An online sequential algorithm for the estimation of transition probabilities forjump Markov linear systems

This paper describes a new method to estimate the transition probabilities associated with a jump Markov linear system. The new algorithm uses stochastic approximation type recursions to minimize the Kullback-Leibler divergence between the likelihood function of the transition probabilities and the true likelihood function. Since the calculation of the likelihood function of the transition probabilities is impossible, an incomplete data paradigm, which has been previously applied to a similar problem for hidden Markov models, is used. The algorithm differs from the existing algorithms in that it assumes that the transition probabilities are deterministic quantities whereas the existing approaches consider them to be random variables with prior distributions.


Maximum likelihood estimation of transition probabilities of jump Markov linear systems
Orguner, Umut (Institute of Electrical and Electronics Engineers (IEEE), 2008-10-01)
This paper describes an online maximum likelihood estimator for the transition probabilities associated with a jump Markov linear system (JMLS). The maximum likelihood estimator is derived using the reference probability method, which exploits an hypothetical probability measure to find recursions for complex expectations. Expectation maximization (EM) procedure is utilized for maximizing the likelihood function. In order to avoid the exponential increase in the number of statistics of the optimal EM algori...
Quantitative measure of observability for linear stochastic systems
Subasi, Yuksel; Demirekler, Mübeccel (Elsevier BV, 2014-06-01)
In this study we define a new observability measure for stochastic systems: the mutual information between the state sequence and the corresponding measurement sequence for a given time horizon. Although the definition is given for a general system representation, the paper focuses on the linear time invariant Gaussian case. Some basic analytical results are derived for this special case. The measure is extended to the observability of a subspace of the state space, specifically an individual state and/or t...
An Efficient Formula Synthesis Method with Past Signal Temporal Logic
Ergurtuna, Mert; Aydın Göl, Ebru (2019-01-01)
In this work, we propose a novel method to find temporal properties that lead to the unexpected behaviors from labeled dataset. We express these properties in past time Signal Temporal Logic (ptSTL). First, we present a novel approach for finding parameters of a template ptSTL formula, which extends the results on monotonicity based parameter synthesis. The proposed method optimizes a given monotone criteria while bounding an error. Then, we employ the parameter synthesis method in an iterative unguided for...
An improved method for inference of piecewise linear systems by detecting jumps using derivative estimation
Selcuk, A. M.; Öktem, Hüseyin Avni (Elsevier BV, 2009-08-01)
Inference of dynamical systems using piecewise linear models is a promising active research area. Most of the investigations in this field have been stimulated by the research in functional genomics. In this article we study the inference problem in piecewise linear systems. We propose first identifying the state transitions by detecting the jumps of the derivative estimates, then finding the guard conditions of the state transitions (thresholds) from the values of the state variables at the state transitio...
Efficient parallelization of the multilevel fast multipole algorithm for the solution of large-scale scattering problems
Ergül, Özgür Salih (Institute of Electrical and Electronics Engineers (IEEE), 2008-08-01)
We present fast and accurate solutions of large-scale scattering problems involving three-dimensional closed conductors with arbitrary shapes using the multilevel fast multipole algorithm (MLFMA). With an efficient parallelization of MLFMA, scattering problems that are discretized with tens of millions of unknowns are easily solved on a cluster of computers. We extensively investigate the parallelization of MLFMA, identify the bottlenecks, and provide remedial procedures to improve the efficiency of the imp...
Citation Formats
U. Orguner, “An online sequential algorithm for the estimation of transition probabilities forjump Markov linear systems,” AUTOMATICA, pp. 1735–1744, 2006, Accessed: 00, 2020. [Online]. Available: