Maximum likelihood estimation of transition probabilities of jump Markov linear systems

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 algorithm, we make interacting multiple model (IMM)-type approximations. The resulting method needs the mode weights of an IMM filter with N(3) components, where N is the number of models in the JMLS. The algorithm can also supply base-state estimates and covariances as a by-product. The performance of the estimator is illustrated on two simulated examples and compared to a recently proposed alternative.


An online sequential algorithm for the estimation of transition probabilities forjump Markov linear systems
Orguner, Umut (Elsevier BV, 2006-10-01)
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 hi...
On higher order approximations for hermite-gaussian functions and discrete fractional Fourier transforms
Candan, Çağatay (Institute of Electrical and Electronics Engineers (IEEE), 2007-10-01)
Discrete equivalents of Hermite-Gaussian functions play a critical role in the definition of a discrete fractional Fourier transform. The discrete equivalents are typically calculated through the eigendecomposition of a commutator matrix. In this letter, we first characterize the space of DFT-commuting matrices and then construct matrices approximating the Hermite-Gaussian generating differential equation and use the matrices to accurately generate the discrete equivalents of Hermite-Gaussians.
Multipath Characteristics of Frequency Diverse Arrays Over a Ground Plane
Cetintepe, Cagri; Demir, Şimşek (Institute of Electrical and Electronics Engineers (IEEE), 2014-07-01)
This paper presents a theoretical framework for an analytical investigation of multipath characteristics of frequency diverse arrays (FDAs), a task which is attempted for the first time in the open literature. In particular, transmitted field expressions are formulated for an FDA over a perfectly conducting ground plane first in a general analytical form, and these expressions are later simplified under reasonable assumptions. Developed formulation is then applied to a uniform, linear, continuous-wave opera...
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...
Properly Handling Complex Differentiation in Optimization and Approximation Problems
Candan, Çağatay (Institute of Electrical and Electronics Engineers (IEEE), 2019-03-01)
Functions of complex variables arise frequently in the formulation of signal processing problems. The basic calculus rules on differentiation and integration for functions of complex variables resemble, but are not identical to, the rules of their real variable counterparts. On the contrary, the standard calculus rules on differentiation, integration, series expansion, and so on are the special cases of the complex analysis with the restriction of the complex variable to the real line. The goal of this lect...
Citation Formats
U. Orguner, “Maximum likelihood estimation of transition probabilities of jump Markov linear systems,” IEEE TRANSACTIONS ON SIGNAL PROCESSING, pp. 5093–5108, 2008, Accessed: 00, 2020. [Online]. Available: