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

topology recognition with advice in topology recognition each node of an anonymous network has to deterministically produce an isomorphic copy of the underlying graph with all ports correctly marked this task is usually unfeasible without any a priori information such information can be provided to nodes as advice an oracle knowing the network can give a possibly different string of bits to each node and all nodes must reconstruct the network using this advice after a given number of rounds of communication during each round each node can exchange arbitrary messages with all its neighbors and perform arbitrary local computations the time of completing topology recognition is the number of rounds it takes and the size of advice is the maximum length of a string given to nodes we investigate tradeoffs between the time in which topology recognition is accomplished and the minimum size of advice that has to be given to nodes we provide upper and lower bounds on the minimum size of advice that is sufficient to perform topology recognition in a given time in the class of all graphs of size n and diameter d n for any constant 1 in most cases our bounds are asymptotically tight

optimal particle filters for tracking a time varying harmonic or chirp signal we consider the problem of tracking the time varying tv parameters of a harmonic or chirp signal using particle filtering pf tools similar to previous pf approaches to tv spectral analysis we assume that the model parameters complex amplitude frequency and frequency rate in the chirp case evolve according to a gaussian ar 1 model but we concentrate on the important special case of a single tv harmonic or chirp we show that the optimal importance function that minimizes the variance of the particle weights can be computed in closed form and develop procedures to draw samples from it we further employ rao blackwellization to come up with reduced complexity versions of the optimal filters the end result is custom pf solutions that are considerably more efficient than generic ones and can be used in a broad range of important applications that involve a single tv harmonic or chirp signal e g tv doppler estimation in communications and radar

state estimation in stochastic hybrid systems with sparse observations in this note we study the problem of state estimation for a class of sampled measurement stochastic hybrid systems where the continuous state x satisfies a linear stochastic differential equation and noisy measurements y are taken at assigned discrete time instants the parameters of both the state and measurement equation depend on the discrete state q of a continuous time finite markov chain even in the fault detection setting we consider at most one transition for q is admissible the switch may occur between two observations whence it turns out that the optimal estimates cannot be expressed in parametric form and time integrations are unavoidable so that the known estimation techniques cannot be applied we derive and implement an algorithm for the estimation of the states x q and of the discrete state switching time that is convenient for both recursive update and the eventual numerical quadrature numerical simulations are illustrated

realization of an autonomous integrated suite of strapdown astro inertial navigation systems using unscented particle filtering multisensor navigation data synthesis mnds is the process of fusing outputs from inertial sensors with information from other sensors and information processing blocks into one representational form this technique is anticipated to accomplish enhanced accuracy and more specific inferences than could be achieved by the use of a single sensor alone therefore this research work expounds innovative filtering methodology for the multisensor navigation data synthesis for a ballistic missile application that augments navigation system performance the premise and characteristics of strapdown inertial navigation system sins integrated with the astronavigation system ans based on the unscented particle filter upf are investigated in this paper configuration of the integrated navigation system is presented with its canonical model and system dynamic and stochastic models required for the filtering algorithm are presented to exemplify integrated navigation filter mechanization is the foremost aspiration of this research to validate and corroborate the designed mnds technique simulations are carried out that demonstrate the validity of this method on enhancing the navigation system s accuracy with estimation and compensation for the gyro s drift this integrated system results in a significant reduction in impact point dispersion of a re entry vehicle

deinterleaving pulse trains using discrete time stochastic dynamic linear models pulse trains from a number of different sources are often received on the one communication channel it is then of interest to identify which pulses are from which source based on different source characteristics this sorting task is termed deinterleaving the authors propose time domain techniques for deinterleaving pulse trains from a finite number of periodic sources based on the time of arrival toa and pulse energy if available of the pulses received on the one communication channel they formulate the pulse train deinterleaving problem as a stochastic discrete time dynamic linear model dlm the discrete time variable k being associated with the kth received pulse the time varying parameters of the dlm depend on the sequence of active sources the deinterleaving detection estimation task can then be done optimally via linear signal processing using the kalman filter or recursive least squares when the source periods are constant and tree searching the optimal solution however is computationally infeasible for other than small data lengths since the number of possible sequences grow exponentially with data length the authors propose and study two of a number of possible suboptimal solutions 1 forward dynamic programming with fixed look ahead rather than total look ahead as required for the optimal scheme 2 a probabilistic teacher kalman filtering for the detection estimation task

state estimation for discrete time markov jump linear systems with time correlated measurement noise abstract in this paper the state estimation problem for discrete time markov jump linear systems affected by time correlated measurement noise is considered where the time correlated measurement noise is described by a linear system model with white noise as a result two algorithms are proposed to estimate the state of the system under consideration based on a measurement sequence the first algorithm is optimal in the sense of minimum mean square error which is obtained based on the measurement differencing method bayes rule and some results derived in this paper the second algorithm is a suboptimal algorithm obtained by using a lot of gaussian hypotheses the proposed suboptimal algorithm is finite dimensionally computable and does not increase computational and storage load with time computer simulations are carried out to evaluate the performance of the proposed suboptimal algorithm

solving quadratic distance problems an lmi based approach the computation of the minimum distance of a point to a surface in a finite dimensional space is a key issue in several system analysis and control problems the paper presents a general framework in which some classes of minimum distance problems are tackled via linear matrix inequality lmi techniques exploiting a suitable representation of homogeneous forms a lower bound to the solution of a canonical quadratic distance problem is obtained by solving a one parameter family of lmi optimization problems several properties of the proposed technique are discussed in particular tightness of the lower bound is investigated providing both a simple algorithmic procedure for a posteriori optimality testing and a structural condition on the related homogeneous form that ensures optimality a priori extensive numerical simulations are reported showing promising performances of the proposed method

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

topology recognition and leader election in colored networks topology recognition and leader election are fundamental tasks in distributed computing in networks the first of them requires each node to find a labeled isomorphic copy of the network while the result of the second one consists in a single node adopting the label 1 leader with all other nodes adopting the label 0 and learning a path to the leader we consider both these problems in networks whose nodes are equipped with not necessarily distinct labels called colors and ports at each node of degree d are arbitrarily numbered 0 1 d 1 colored networks are generalizations both of labeled networks in which nodes have distinct labels and of anonymous networks in which nodes do not have labels all nodes have the same color in colored networks topology recognition and leader election are not always feasible hence we study two more general problems consider a colored network and an input i given to its nodes the aim of the problem top for this colored network and for i is to solve topology recognition in this network if this is possible under input i and to have all nodes answer unsolvable otherwise likewise the aim of the problem le is to solve leader election in this network if this is possible under input i and to have all nodes answer unsolvable otherwise we show that nodes of a network can solve problems top and le if they are given as input i an upper bound k on the number of nodes of a given color called the size of this color on the other hand we show that if the nodes are given an input that does not bound the size of any color then the answer to top and le must be unsolvable even for the class of rings under the assumption that nodes are given an upper bound k on the size of a given color we study the time of solving problems top and le in the local model in which during each round each node can exchange arbitrary messages with all its neighbors and perform arbitrary local computations we give an algorithm to solve each of these problems in arbitrary networks in time o k d d log n d where d is the diameter of the network and n is its size we also show that this time is optimal by exhibiting classes of networks in which every algorithm solving problems top or le must use time k d d log n d

a class of fast exact bayesian filters in dynamical models with jumps we address the statistical filtering problem in dynamical models with jumps when a particular application is adequately modeled by linear and gaussian probability density functions with jumps a usual method consists in approximating the optimal bayesian estimate in the sense of the minimum mean square error mmse in a linear and gaussian jump markov state space system jmss practical solutions include algorithms based on numerical approximations or on sequential monte carlo smc methods in this paper we propose a class of alternative methods which consists in building statistical models which locally similarly model the problem of interest but in which the computation of the mmse estimate can be be computed exactly without numerical nor smc approximations and at a computational cost which is linear in the number of observations

efficient particle filtering for jump markov systems application to time varying autoregressions we present an efficient particle filtering method to perform optimal estimation in jump markov nonlinear systems jmss such processes consist of a mixture of heterogeneous models and possess a natural hierarchical structure we take advantage of these specificities in order to develop a generic filtering methodology for these models the method relies on an original and nontrivial combination of techniques that have been presented recently in the filtering literature namely the auxiliary particle filter and the unscented transform this algorithm is applied to the complex problem of time varying autoregressive estimation with an unknown time varying model order more precisely we develop an attractive and original probabilistic model that relies on a flexible pole representation that easily lends itself to interpretations we show that this problem can be formulated as a jms and that the associated filtering problem can be efficiently addressed using the generic methodology developed in this paper simulations demonstrate the performance of our method compared to standard particle filtering techniques

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

nonparametric estimation for normalized coprime factors of a mimo system this paper extends to multi input multi output mimo systems the results on frequency response estimation for normalized coprime factors ncf under a stochastic framework from closed loop frequency domain experimental data under the condition that the covariance matrices are available for the external disturbances and measurement errors an analytic solution has been obtained for the maximum likelihood estimate mle on the basis of a linear fractional transformation lft representation for all the plant possible normalized right coprime factors nrcf it is proved that the estimate can be expressed by a linear combination of a normalized random matrix with all its columns having independent complex normal distributions some methods are suggested to reduce the estimation bias when high quality experimental data can be obtained a numerical example is included that confirms the theoretical results

one step fixed lag smoothers for markovian switching systems suboptimal approaches to the one step fixed lag smoothing problem for markovian switching systems are examined in this paper two algorithms are developed for obtaining one step fixed lag smoothed estimates the first algorithm is an approximation that considers the models over the two most recent sampling periods while the second one considers only the models over the most recent sampling period simulation results are presented to compare the performances of these smoothing algorithms

iterative algorithms for state estimation of jump markov linear systems jump markov linear systems jmlss are linear systems whose parameters evolve with time according to a finite state markov chain given a set of observations our aim is to estimate the states of the finite state markov chain and the continuous in space states of the linear system in this paper we present original deterministic and stochastic iterative algorithms for optimal state estimation of jmlss the first stochastic algorithm yields minimum mean square error mmse estimates of the finite state space markov chain and of the continuous state of the jmls a deterministic and a stochastic algorithm are given to obtain the marginal maximum a posteriori mmap sequence estimate of the finite state markov chain finally a deterministic and a stochastic algorithm are derived to obtain the mmap sequence estimate of the continuous state of the jmls computer simulations are carried out to evaluate the performance of the proposed algorithms the problem of deconvolution of bernoulli gaussian bg processes and the problem of tracking a maneuvering target are addressed

ukf based nonlinear filtering using minimum entropy criterion a novel filter for nonlinear and non gaussian systems is proposed in this paper the unscented kalman filter is designed to give a preliminary estimation of the state an additional rbf network is added to the ukf innovation term to compensate for the non gaussianity of the whole system the renyi s entropy of the innovation is introduced and parameters of the rbf network are updated using minimum entropy criterion at each time step it has been shown that the proposed algorithm has a high accuracy in estimation because entropy can characterize all the randomness of the residual while ukf only cares for the mean and the covariance it has been proved that with properly chosen bandwidth the minimum entropy problem of the innovation is convex therefore the proposed adaptive nonlinear filter will be globally convergent and the misadjustment will be proportional to the step size the effectiveness of the proposed method is shown by simulation

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 n3 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

adaptive nonlinear filters for narrow band interference suppression in spread spectrum cdma systems this paper presents a novel nonlinear filter and parameter estimator for narrow band interference suppression in code division multiple access spread spectrum systems as in the article by rusch and poor 1994 the received sampled signal is modeled as the sum of the spread spectrum signal modeled as a finite state independently identically distributed i i d process here we generalize to a finite state markov chain narrow band interference modeled as a gaussian autoregressive process and observation noise modeled as a zero mean white gaussian process the proposed algorithm combines a recursive hidden markov model hmm estimator kalman filter kf and the recursive expectation maximization algorithm the nonlinear filtering techniques for narrow band interference suppression presented in rusch and poor and our proposed hmm kf algorithm have the same computational cost detailed simulation studies show that the hmm kf algorithm outperforms the filtering techniques in rusch and poor in particular significant improvements in the bit error rate and signal to noise ratio snr enhancement are obtained in low to medium snr furthermore in simulation studies we investigate the effect on the performance of the hmm kf and the approximate conditional mean acm filter in the paper by rusch and poor when the observation noise variance is increased as expected the performance of the hmm kf and acm algorithms worsen with increasing observation noise and number of users however hmm kf significantly outperforms acm in medium to high observation noise

derivation of fixed interval smoothing algorithm using covariance information in distributed parameter systems this paper proposes a recursive least mean squared error fixed interval smoothing algorithm in distributed parameter systems it is assumed that the state space model of the signal to be estimated is unknown and the algorithm only requires the second order moments of the signal and the white noise perturbing its observations practical application of the proposed algorithm is illustrated with a restoration image problem

identification of normalized coprime factors through constrained curve fitting this paper deals with identifying finite dimensional normalized right coprime factors nrcfs under a stochastic framework from a sequence of their frequency response estimates a two step procedure is suggested for the estimation in which two cost functions are sequentially minimized these cost functions are constructed on the basis of weighted curve fitting and the conditions on nrcfs a numerical procedure is proposed for computing the estimate moreover it is proved that under some conditions the estimate converges with probability 1 w p 1 to its actual value with increasing the data length and in general the optimal estimate is asymptotically approximately gaussian the efficiency of the proposed method in nrcf identification is illustrated by numerical simulations

bayesian inference for linear dynamic models with dirichlet process mixtures using kalman techniques it is possible to perform optimal estimation in linear gaussian state space models here we address the case where the noise probability density functions are of unknown functional form a flexible bayesian nonparametric noise model based on dirichlet process mixtures is introduced efficient markov chain monte carlo and sequential monte carlo methods are then developed to perform optimal batch and sequential estimation in such contexts the algorithms are applied to blind deconvolution and change point detection experimental results on synthetic and real data demonstrate the efficiency of this approach in various contexts

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

frequency response estimation for ncfs of an mimo plant from closed loop time domain experimental data frequency response estimation from closed loop time domain experimental data is investigated in this paper for normalized coprime factors ncf of a multiple input multiple output mimo plant based on a linear fractional transformation lft representation for all the ncfs of plants internally stabilizable by a known controller this estimation problem is converted into the open loop nonparametric estimation of an inner transfer function matrix tfm an estimate is derived through constrained data matching it is proved that when the probing signals are periodic and the ncfs of the auxiliary plant are appropriately selected the estimate is asymptotically unbiased and with a normal complex normal distribution it has been made clear that the estimation bias and the estimation variance are always finite computationally tractable procedures are suggested for choosing the desirable auxiliary tfms

mixed discrete continuous bayesian inference censored measurements of sparse signals this paper addresses bayesian inference of sparse signals by censored measurements to reduce the sensor s duty cycle signals below a threshold are censored i e are set to zero sparse signals are random vectors that or whose elements are zero with given probabilities the corresponding probabilistic model induces random measurement and signal vectors of mixed absolute continuous discrete and singular continuous nature therefore mixed probability densities the expectation regarding these densities and a generalized bayes rule are constructively derived for the inference proper a posteriori expected loss functions are defined their derivative free minimizations gives bayesian inferrers similar to traditional minimum mean square error mmse maximum a posteriori map and median estimators and detectors the result provides a unified bayesian inference framework eventually this leads to closed form solutions for the inference problem numerical results and the analysis of the probability of censorship

brief paper detection and estimation for abruptly changing systems the problem of state estimation and system structure detection for discrete stochastic dynamical systems with parameters which may switch among a finite set of values is considered the switchings are modelled by a markov chain with known transition probabilities a brief survey and a unified treatment of the existing suboptimal algorithms are provided the optimal algorithms require exponentially increasing memory and computations with time simulation results comparing the various suboptimal algorithms are presented

