recursive maximum likelihood identification of jump markov nonlinear systems we present an online method for joint state and parameter estimation in jump markov non linear systems jmnls state inference is enabled via the use of particle filters which makes the method applicable to a wide range of non linear models to exploit the inherent structure of jmnls we design a rao blackwellized particle filter rbpf where the discrete mode is marginalized out analytically this results in an efficient implementation of the algorithm and reduces the estimation error variance the proposed rbpf is then used to compute recursively in time smoothed estimates of complete data sufficient statistics together with the online expectation maximization algorithm this enables recursive identification of unknown model parameters including the transition probability matrix the method is also applicable to online identification of jump markov linear systems jmls the performance of the method is illustrated in simulations and on a localization problem in wireless networks using real data

analysis of the annular ring loaded circular disk microstrip antenna a rigorous analysis of the natural resonance frequencies and input impedance characteristics of an annular ring loaded arl circular disk microstrip antenna is presented using vector hankel transforms the problem is formulated in terms of vector dual integral equations galerkin s method is then used to solve the equations to obtain the resonance frequencies and the current distribution on the conductive patches arising from a probe excitation due to the singular nature of the current distribution the singularity subtraction method has been used to accelerate the convergence of basis function expansions experiments for determining resonance frequencies and input impedance characteristics of an arl circular disk microstrip antenna with various substrate thicknesses have been made the theoretical results are in good agreement with the experimental data even when the thickness of the substrate is 0 1 substrate wavelength it is shown that this theory can be used to analyze some microstrip antennas with an electrically thick substrate including the analysis of mutual coupling between conductive patches or between the path and the feed of a microstrip antenna

input impedance of a probe fed stacked circular microstrip antenna the input impedance of a microstrip antenna consisting of two circular microstrip disks in a stacked configuration driven by a coaxial probe is investigated a rigorous analysis is performed using a dyadic green s function formulation whereby the mixed boundary value problem is reduced to a set of coupled vector integral equations using the vector hankel transform galerkin s method is used in the spectral domain using two sets of disk current expansions one set is based on the complete set of orthogonal modes of the magnetic cavity and the other uses chebyshev polynomials with the proper edge condition for the disk currents an additional term is added to the disk current expansion to model the current properly in the vicinity of the probe disk junction the input impedance of the antenna including the probe self impedance is calculated as a function of the layered parameters and the ratio of the two disk radii disk current distributions and radiation patterns are presented the calculated results are shown to be in good agreement with experimental data

the interacting multiple model algorithm for systems with markovian switching coefficients an important problem in filtering for linear systems with markovian switching coefficients dynamic multiple model systems is the management of hypotheses which is necessary to limit the computational requirements a novel approach to hypotheses merging is presented for this problem the novelty lies in the timing of hypotheses merging when applied to the problem of filtering for a linear system with markovian coefficients the method is an elegant way to derive the interacting multiple model imm algorithm evaluation of the imm algorithm shows that it performs well at a relatively low computational load these results imply a significant change in the state of the art of approximate bayesian filtering for systems with markovian coefficients

multiple model estimation with variable structure existing multiple model mm estimation algorithms have a fixed structure i e they use a fixed set of models an important fact that has been overlooked for a long time is how the performance of these algorithms depends on the set of models used limitations of the fixed structure algorithms are addressed first in particular it is shown theoretically that the use of too many models is performance wise as bad as that of too few models apart from the increase in computation this paper then presents theoretical results pertaining to the two ways of overcoming these limitations select construct a better set of models and or use a variable set of models this is in contrast to the existing efforts of developing better implementable fixed structure estimators both the optimal mm estimator and practical suboptimal algorithms with variable structure are presented a graph theoretic formulation of multiple model estimation is also given which leads to a systematic treatment of model set adaptation and opens up new avenues for the study and design of the mm estimation algorithms the new approach is illustrated in an example of a nonstationary noise identification problem

particle filters for state estimation of jump markov linear systems jump markov linear systems jmls are linear systems whose parameters evolve with time according to a finite state markov chain in this paper our aim is to recursively compute optimal state estimates for this class of systems we present efficient simulation based algorithms called particle filters to solve the optimal filtering problem as well as the optimal fixed lag smoothing problem our algorithms combine sequential importance sampling a selection scheme and markov chain monte carlo methods they use several variance reduction methods to make the most of the statistical structure of jmls computer simulations are carried out to evaluate the performance of the proposed algorithms the problems of on line deconvolution of impulsive processes and of tracking a maneuvering target are considered it is shown that our algorithms outperform the current methods

vector hankel transform analysis of annular ring microstrip antenna a rigorous analysis of the resonant frequency characteristics of an annular ring conductor printed on a dielectric substrate backed by a ground plane is presented the problem is cast into a set of vector dual integral equations by using vector hankel transform vht galerkin s method is then applied to compute the resonant frequencies of both transverse magnetic modes tm 11 and tm 12 of the microstrip antenna the real part of the resonant frequency shift of the tm 11 mode increases with increasing dielectric thickness in contrast to the tm 12 mode while the tm 11 mode has a high q it is a poor radiating mode the tm 12 mode is more suitable for antenna applications for a probe excitation the input impedance is obtained using single mode approximation for both the tm 11 and tm 12 modes it is shown that the tm 12 mode of the annular ring has a greater bandwidth than the tm 11 mode

an online sequential algorithm for the estimation of transition probabilities for jump 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

brief paper risk sensitive filtering for jump markov linear systems in this paper a risk sensitive multiple model filtering algorithm is derived using the reference probability methods first the approximation of the interacting multiple model imm algorithm is identified in the reference probability domain then the same type of approximation is used to derive the finite dimensional risk sensitive filtering algorithm the derived algorithm reduces to the imm filter when the risk sensitive parameter goes to zero and reduces to the risk sensitive filter for linear gauss markov systems when the number of models is unity the algorithm performs better in a simulated uncertain parameter scenario than the imm filter

variational learning for switching state space models we introduce a new statistical model for time series that iteratively segments data into regimes with approximately linear dynamics and learns the parameters of each of these linear regimes this model combines and generalizes two of the most widely used stochastic time series models hidden markov models and linear dynamical systems and is closely related to models that are widely used in the control and econometrics literatures it can also be derived by extending the mixture of experts neural network jacobs jordan nowlan hinton 1991 to its fully dynamical version in which both expert and gating networks are recurrent inferring the posterior probabilities of the hidden states of this model is computationally intractable and therefore the exact expectation maximization em algorithm cannot be applied however we present a variational approximation that maximizes a lower bound on the log likelihood and makes use of both the forward and backward recursions for hidden markov models and the kalman filter recursions for linear dynamical systems we tested the algorithm on artificial data sets and a natural data set of respiration force from a patient with sleep apnea the results suggest that variational approximations are a viable method for inference and learning in switching state space models

an improvement to the interacting multiple model imm algorithm computing the optimal conditional mean state estimate for a jump markov linear system requires exponential complexity and hence practical filtering algorithms are necessarily suboptimal in the target tracking literature suboptimal multiple model filtering algorithms such as the interacting multiple model imm method and generalized pseudo bayesian gpb schemes are widely used for state estimation of such systems we derive a reweighted interacting multiple model algorithm although the imm algorithm is an approximation of the conditional mean state estimator our algorithm is a recursive implementation of a maximum a posteriori map state sequence estimator this map estimator is an instance of a previous version of the em algorithm known as the alternating expectation conditional maximization aecm algorithm computer simulations indicate that the proposed reweighted imm algorithm is a competitive alternative to the popular imm algorithm and gpb methods

