An adaptive approach for estimation of transition probability matrix in the interacting multiple model filter

2021 ◽  
pp. 1-12
Author(s):  
Luciana Balieiro Cosme ◽  
Marcos Flávio Silveira Vasconcelos D’Angelo ◽  
Walmir Matos Caminhas ◽  
Murilo Osorio Camargos ◽  
Reinaldo Martínez Palhares
Keyword(s):  
Transition Probabilities ◽  
Transition Probability ◽  
Computational Cost ◽  
Transition Probability Matrix ◽  
World Health ◽  
Interacting Multiple Model ◽  
Multiple Model ◽  
Data Set ◽  
Retention Models ◽  
System States

The traditional Interacting Multiple Model (IMM) filters usually consider that the Transition Probability Matrix (TPM) is known, however, when the IMM is associated with time-varying or inaccurate transition probabilities the estimation of system states may not be predicted adequately. The main methodological contribution of this paper is an approach based on the IMM filter and retention models to determine the TPM adaptively and automatically with relatively low computational cost and no need for complex operations or storing the measurement history. The proposed method is compared to the traditional IMM filter, IMM with Bayesian Network (BNs) and a state-of-the-art Adaptive TPM-based parallel IMM (ATPM-PIMM) algorithm. The experiments were carried out in an artificial numerical example as well as in two real-world health monitoring applications: the PRONOSTIA platform and the Li-ion batteries data set provided by NASA. The Retention Interacting Multiple Model (R-IMM) results indicate that a better prediction performance can be obtained when the TPM is not properly adjusted or not precisely known.

scholarly journals Fuzzy-Logic-Based, Obstacle Information-Aided Multiple-Model Target Tracking

Information ◽  
2019 ◽  
Vol 10 (2) ◽  
pp. 48 ◽  
Author(s):  
Quanhui Wang ◽  
En Fan ◽  
Pengfei Li
Keyword(s):  
Fuzzy Logic ◽  
Target Tracking ◽  
Transition Probability ◽  
Target Position ◽  
Transition Probability Matrix ◽  
Interacting Multiple Model ◽  
Multiple Model ◽  
Convex Polygons ◽  
Maneuvering Target Tracking ◽  
Inference Systems

Incorporating obstacle information into maneuvering target-tracking algorithms may lead to a better performance when the target when the target maneuver is caused by avoiding collision with obstacles. In this paper, we propose a fuzzy-logic-based method incorporating new obstacle information into the interacting multiple-model (IMM) algorithm (FOIA-MM). We use convex polygons to describe the obstacles and then extract the distance from and the field angle of these obstacle convex polygons to the predicted target position as obstacle information. This information is fed to two fuzzy logic inference systems; one system outputs the model weights to their probabilities, the other yields the expected sojourn time of the models for the transition probability matrix assignment. Finally, simulation experiments and an Unmanned Aerial Vehicle experiment are carried out to demonstrate the efficiency and effectiveness of the proposed algorithm.

Further enhancement on H∞ sliding mode control design for singular Markovian jump systems with partly known transition probabilities

2021 ◽  
pp. 107754632198920
Author(s):  
Zeinab Fallah ◽  
Mahdi Baradarannia ◽  
Hamed Kharrati ◽  
Farzad Hashemzadeh
Keyword(s):  
Transition Probabilities ◽  
Sliding Mode ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Linear Matrix ◽  
Sliding Mode Controller ◽  
Sliding Surface ◽  
Markovian Jump ◽  
Markovian Jump System ◽  
Singular Markovian Jump Systems

This study considers the designing of the H ∞ sliding mode controller for a singular Markovian jump system described by discrete-time state-space realization. The system under investigation is subject to both matched and mismatched external disturbances, and the transition probability matrix of the underlying Markov chain is considered to be partly available. A new sufficient condition is developed in terms of linear matrix inequalities to determine the mode-dependent parameter of the proposed quasi-sliding surface such that the stochastic admissibility with a prescribed H ∞ performance of the sliding mode dynamics is guaranteed. Furthermore, the sliding mode controller is designed to assure that the state trajectories of the system will be driven onto the quasi-sliding surface and remain in there afterward. Finally, two numerical examples are given to illustrate the effectiveness of the proposed design algorithms.

scholarly journals Stochastic Stability for Time-Delay Markovian Jump Systems with Sector-Bounded Nonlinearities and More General Transition Probabilities

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Dan Ye ◽  
Quan-Yong Fan ◽  
Xin-Gang Zhao ◽  
Guang-Hong Yang
Keyword(s):  
Time Delay ◽  
Stochastic Stability ◽  
Transition Probabilities ◽  
Transition Probability ◽  
Sufficient Conditions ◽  
Transition Probability Matrix ◽  
Markovian Jump Systems ◽  
Markovian Jump ◽  
Delay Dependent ◽  
Jump Systems

This paper is concerned with delay-dependent stochastic stability for time-delay Markovian jump systems (MJSs) with sector-bounded nonlinearities and more general transition probabilities. Different from the previous results where the transition probability matrix is completely known, a more general transition probability matrix is considered which includes completely known elements, boundary known elements, and completely unknown ones. In order to get less conservative criterion, the state and transition probability information is used as much as possible to construct the Lyapunov-Krasovskii functional and deal with stability analysis. The delay-dependent sufficient conditions are derived in terms of linear matrix inequalities to guarantee the stability of systems. Finally, numerical examples are exploited to demonstrate the effectiveness of the proposed method.

Transition probabilities between synoptic weather types as a fingerprint for climate model evaluation

2021 ◽  
Author(s):  
Juan Antonio Fernandez-Granja ◽  
Ana Casanueva ◽  
Joaquín Bedia ◽  
Jesús Fernández
Keyword(s):  
Atmospheric Circulation ◽  
Large Scale ◽  
Transition Probabilities ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Weather Types ◽  
Observational Uncertainty ◽  
Leibler Divergence ◽  
Synoptic Conditions ◽  
Large Scale Atmospheric Circulation

<p>Global Climate Models (GCMs) generally exhibit significant biases in the representation of large-scale atmospheric circulation. Even after bias adjustment, these errors remain and are inherited to some extent by the derived downscaling products, impairing the credibility of future regional projections. </p><p>We perform a process-based evaluation of state-of-the-art GCMs from CMIP5 and CMIP6, with a focus on the simulation of the synoptic climatological patterns having a most prominent effect on the European climate. To this aim, we use the Lamb Weather Type Classification (LWT, Lamb, 1972). We undertake a comprehensive assessment based on several evaluation measures, such as Kullback-Leibler divergence (KL), Relative Bias and Transition Probability Matrix Score (TPMS), used to assess the ability of the GCMs in reproducing not only the frequencies of the different Lamb Weather Types (LWTs), but also the daily probabilities of transitions among them. We show that the novel TPMS score poses a stringent test on the GCM performance, allowing for a convenient model ranking based on each model’s transition probability matrix fingerprint. Deficiencies in the transition probabilities from one LWT to another might explain the misrepresentation of the synoptic conditions and their frequencies by the GCMs. Four different reanalysis products of varying characteristics are considered as pseudo-observational reference in order to assess observational uncertainty. </p><p>Our results unveil an overall improvement of salient atmospheric circulation features of CMIP6 with respect to CMIP5, demonstrating the ability of the new models to better capture key synoptic conditions. The improvement is consistent across observational references, although it is uneven across models and large frequency biases still remain for the dominant LWTs in many cases. In particular, some CMIP6 models attain similar or even worse results than their CMIP5 counterparts. In light of the large differences found across models, we advocate for a careful selection of driving GCMs in downscaling experiments with a special focus on large-scale atmospheric circulation aspects.</p><p> </p>

scholarly journals Stochastic LU factorizations, Darboux transformations and urn models

2018 ◽  
Vol 55 (3) ◽  
pp. 862-886 ◽  
Author(s):  
F. Alberto Grünbaum ◽  
Manuel D. de la Iglesia
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Free Parameter ◽  
Transition Probabilities ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Urn Models ◽  
Triangular Matrices ◽  
New Family ◽  
Step Transition

Abstract We consider upper‒lower (UL) (and lower‒upper (LU)) factorizations of the one-step transition probability matrix of a random walk with the state space of nonnegative integers, with the condition that both upper and lower triangular matrices in the factorization are also stochastic matrices. We provide conditions on the free parameter of the UL factorization in terms of certain continued fractions such that this stochastic factorization is possible. By inverting the order of the factors (also known as a Darboux transformation) we obtain a new family of random walks where it is possible to state the spectral measures in terms of a Geronimus transformation. We repeat this for the LU factorization but without a free parameter. Finally, we apply our results in two examples; the random walk with constant transition probabilities, and the random walk generated by the Jacobi orthogonal polynomials. In both situations we obtain urn models associated with all the random walks in question.

Some explicit results for correlated random walks

1989 ◽  
Vol 26 (4) ◽  
pp. 757-766 ◽  
Author(s):  
Ram Lal ◽  
U. Narayan Bhat
Keyword(s):  
Markov Chain ◽  
State Space ◽  
Equilibrium Distribution ◽  
Transition Probabilities ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Correlated Random Walks ◽  
Finite State ◽  
Direction Of Movement ◽  
Step Transition

In a correlated random walk (CRW) the probabilities of movement in the positive and negative direction are given by the transition probabilities of a Markov chain. The walk can be represented as a Markov chain if we use a bivariate state space, with the location of the particle and the direction of movement as the two variables. In this paper we derive explicit results for the following characteristics of the walk directly from its transition probability matrix: (i) n -step transition probabilities for the unrestricted CRW, (ii) equilibrium distribution for the CRW restricted on one side, and (iii) equilibrium distribution and first-passage characteristics for the CRW restricted on both sides (i.e., with finite state space).

The square root law in the embedding detection problem for Markov chains with unknown matrix of transition probabilities

2019 ◽  
Vol 29 (1) ◽  
pp. 59-68
Author(s):  
Artem V. Volgin
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Transition Probabilities ◽  
Transition Probability ◽  
Classical Model ◽  
Transition Probability Matrix ◽  
Square Root ◽  
Detection Problem ◽  
Asymptotic Growth

Abstract We consider the classical model of embeddings in a simple binary Markov chain with unknown transition probability matrix. We obtain conditions on the asymptotic growth of lengths of the original and embedded sequences sufficient for the consistency of the proposed statistical embedding detection test.

scholarly journals Computing reliability for closed-cycle cooling system in thermo-electric power plants by modelling to circular consecutive-2-out-of-n:F system

2018 ◽  
Vol 22 (Suppl. 1) ◽  
pp. 177-184
Author(s):  
Mehmet Gurcan ◽  
Gokhan Gokdere
Keyword(s):  
Power Plants ◽  
State Transition ◽  
Transition Probabilities ◽  
Cooling System ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
The State ◽  
Thermo Electric ◽  
Water Pumps ◽  
Electric Plant

The main motivation of this paper is to compute a reliability for a closed recurring water supply system with n water pumps in a thermo-electric plant by modelling to a repairable circular consecutive-2-out-of-n:F system. In a thermo-electric plant system, let us have n water pumps for pumping the water and steam expelled from a turbine to a cooling tower. These pumps are installed around the system and each pump must be powerful enough to pump water and steam to at least the next two consecutive pumps. If any two or more consecutive pumps in the system are failed, the system is failed. For this system, it is important to determine the reliability. First, we developed mathematical formulations for the state transition probabilities in the system by using the definition of generalized transition probability and the concept of critical component under the assumption that pumps have unequal failure rates. Then, using these formulations we derived the state transition probability matrix of the system. Finally, a special model is given to calculate the system reliability.

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