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

fixed interval smoothing problem from uncertain observations with correlated signal and noise this paper presents recursive filtering and fixed interval smoothing algorithms from observations corrupted by additive and multiplicative noises additive noise is a white process correlated with the signal and multiplicative noise is modelled by a sequence of independent bernoulli random variables it is assumed that both autocovariance function of signal and crosscovariance function about signal and observation noise are expressed in a semi degenerate kernel form the algorithms are obtained by an innovation approach without using the state space model but only covariance information of signal and observation noise and probability that signal exists in the observed values

fixed interval smoothing for markovian switching systems a suboptimal approach to the fixed interval smoothing problem for markovian switching systems is examined a smoothing algorithm is developed that uses two multiple model filters where one of the filters propagates in the forward time direction and the other one propagates in the backward time direction a backward time filtering algorithm based on the interacting multiple model concept is also developed results from a simulation example are given to illustrate the performance of the smoothing algorithm with respect to that of filtering the example involves radar tracking of a mach 1 aircraft

doubly robust smoothing of dynamical processes via outlier sparsity constraints coping with outliers contaminating dynamical processes is of major importance in various applications because mismatches from nominal models are not uncommon in practice in this context the present paper develops novel fixed lag and fixed interval smoothing algorithms that are robust to outliers simultaneously present in the measurements and in the state dynamics outliers are handled through auxiliary unknown variables that are jointly estimated along with the state based on the least squares criterion that is regularized with the l1 norm of the outliers in order to effect sparsity control the resultant iterative estimators rely on coordinate descent and the alternating direction method of multipliers are expressed in closed form per iteration and are provably convergent additional attractive features of the novel doubly robust smoother include i ability to handle both types of outliers ii universality to unknown nominal noise and outlier distributions iii flexibility to encompass maximum a posteriori optimal estimators with reliable performance under nominal conditions and iv improved pcoping with outliers contaminating dynamical processes is of major importance in various applications because mismatches from nominal models are not uncommon in practice in this context the present paper develops novel fixed lag and fixed interval smoothing algorithms that are robust to outliers simultaneously present in the measurements and in the state dynamics outliers are handled through auxiliary unknown variables that are jointly estimated along with the state based on the least squares criterion that is regularized with the l1 norm of the outliers in order to effect sparsity control the resultant iterative estimators rely on coordinate descent and the alternating direction method of multipliers are expressed in closed form per iteration and are provably convergent additional attractive features of the novel doubly robust smoother include i ability to handle both types of outliers ii universality to unknown nominal noise and outlier distributions iii flexibility to encompass maximum a posteriori optimal estimators with reliable performance under nominal conditions and iv improved performance relative to competing alternatives at comparable complexity as corroborated via simulated tests erformance relative to competing alternatives at comparable complexity as corroborated via simulated tests

marginalized particle filters for mixed linear nonlinear state space models the particle filter offers a general numerical tool to approximate the posterior density function for the state in nonlinear and non gaussian filtering problems while the particle filter is fairly easy to implement and tune its main drawback is that it is quite computer intensive with the computational complexity increasing quickly with the state dimension one remedy to this problem is to marginalize out the states appearing linearly in the dynamics the result is that one kalman filter is associated with each particle the main contribution in this paper is the derivation of the details for the marginalized particle filter for a general nonlinear state space model several important special cases occurring in typical signal processing applications will also be discussed the marginalized particle filter is applied to an integrated navigation system for aircraft it is demonstrated that the complete high dimensional system can be based on a particle filter using marginalization for all but three states excellent performance on real flight data is reported

independent particle filters sequential monte carlo methods especially the particle filter pf and its various modifications have been used effectively in dealing with stochastic dynamic systems the standard pf samples the current state through the underlying state dynamics then uses the current observation to evaluate the sample s importance weight however there is a set of problems in which the current observation provides significant information about the current state but the state dynamics are weak and thus sampling using the current observation often produces more efficient samples than sampling using the state dynamics in this article we propose a new variant of the pf the independent particle filter ipf to deal with these problems the ipf generates exchangeable samples of the current state from a sampling distribution that is conditionally independent of the previous states a special case of which uses only the current observation each sample can then be matched with multiple samples of the previous states in

brief paper consistency in least squares estimation in a previous paper the convenience of using martingale theory in the analysis of bayesian least squares estimation was demonstrated however certain restrictions had to be imposed on either the feedback structure or on the initial values for the estimation in the present paper these restrictions are removed and necessary and sufficient conditions for strong consistency in a bayesian sense are given for the gaussian white noise case without any assumptions on closed loop stability or on the feedback structure in the open loop case the poles are shown to be consistently estimated almost everywhere and in the closed loop case certain choices of control law are shown to assure consistency finally adaptive control laws are treated and implicit self tuning regulators are shown to converge to the desired control laws

an interval amplitude algorithm for deinterleaving stochastic pulse train sources we consider the deinterleaving of pulse trains transmitted by n independent sources the deinterleaving problem considered has applications in spectral estimation where n known number stochastic parameterized sources are sampled using a fast sensor recording the sign of the signal from each source due to communication constraints the recorded signals pulse trains or sequences of zeros and ones are superimposed and transmitted through a single gaussian communication channel the aim of this paper is to estimate the parameters that characterize the sources and identify those sources that are responsible for the observed noisy pulses our proposed algorithm subject to modeling assumptions optimally combines hidden markov model and binary time series estimation techniques and yields maximum likelihood parameter estimates of the sources

approximate conditional mean particle filtering for linear nonlinear dynamic state space models we consider linear systems whose state parameters are separable into linear and nonlinear sets and evolve according to some known transition distribution and whose measurement noise is distributed according to a mixture of gaussians in doing so we propose a novel particle filter that addresses the optimal state estimation problem for the aforementioned class of systems the proposed filter referred to as the approximate conditional mean particle filter acm pf is a combination of the approximate conditional mean filter and the sequential importance sampling particle filter the algorithm development depends on approximating a mixture of gaussians distribution with a moment matched gaussian in the weight update recursion a condition indicating when this approximation is valid is given in order to evaluate the performance of the proposed algorithm we address the blind signal detection problem for an impulsive flat fading channel and the tracking of a maneuvering target in the presence of glint noise extensive computer simulations were carried out for computationally intensive implementations large number of particles the proposed algorithm offers performance that is comparable to other state of the art particle filtering algorithms in the scenario where computational horsepower is heavily constrained it is shown that the proposed algorithm offers the best performance amongst the considered algorithms for these specific examples

