Results 1  10
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15
Particle Filters for State Estimation of Jump Markov Linear Systems
, 2001
"... 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 simulationbased algorithms called particle filter ..."
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Cited by 122 (11 self)
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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 simulationbased algorithms called particle filters to solve the optimal filtering problem as well as the optimal fixedlag 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
Observability and Identifiability of Jump Linear Systems
 In Proc. of IEEE Conference on Decision and Control
, 2002
"... We analyze the observability of the continuous and discrete states of a class of linear hybrid systems. We derive rank conditions that the structural parameters of the model must satisfy in order for filtering and smoothing algorithms to operate correctly. We also study the identifiability of the mo ..."
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Cited by 37 (8 self)
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We analyze the observability of the continuous and discrete states of a class of linear hybrid systems. We derive rank conditions that the structural parameters of the model must satisfy in order for filtering and smoothing algorithms to operate correctly. We also study the identifiability of the model parameters by characterizing the set of models that produce the same output measurements. Finally, when the data are generated by a model in the class, we give conditions under which the true model can be identified.
An Algebraic Geometric Approach to the Identification of a Class of Linear Hybrid Systems
 In Proc. of IEEE Conference on Decision and Control
, 2003
"... We propose an algebraic geometric solution to the identification of a class of linear hybrid systems. We show that the identification of the model parameters can be decoupled from the inference of the hybrid state and the switching mechanism generating the transitions, hence we do not constraint the ..."
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Cited by 37 (11 self)
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We propose an algebraic geometric solution to the identification of a class of linear hybrid systems. We show that the identification of the model parameters can be decoupled from the inference of the hybrid state and the switching mechanism generating the transitions, hence we do not constraint the switches to be separated by a minimum dwell time. The decoupling is obtained from the socalled hybrid decoupling constraint, which establishes a connection between linear hybrid system identification, polynomial factorization and hyperplane clustering. In essence, we represent the number of discrete states n as the degree of a homogeneous polynomial p and the model parameters as factors of p. We then show that one can estimate n from a rank constraint on the data, the coe#cients of p from a linear system, and the model parameters from the derivatives of p. The solution is closed form if and only if n 4. Once the model parameters have been identified, the estimation of the hybrid state becomes a simpler problem. Although our algorithm is designed for noiseless data, we also present simulation results with noisy data. 1
Asymptotic properties of the maximum likelihood estimator in autoregressive models with Markov regime
 ANN. STATIST
, 2004
"... An autoregressive process with Markov regime is an autoregressive process for which the regression function at each time point is given by a nonobservable Markov chain. In this paper we consider the asymptotic properties of the maximum likelihood estimator in a possibly nonstationary process of this ..."
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Cited by 34 (6 self)
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An autoregressive process with Markov regime is an autoregressive process for which the regression function at each time point is given by a nonobservable Markov chain. In this paper we consider the asymptotic properties of the maximum likelihood estimator in a possibly nonstationary process of this kind for which the hidden state space is compact but not necessarily finite. Consistency and asymptotic normality are shown to follow from uniform exponential forgetting of the initial distribution for the hidden Markov chain conditional on the observations.
Iterative Algorithms for State Estimation of Jump Markov Linear Systems
, 1999
"... 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. ..."
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Cited by 29 (3 self)
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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.
Identification of PWARX Hybrid Models with Unknown and Possibly Different Orders
 In Proceedings of IEEE American Control Conference
, 2004
"... We consider the problem of identifying the orders and the model parameters of PWARX hybrid models from noiseless input/output data. We cast the identification problem in an algebraic geometric framework in which the number of discrete states corresponds to the degree of a multivariate polynomial p a ..."
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Cited by 8 (4 self)
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We consider the problem of identifying the orders and the model parameters of PWARX hybrid models from noiseless input/output data. We cast the identification problem in an algebraic geometric framework in which the number of discrete states corresponds to the degree of a multivariate polynomial p and the orders and the model parameters are encoded on the factors of p. We derive a rank constraint on the input/output data from which one can estimate the coefficients of p. Given p, we show that one can estimate the orders and the parameters of each ARX model from the derivatives of p at a collection of regressors that minimize a certain objective function. Our solution does not require previous knowledge about the orders of the ARX models (only an upper bound is needed), nor does it constraint the orders to be equal. Also the switching mechanism can be arbitrary, hence the switches need not be separated by a minimum dwell time. We illustrate our approach with an algebraic example of a switching circuit and with simulation results in the presence of noisy data.