decomposition of electromagnetic boundary conditions at planar interfaces with applications to te and tm field solutions electromagnetic fields in homogeneous source free regions can be decomposed into fields that are te and tm with respect to a particular reference direction e g the z direction if transverse sources exist both te and tm fields may be excited simultaneously this paper considers the case of two infinite regions having a common planar interface and prescribed sources surface currents on the interface the source currents are decomposed in a manner consistent with the decomposition of the fields accordingly a procedure is established for describing the boundary conditions at the interface in terms of the longitudinal field components e sub z h sub z and the surface currents j sub s the development is unique in that the continuity of the transverse field components at the boundary are not explicitly considered but interpreted in terms of z directed fields this boundary condition approach is shown to give results consistent with those obtained by matching the tangential fields at the interface using vector transforms a simple example illustrating the procedure using a ring of current in free space is presented

the use of vector transforms in solving some electromagnetic scattering problems it is shown that there exists a class of vector transforms and vector series expansions that are independent of their scalar counterparts they can be used to simplify the solutions of a class of vector electromagnetic scattering problems the applications are shown of vector fourier hankel and mathieu transforms and series expansions to the formal solutions of scattering by rectangular circular and elliptical disks and open ended waveguides the problems solved are canonical problems however more complex problems for applications in microwaves microstrip integrated circuits geophysical probing etc can be solved in a similar fashion

frequency domain criteria for l sup p robust stability of continuous linear systems necessary and sufficient criteria in the frequency domain for robust stability are given under the assumption that coefficients of a characteristic polynomial belong to a transformed l sup p ball three cases are considered in detail p infinity interval uncertainty p 2 ellipsoidal uncertainty and p 1 octahedral uncertainty it is shown that frequency domain stability criteria are efficient when one deals with robust stability problems the frequency domain approach considered can be extended to various problems of robust stability

optimal simultaneous detection and estimation of filtered discrete semi markov chains an optimal algorithm for the detection of noisy filtered discrete semi markov chains is presented estimation of the underlying model parameters is also considered for a given path of the discrete semi markov chain the optimum estimates of the model parameters obtained by the maximum likelihood method are expressed as functions of the path these functions are then used to derive a single maximum a posteriori criterion for the optimal detection of the unknown single path the final optimization is carried out numerically by a combination of gradient divide and conquer and search techniques this set of techniques is referred to as the integer most likely search detector experimental results using synthetic data demonstrate the potential of the algorithm

bayesian nonparametric inference of switching dynamic linear models many complex dynamical phenomena can be effectively modeled by a system that switches among a set of conditionally linear dynamical modes we consider two such models the switching linear dynamical system slds and the switching vector autoregressive var process our bayesian nonparametric approach utilizes a hierarchical dirichlet process prior to learn an unknown number of persistent smooth dynamical modes we additionally employ automatic relevance determination to infer a sparse set of dynamic dependencies allowing us to learn slds with varying state dimension or switching var processes with varying autoregressive order we develop a sampling algorithm that combines a truncated approximation to the dirichlet process with efficient joint sampling of the mode and state sequences the utility and flexibility of our model are demonstrated on synthetic data sequences of dancing honey bees the ibovespa stock index and a maneuvering target tracking application

interacting multiview tracker a robust algorithm is proposed for tracking a target object in dynamic conditions including motion blurs illumination changes pose variations and occlusions to cope with these challenging factors multiple trackers based on different feature representations are integrated within a probabilistic framework each view of the proposed multiview multi channel feature learning algorithm is concerned with one particular feature representation of a target object from which a tracker is developed with different levels of reliability with the multiple trackers the proposed algorithm exploits tracker interaction and selection for robust tracking performance in the tracker interaction a transition probability matrix is used to estimate dependencies between trackers multiple trackers communicate with each other by sharing information of sample distributions the tracker selection process determines the most reliable tracker with the highest probability to account for object appearance changes the transition probability matrix and tracker probability are updated in a recursive bayesian framework by reflecting the tracker reliability measured by a robust tracker likelihood function that learns to account for both transient and stable appearance changes experimental results on benchmark datasets demonstrate that the proposed interacting multiview algorithm performs robustly and favorably against state of the art methods in terms of several quantitative metrics

analysis of single gaussian approximation of gaussian mixtures in bayesian filtering applied to mixed multiple model estimation this paper examines the effect of the moment matched single gaussian approximation which is made in various multiple model filtering applications to approximate a gaussian mixture on the bayesian filter performance the estimation error caused by the approximation is analysed for both the prediction and the measurement updates of a bayesian filter an approximate formula is found for the covariance of the error caused by the approximation for a general gaussian mixture with arbitrary components the calculated error covariance is used for obtaining a mixed multiple model estimation algorithm which has a performance near that of gpb2 with less computations

analysis of a circular microstrip disk antenna with a thick dielectric substrate the problem of a circular microstrip disk excited by a probe is solved using rigorous analysis the disk is assumed to have zero thickness and the current on the probe is taken to be uniform using vector hankel transforms the problem is formulated in terms of vector dual integral equations from which the unknown current can be solved for due to the singular nature of the current distribution arising from probe excitation the direct application of galerkin s basis function expansion method gives a slowly convergent result therefore the singular part of the current is removed since the singularity is known a priori the unknown current to be solved for is then regular and tenable to galerkin s method of analysis it is shown that this analysis agrees with the single mode approximation when the dielectric substrate layer is thin and that it deviates from the single mode approximation when the substrate layer is thick excellent agreement of both the computed real and imaginary parts of the input impedance with experimental data is noted the radiation patterns and the current distributions on the disk are also presented

resonance frequency of a rectangular microstrip patch the microstrip patch resonant frequency problem is formulated in terms of an integral equation using vector fourier transforms using galerkins s method in solving the integral equation the resonant frequency of the microstrip patch is studied with both chebyshev polynomials and sinusoidal functions as basis functions in the case of the chebyshev polynomials the edge singularity is included but it is not important for convergence furthermore the resonant frequency of the microstrip patch is ascertained with a perturbation calculation the results for galerkin s method and experiments are in good agreement the perturbation calculation agrees asymptotically with galerkin s method with the aim of developing a computer aided design formula the solutions obtained by galerkin s method are interpolated with a three variable polynomial

online bayesian estimation of transition probabilities for markovian jump systems markovian jump systems mjss evolve in a jump wise manner by switching among simpler models according to a finite markov chain whose parameters are commonly assumed known this paper addresses the problem of state estimation of mjs with unknown transition probability matrix tpm of the embedded markov chain governing the jumps under the assumption of a time invariant but random tpm an approximate recursion for the tpms posterior probability density function pdf within the bayesian framework is obtained based on this recursion four algorithms for online minimum mean square error mmse estimation of the tpm are derived the first algorithm for the case of a two state markov chain computes the mmse estimate exactly if the likelihood of the tpm is linear in the transition probabilities its computational load is however increasing with the data length to limit the computational cost three alternative algorithms are further developed based on different approximation techniques truncation of high order moments quasi bayesian approximation and numerical integration respectively the proposed tpm estimation is naturally incorporable into a typical online bayesian estimation scheme for mjs e g generalized pseudo bayesian gpb or interacting multiple model imm thus adaptive versions of mjs state estimators with unknown tpm are provided simulation results of tpm adaptive imm algorithms for a system with failures and maneuvering target tracking are presented

expectation maximization algorithms for map estimation of jump markov linear systems in a jump markov linear system the state matrix observation matrix and the noise covariance matrices evolve according to the realization of a finite state markov chain given a realization of the observation process the aim is to estimate the state of the markov chain assuming known model parameters computing conditional mean estimates is infeasible as it involves a cost that grows exponentially with the number of observations we present three expectation maximization em algorithms for state estimation to compute maximum a posteriori map state sequence estimates which are also known as bayesian maximum likelihood state sequence estimates mlses the first em algorithm yields the map estimate for the entire sequence of the finite state markov chain the second em algorithm yields the map estimate of the continuous state of the jump linear system the third em algorithm computes the joint map estimate of the finite and continuous states the three em algorithms optimally combine a hidden markov model hmm estimator and a kalman smoother ks in three different ways to compute the desired map state sequence estimates unlike the conditional mean state estimates which require computational cost exponential in the data length the proposed iterative schemes are linear in the data length