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

stochastic sampling algorithms for state estimation of jump markov linear systems jump markov linear systems are linear systems whose parameters evolve with time according to a finite state markov chain given a set of observations our aim is to estimate the states of the finite state markov chain and the continuous in space states of the linear system the computational cost in computing conditional mean or maximum a posteriori map state estimates of the markov chain or the state of the jump markov linear system grows exponentially in the number of observations we present three globally convergent algorithms based on stochastic sampling methods for state estimation of jump markov linear systems the cost per iteration is linear in the data length the first proposed algorithm is a data augmentation da scheme that yields conditional mean state estimates the second proposed scheme is a stochastic annealing sa version of da that computes the joint map sequence estimate of the finite and continuous states finally a metropolis hastings da scheme based on sa is designed to yield the map estimate of the finite state markov chain convergence results of the three above mentioned stochastic algorithms are obtained computer simulations are carried out to evaluate the performances of the proposed algorithms the problem of estimating a sparse signal developing from a neutron sensor based on a set of noisy data from a neutron sensor and the problem of narrow band interference suppression in spread spectrum code division multiple access cdma systems are considered

sequential estimation of hidden arma processes by particle filtering part ii this is part ii of a series of two papers where we address sequential estimation of wide sense stationary autoregressive moving average arma state processes by particle filtering in part i we considered a state space model where the state was an arma process of known order and where the parameters of the process could be known or unknown in this paper we extend our work from part i by considering the same type of models with the added complexity that the arma processes are now of unknown order instead of working on a scheme that first tracks the state by operating with different assumed models and then selects the best model by using a predefined criterion we present a method that directly estimates the state without the need of knowing the model order we derive the transition density of the state for unknown arma model order and propose a particle filter based on that density and the empirical bayesian methodology we demonstrate the performance of the proposed method with computer simulations and compare it with the methods from part i

the shifted rayleigh mixture filter for bearings only tracking of maneuvering targets this paper introduces the shifted rayleigh mixture filter srmf which is based on jump markov linear systems the formulation permits the presence of clutter for bearings only tracking problems involving maneuvering targets the conditional density of the target state given the available measurements evolves as a growing mixture of probability density functions associated with a history of manoeuvre modes similar to other mixture algorithms the srmf approximates this conditional density by a gaussian mixture of fixed order unlike the extended or unscented kalman filters the shifted rayleigh filter incorporates an exact calculation of the posterior density when the prior is assumed to be gaussian given the latest bearings measurement computer simulations are provided to demonstrate the performance of the algorithm

convergence rates of distributed average consensus with stochastic link failures we consider a distributed average consensus algorithm over a network in which communication links fail with independent probability in such stochastic networks convergence is defined in terms of the variance of deviation from average we first show how the problem can be recast as a linear system with multiplicative random inputs which model link failures we then use our formulation to derive recursion equations for the second order statistics of the deviation from average in networks with and without additive noise we give expressions for the convergence behavior in the asymptotic limits of small failure probability and large networks we also present simulation free methods for computing the second order statistics in each network model and use these methods to study the behavior of various network examples as a function of link failure probability

sequential imputations and bayesian missing data problems abstract for missing data problems tanner and wong have described a data augmentation procedure that approximates the actual posterior distribution of the parameter vector by a mixture of complete data posteriors their method of constructing the complete data sets is closely related to the gibbs sampler both required iterations and similar to the em algorithm convergence can be slow we introduce in this article an alternative procedure that involves imputing the missing data sequentially and computing appropriate importance sampling weights in many applications this new procedure works very well without the need for iterations sensitivity analysis influence analysis and updating with new data can be performed cheaply bayesian prediction and model selection can also be incorporated examples taken from a wide range of applications are used for illustration

time reversion of a hybrid state stochastic difference system with a jump linear smoothing application the reversion in time of a stochastic difference equation in a hybrid space with a markovian solution is presented the reversion is obtained by a martingale approach which previously led to reverse time forms for stochastic equations with gauss markov or diffusion solutions the reverse time equations follow from a particular noncanonical martingale decomposition while the reverse time equations for gauss markov and diffusion solutions followed from the canonical martingale decomposition the need for this noncanonical decomposition stems from the hybrid state space situation moreover the nongaussian discrete time situation leads to reverse time equations that incorporate a bayesian estimation step the latter step is carried out for linear systems with markovian switching coefficients and the result is shown to provide the solution to the problem of fixed interval smoothing for an application of this smoothing approach to a trajectory with sudden maneuvers simulation results are given to illustrate the practical use of the reverse time equations obtained

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

brief paper a maximum likelihood kalman filter for switching discrete time linear systems state estimation is addressed for a class of discrete time systems that may switch among different modes taken from a finite set the system and measurement equations of each mode are assumed to be linear and perfectly known but the current mode of the system is unknown moreover additive independent normally distributed noises are assumed to affect the dynamics and the measurements first relying on a well established notion of mode observability developed ad hoc for switching systems an approach to system mode estimation based on a maximum likelihood criterion is proposed second such a mode estimator is embedded in a kalman filtering framework to estimate the continuous state under the unique assumption of mode observability stability properties in terms of boundedness of the mean square estimation error are proved for the resulting filter simulation results showing the effectiveness of the proposed filter are reported

brief paper a convex optimization approach to filtering in jump linear systems with state dependent transitions we introduce a new methodology to construct a gaussian mixture approximation to the true filter density in hybrid markovian switching systems we relax the assumption that the mode transition process is a markov chain and allow it to depend on the actual and unobservable state of the system the main feature of the method is that the gaussian densities used in the approximation are selected as the solution of a convex programming problem which trades off sparsity of the solution with goodness of fit a meaningful example shows that the proposed method can outperform the widely used interacting multiple model imm filter and gpb2 in terms of accuracy at the expenses of an increase in computational time

nonstationary source separation using sequential and variational bayesian learning independent component analysis ica is a popular approach for blind source separation where the mixing process is assumed to be unchanged with a fixed set of stationary source signals however the mixing system and source signals are nonstationary in real world applications e g the source signals may abruptly appear or disappear the sources may be replaced by new ones or even moving by time this paper presents an online learning algorithm for the gaussian process gp and establishes a separation procedure in the presence of nonstationary and temporally correlated mixing coefficients and source signals in this procedure we capture the evolved statistics from sequential signals according to online bayesian learning the activity of nonstationary sources is reflected by an automatic relevance determination which is incrementally estimated at each frame and continuously propagated to the next frame we employ the gp to characterize the temporal structures of time varying mixing coefficients and source signals a variational bayesian inference is developed to approximate the true posterior for estimating the nonstationary ica parameters and for characterizing the activity of latent sources the differences between this ica method and the sequential monte carlo ica are illustrated in the experiments the proposed algorithm outperforms the other ica methods for the separation of audio signals in the presence of different nonstationary scenarios

risk sensitive particle filters for mitigating sample impoverishment risk sensitive filters rsf put a penalty to higher order moments of the estimation error compared to conventional filters as the kalman filter minimizing the mean square error mse the result is a more cautious filter which can be interpreted as an implicit and automatic way to increase the state noise covariance on the other hand the process of jittering or roughening is well known in particle filters to mitigate sample impoverishment the purpose of this contribution is to introduce risk sensitive particle filters rspf as an alternative approach to mitigate sample impoverishment based on constructing explicit risk functions from a general class of factorizable functions it is first shown that rsf can be done in nonlinear systems using a recursion of an infinite dimensional information state which involves general risk functions then this information state calculation is carried out using particle approximations some alternative approaches generalizations specific cases comparison to existing methods of sample impoverishment mitigation and issues related to the selection of risk functions and parameters are examined performance of the resulting filter using various risk functions is illustrated on a simulated scenario and compared with the roughening method

sequential monte carlo methods for state and parameter estimation in abruptly changing environments this paper develops a novel sequential monte carlo smc approach for joint state and parameter estimation that can deal efficiently with abruptly changing parameters which is a common case when tracking maneuvering targets the approach combines bayesian methods for dealing with change points with methods for estimating static parameters within the smc framework the result is an approach that adaptively estimates the model parameters in accordance with changes to the target s trajectory the developed approach is compared against the interacting multiple model imm filter for tracking a maneuvering target over a complex maneuvering scenario with nonlinear observations in the imm filter a large combination of models is required to account for unknown parameters in contrast the proposed approach circumvents the combinatorial complexity of applying multiple models in the imm filter through bayesian parameter estimation techniques the developed approach is validated over complex maneuvering scenarios where both the system parameters and measurement noise parameters are unknown accurate estimation results are presented

bayesian conditional monte carlo algorithms for nonlinear time series state estimation bayesian filtering aims at estimating sequentially a hidden process from an observed one in particular sequential monte carlo smc techniques propagate in time weighted trajectories which represent the posterior probability density function pdf of the hidden process given the available observations on the other hand conditional monte carlo cmc is a variance reduction technique which replaces the estimator of a moment of interest by its conditional expectation given another variable in this paper we show that up to some adaptations one can make use of the time recursive nature of smc algorithms in order to propose natural temporal cmc estimators of some point estimates of the hidden process which outperform the associated crude monte carlo mc estimator whatever the number of samples we next show that our bayesian cmc estimators can be computed exactly or approximated efficiently in some hidden markov chain hmc models in some jump markov state space systems jmss as well as in multitarget filtering finally our algorithms are validated via simulations

a sequential monte carlo filter for joint linear nonlinear state estimation with application to ds cdma a sequential monte carlo filter is considered which combines previously developed sequential importance sampling sis techniques for conditional linear gaussian models with measurement linearization for construction of approximate simulation densities the resulting sequential monte carlo kalman filter smc kf consists of a bank of conventional kalman filters individually tuned to sampled trajectories of the nonlinear state variables sampling is according to a gaussian distribution with mean and covariance determined by extended kalman filter type equations the smc kf is then applied to joint delay and multipath channel estimation in direct sequence code division multiple access ds cdma a combined analytical simulation technique is employed to compare performance of the smc kf and a previously derived extended kalman filter ekf based ds cdma channel estimator

convergence rate of least squares identification and adaptive control for stochastic systems the strong consistency and the convergence rate of least squares identification for the multidimensional armax model are established under some decaying excitation conditions which are satisfied if both input and output do not grow too fast and the attenuating excitation technique is applied the parameter identification results are applied to adaptive control systems with a quadratic loss function the rate of convergence of the loss function to its minimum is also obtained

