research-article

Models and Representations of Gaussian Reciprocal and Conditionally Markov Sequences

Authors:

X. Rong LiAuthors Info & Claims

ICVISP 2018: Proceedings of the 2nd International Conference on Vision, Image and Signal Processing

Article No.: 65, Pages 1 - 6

https://doi.org/10.1145/3271553.3271598

Published: 27 August 2018 Publication History

Abstract

Conditionally Markov (CM) sequences are powerful mathematical tools for modeling random phenomena. There are several classes of CM sequences one of which is the reciprocal sequence. Reciprocal sequences have been widely used in many areas including image processing, intelligent systems, and acausal systems. To use them in application, we need not only their applicable dynamic models, but also some general approaches to designing parameters of dynamic models. Dynamic models governing two important classes of nonsingular Gaussian (NG) CM sequences (called CML and CMF models), and a dynamic model governing the NG reciprocal sequence (called reciprocal CML model) were presented in our previous work. In this paper, these models are studied in more detail and general approaches are presented for their parameter design. It is shown that every reciprocal CML model can be induced by a Markov model and parameters of the reciprocal CML model can be obtained from those of the Markov model. Also, it is shown how NG CM sequences can be represented in terms of a NG Markov sequence and an independent NG vector. This representation provides a general approach for parameter design of CML and CMF models. In addition, it leads to a better understanding of CM sequences, including the reciprocal sequence.

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Cited By

Rezaie RLi X(2021)Destination-Directed Trajectory Modeling, Filtering, and Prediction Using Conditionally Markov SequencesIEEE Transactions on Aerospace and Electronic Systems10.1109/TAES.2020.303183657:2(820-833)Online publication date: Apr-2021
https://doi.org/10.1109/TAES.2020.3031836
Rezaie RLi X(2021)Gaussian conditionally Markov sequencesAutomatica (Journal of IFAC)10.1016/j.automatica.2021.109780131:COnline publication date: 1-Sep-2021
https://dl.acm.org/doi/10.1016/j.automatica.2021.109780
Rezaie RLi X(2020)Gaussian Conditionally Markov Sequences: Algebraically Equivalent Dynamic ModelsIEEE Transactions on Aerospace and Electronic Systems10.1109/TAES.2019.295118856:3(2390-2405)Online publication date: Jun-2020
https://doi.org/10.1109/TAES.2019.2951188
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Index Terms

Models and Representations of Gaussian Reciprocal and Conditionally Markov Sequences
1. Computing methodologies
  1. Artificial intelligence
    1. Computer vision
      1. Computer vision problems
        Tracking
2. Mathematics of computing
  1. Probability and statistics
    1. Probabilistic representations
      1. Markov networks
      2. Stochastic differential equations
    2. Stochastic processes
      1. Markov processes

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ICVISP 2018: Proceedings of the 2nd International Conference on Vision, Image and Signal Processing

August 2018

402 pages

ISBN:9781450365291

DOI:10.1145/3271553

Copyright © 2018 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

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Published: 27 August 2018

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ICVISP 2018: The 2nd International Conference on Vision, Image and Signal Processing

August 27 - 29, 2018

NV, Las Vegas, USA

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Cited By

Rezaie RLi X(2021)Destination-Directed Trajectory Modeling, Filtering, and Prediction Using Conditionally Markov SequencesIEEE Transactions on Aerospace and Electronic Systems10.1109/TAES.2020.303183657:2(820-833)Online publication date: Apr-2021
https://doi.org/10.1109/TAES.2020.3031836
Rezaie RLi X(2021)Gaussian conditionally Markov sequencesAutomatica (Journal of IFAC)10.1016/j.automatica.2021.109780131:COnline publication date: 1-Sep-2021
https://dl.acm.org/doi/10.1016/j.automatica.2021.109780
Rezaie RLi X(2020)Gaussian Conditionally Markov Sequences: Algebraically Equivalent Dynamic ModelsIEEE Transactions on Aerospace and Electronic Systems10.1109/TAES.2019.295118856:3(2390-2405)Online publication date: Jun-2020
https://doi.org/10.1109/TAES.2019.2951188
Rezaie RLi X(2018)Gaussian Reciprocal Sequences from the Viewpoint of Conditionally Markov SequencesProceedings of the 2nd International Conference on Vision, Image and Signal Processing10.1145/3271553.3271587(1-6)Online publication date: 27-Aug-2018
https://dl.acm.org/doi/10.1145/3271553.3271587
Rezaie RLi X(2018)Trajectory Modeling and Prediction with Waypoint Information Using a Conditionally Markov Sequence2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton)10.1109/ALLERTON.2018.8635996(486-493)Online publication date: Oct-2018
https://doi.org/10.1109/ALLERTON.2018.8635996

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