transition Probabilities ◽  
Asymptotic Nature ◽  
Finite Markov Process ◽  
One Step ◽  
Step Transition ◽  
The One ◽  
Image Position

Consider a finite Markov process {Xn } described by the one-step transition probabilities In describing the transition probabilities in the above manner we are adopting the convention that (0)0 = 1 so that the states 0 and M are absorbing, and the states 1,2,···,M-1 are transient.

The departure process from the GI/G/1 Queue

1969 ◽  
Vol 6 (03) ◽  
pp. 704-707 ◽  
Author(s):  
Thomas L. Vlach ◽  
Ralph L. Disney
Keyword(s):  
Markov Chain ◽  
Markov Process ◽  
Transition Probabilities ◽  
Two Dimensional ◽  
Departure Process ◽  
Dimensional State Space ◽  
Semi Markov Process ◽  
One Step ◽  
Step Transition ◽  
The One

The departure process from the GI/G/1 queue is shown to be a semi-Markov process imbedded at departure points with a two-dimensional state space. Transition probabilities for this process are defined and derived from the distributions of the arrival and service processes. The one step transition probabilities and a stationary distribution are obtained for the imbedded two-dimensional Markov chain.

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