a tutorial on particle filters for online nonlinear non gaussian bayesian tracking increasingly for many application areas it is becoming important to include elements of nonlinearity and non gaussianity in order to model accurately the underlying dynamics of a physical system moreover it is typically crucial to process data on line as it arrives both from the point of view of storage costs as well as for rapid adaptation to changing signal characteristics in this paper we review both optimal and suboptimal bayesian algorithms for nonlinear non gaussian tracking problems with a focus on particle filters particle filters are sequential monte carlo methods based on point mass or particle representations of probability densities which can be applied to any state space model and which generalize the traditional kalman filtering methods several variants of the particle filter such as sir asir and rpf are introduced within a generic framework of the sequential importance sampling sis algorithm these are discussed and compared with the standard ekf through an illustrative example

particle filters for joint blind equalization and decoding in frequency selective channels this paper introduces new algorithms for joint blind equalization and decoding of convolutionally coded communication systems operating on frequency selective channels the proposed method is based on particle filters pf recursively approximating maximum a posteriori map estimates of the transmitted data without explicitly determining channel parameters further elaborating on previous works we assume that both the channel order and the noise variance are unknown random variables and develop a new formulation for pf weight propagation which allows these quantities to be analytically integrated out we verify via numerical simulations that the proposed methods lead to near optimal performance closely approximating that of algorithms that require exact knowledge of all channel parameters

a bayesian approach to multiple target detection and tracking this paper considers the problem of simultaneously detecting and tracking multiple targets the problem can be formulated in a bayesian framework and solved in principle by computation of the joint multitarget probability density jmpd in practice exact computation of the jmpd is impossible and the predominant challenge is to arrive at a computationally tractable approximation a particle filtering scheme is developed for this purpose in which each particle is a hypothesis on the number of targets present and the states of those targets the importance density for the particle filter is designed in such a way that the measurements can guide sampling of both the target number and the target states simulation results with measurements generated from real target trajectories demonstrate the ability of the proposed procedure to simultaneously detect and track ten targets with a reasonable sample size

frequency response estimation for normalized coprime factors this paper investigates estimating the frequency response of the normalized coprime factors of a possibly unstable transfer function from closed loop frequency domain experimental data a stochastic framework has been adopted the dual youla kucera parametrization approach in closed loop system identification has been developed to guarantee the normality of the estimated frequency response a parametrization of all the normalized coprime factors has been established for transfer functions internally stabilizable by a known controller based on this parametrization interpolation conditions have been derived for the measurement errors being consistent with the stabilizing controller and experimental data an analytic expression has been obtained for the maximum likelihood estimate of the frequency response the effectiveness of the suggested method is confirmed through numerical simulations

computing on anonymous networks with sense of direction sense of direction refers to a set of global consistency constraints of the local labeling of the edges of a network sense of direction has a large impact on the communication complexity of many distributed problems in this paper we study the impact that sense of direction has on computability and we focus on anonymous networks we establish several results in particular we prove that with weak sense of direction the intuitive knowledge computability hierarchy between levels of a priori structural knowledge collapses a powerful implication is the formal proof that shortest path routing is possible in anonymous networks with sense of direction we prove that weak sense of direction is computationally stronger than topological awareness we also consider several fundamental problems for each we provide a complete characterization of the anonymous networks on which it is computable with sense of direction

polynomial filtering of discrete time stochastic linear systems with multiplicative state noise the problem of finding an optimal polynomial state estimate for the class of stochastic linear models with a multiplicative state noise term is studied for such models a technique of state augmentation is used leading to the definition of a general polynomial filter the theory is developed for time varying systems with nonstationary and non gaussian noises moreover the steady state polynomial filter for stationary systems is also studied numerical simulations show the high performances of the proposed method with respect to the classical linear filtering techniques

distinguishing views in symmetric networks the view of a node in a port labeled network is an infinite tree encoding all walks in the network originating from this node we prove that for any integers n d 1 there exists a port labeled network with at most n nodes and diameter at most d which contains a pair of nodes whose infinite views are different but whose views truncated to depth d log n d are identical

simulation based optimal sensor scheduling with application to observer trajectory planning the sensor scheduling problem can be formulated as a controlled hidden markov model and this paper solves the problem when the state observation and action spaces are continuous this general case is important as it is the natural framework for many applications the aim is to minimise the variance of the estimation error of the hidden state w r t the action sequence we present a novel simulation based method that uses a stochastic gradient algorithm to find optimal actions

locally adaptive cooperative kalman smoothing and its application to identification of nonstationary stochastic systems one of the central problems of the stochastic approximation theory is the proper adjustment of the smoothing algorithm to the unknown and possibly time varying rate and mode of variation of the estimated signals parameters in this paper we propose a novel locally adaptive parallel estimation scheme which can be used to solve the problem of fixed interval kalman smoothing in the presence of model uncertainty the proposed solution is based on the idea of cooperative smoothing the bayesian extension of the leave one out cross validation approach to model selection within this approach the smoothed estimates are evaluated as a convex combination of the estimates provided by several competing smoothers we derive computationally attractive algorithms allowing for cooperative kalman smoothing and show how the proposed approach can be applied to identification of nonstationary stochastic systems

robust continuous time smoothers without two sided stochastic integrals we consider the problem of fixed interval smoothing of a continuous time partially observed nonlinear stochastic dynamical system existing results for such smoothers require the use of two sided stochastic calculus the main contribution of the paper is to present a robust formulation of the smoothing equations under this robust formulation the smoothing equations are nonstochastic parabolic partial differential equations with random coefficients and hence the technical machinery associated with two sided stochastic calculus is not required furthermore the robust smoothed state estimates are locally lipschitz in the observations which is useful for numerical simulation as examples finite dimensional robust versions of the benes and hidden markov model smoothers and smoothers for piecewise linear dynamics are derived these finite dimensional smoothers do not involve stochastic integrals

learning and inferring motion patterns using parametric segmental switching linear dynamic systems switching linear dynamic system slds models are a popular technique for modeling complex nonlinear dynamic systems an slds can describe complex temporal patterns more concisely and accurately than an hmm by using continuous hidden states however the use of slds models in practical applications is challenging for three reasons first exact inference in slds models is computationally intractable second the geometric duration model induced in standard sldss limits their representational power third standard sldss do not provide a principled way to interpret systematic variations governed by higher order parameters the contributions in this paper address all of these three challenges first we present a data driven mcmc dd mcmc sampling method for approximate inference in sldss we show dd mcmc provides an efficient method for estimation and learning in slds models second we present segmental sldss s slds where the geometric distributions of the switching state durations are replaced with arbitrary duration models third we extend the standard slds model with additional global parameters that can capture systematic temporal and spatial variations the resulting parametric slds model p slds uses em to robustly interpret parametrized motions by incorporating additional global parameters that underly systematic variations of the overall motion the overall development of the extensions for sldss provide a principled framework to interpret complex motions the framework is applied to the honey bee dance interpretation task in the context of the on going biotracking project at the georgia institute of technology the experimental results suggest that the enhanced models provide an effective framework for a wide range of motion analysis applications

blind deconvolution via sequential imputations abstract the sequential imputation procedure is applied to adaptively and sequentially reconstruct discrete input signals that are blurred by an unknown linear moving average channel and contaminated by additive gaussian noises a problem known as blind deconvolution in digital communication a rejuvenation procedure for improving the efficiency of sequential imputation is introduced and theoretically justified the proposed method does not require the channel to be nonminimum phase and can be used in real time signal restoration two simulated systems are studied to illustrate the proposed method our result shows that the ideas of multiple imputations and flexible simulation techniques are as powerful in engineering as in survey sampling

identification and adaptive control of change point arx models via rao blackwellized particle filters by proper choice of proposal distributions for importance sampling and of resampling schemes for sequentially updating the importance weights we address the problem of on line identification and adaptive control of autoregressive models with exogenous inputs arx models with markov parameter jumps particle filters that can be implemented online via parallel recursions are developed by making use of explicit formulas of the posterior means of the time varying parameters theoretical analysis and simulation studies show improvements of this approach over conventional methods

a bayesian approach to tracking multiple targets using sensor arrays and particle filters we present a bayesian approach to tracking the direction of arrival doa of multiple moving targets using a passive sensor array the prior is a description of the dynamic behavior we expect for the targets which is modeled as constant velocity motion with a gaussian disturbance acting on the target s heading direction the likelihood function is arrived at by defining an uninformative prior for both the signals and noise variance and removing these parameters from the problem by marginalization advances in sequential monte carlo smc techniques specifically the particle filter algorithm allow us to model and track the posterior distribution defined by the bayesian model using a collection of target states that can be viewed as samples from the posterior of interest we describe two versions of this algorithm and finally present results obtained using synthetic data

variance reduction for particle filters of systems with time scale separation we present a particle filter construction for a system that exhibits time scale separation the separation of time scales allows two simplifications that we exploit 1 the use of the averaging principle for the dimensional reduction of the dynamics for each particle during the prediction step and 2 the factorization of the transition probability for the rao blackwellization of the update step the resulting particle filter is faster and has smaller variance than the particle filter based on the original system the method is tested on a multiscale stochastic differential equation and on a multiscale pure jump diffusion motivated by chemical reactions

nonparametric bayesian bioassay including ordered polytomous response abstract previous attempts at implementing fully bayesian nonparametric bioassay have enjoyed limited success due to computational difficulties we show here how this problem may be generally handled using a sampling based approach to develop desired marginal posterior distributions and their features a useful extension is presented which treats the case of ordered polytomous response illustrative examples are provided

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

a blind particle filtering detector of signals transmitted over flat fading channels a new particle filtering detector pfd is proposed for blind signal detection over flat rayleigh fading channels whose model coefficients are unknown the detector employs a hybrid importance function and a mixture kalman filter it also incorporates an auxiliary particle filtering strategy with a smoothing kernel in the resampling step further by considering practical information of communication systems and the physical interpretation of the adopted second order autoregressive ar channel model a fully blind particle filtering implementation is developed the structure of the proposed pfd can be easily adapted to other system requirements simulations are provided that demonstrate the performance of the new pfd

computing boolean functions on anonymous networks abstract we study the bit complexity of computing boolean functions on anonymous networks let n be the number of nodes the diameter and d the maximal node degree of the network for arbitrary anonymous networks we give a general algorithm of polynomial bit complexity o n 3 d 2 log n for computing any boolean function which is computable on the network this improves upon the previous best known algorithm which was of exponential bit complexity o d n 2 for symmetric functions on arbitrary networks we give an algorithm with bit complexity o n 3 d 2 log 2 n this same algorithm is shown to have even lower bit complexity for a number of specific networks for example tori hypercubes and random regular graphs we also consider the class of distance regular unlabeled networks and show that on such networks symmetric functions can be computed efficiently in o n d log n bits