Mixed state estimation for a linear gaussian markov model
 in: Proceedings of the IEEE Conference on Decision and Control
"... We consider a discretetime dynamical system with Boolean and continuous states, with the continuous state propagating linearly in the continuous and Boolean state variables, and an additive Gaussian process noise, and where each Boolean state component follows a simple Markov chain. This model, whi ..."
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Cited by 5 (5 self)
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We consider a discretetime dynamical system with Boolean and continuous states, with the continuous state propagating linearly in the continuous and Boolean state variables, and an additive Gaussian process noise, and where each Boolean state component follows a simple Markov chain. This model, which can be considered a hybrid or jumplinear system with very special form, or a standard linear GaussMarkov dynamical system driven by a Boolean Markov process, arises in dynamic fault detection, in which each Boolean state component represents a fault that can occur. We address the problem of estimating the state, given Gaussian noise corrupted linear measurements. Computing the exact maximum a posteriori (MAP) estimate entails solving a mixed integer quadratic program, which is computationally difficult in general, so we propose an approximate MAP scheme, based on a convex relaxation, followed by rounding and (possibly) further local optimization. Our method has a complexity that grows linearly in the time horizon and cubicly with the state dimension, the same as a standard Kalman filter. Numerical experiments suggest that it performs very well in practice. 1
Causal and Strictly Causal Estimation for Jump Linear Systems: An LMI Analysis
, 2006
"... Jump linear systems are linear statespace systems with random time variations driven by a finite Markov chain. These models are widely used in nonlinear control, and more recently, in the study of communication over lossy channels. This paper considers a general jump linear estimation problem of e ..."
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Cited by 3 (1 self)
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Jump linear systems are linear statespace systems with random time variations driven by a finite Markov chain. These models are widely used in nonlinear control, and more recently, in the study of communication over lossy channels. This paper considers a general jump linear estimation problem of estimating an unknown signal from an observed signal, where both signals are described as outputs of a jump linear system. A bound on the minimum achievable estimation error in terms of linear matrix inequalities (LMIs) is presented, along with a simple jump linear estimator that achieves this bound. While previous analysis has considered only the strictly causal estimation problem, this work presents both strictly causal and causal solutions.
State Estimation and Fault Detection in Stochastic Hybrid Systems
, 2001
"... In this paper we study the problem of state estimation for a particular class of Stochastic Hybrid Systems (SHS). Precisely, given a SHS whose continuoustime evolution is given by a set of stochastic, Gaussian linear systems, and whose discretetime evolution is described by a known probability dis ..."
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Cited by 3 (0 self)
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In this paper we study the problem of state estimation for a particular class of Stochastic Hybrid Systems (SHS). Precisely, given a SHS whose continuoustime evolution is given by a set of stochastic, Gaussian linear systems, and whose discretetime evolution is described by a known probability distribution (not necessarily Markov; in fact, it may depend on the continuoustime evolution) we formulate an algorithm that yields and estimate for the continuous state and a posterior probability distribution on the discrete state, given a sequence of linear, noisy measurements of the continuous state variable only. We also illustrate an application to fault detection in Stochastic Hybrid Systems. The algorithm we illustrate is an adaptation to Stochastic Hybrid Systems of samplingbased estimation method for the so called Conditional Dynamical Linear Models (also known as Switching Kalman Filters).
Improved Target Tracking with Road Network Information.
"... Abstract—In this paper we consider the problem of tracking targets, which can move both onroad and offroad, with particle filters utilizing the roadnetwork information. It is argued that the constraints like speedlimits and/or oneway roads generally incorporated into onroad motion models make i ..."
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Cited by 2 (2 self)
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Abstract—In this paper we consider the problem of tracking targets, which can move both onroad and offroad, with particle filters utilizing the roadnetwork information. It is argued that the constraints like speedlimits and/or oneway roads generally incorporated into onroad motion models make it necessary to consider additional highbandwidth offroad motion models. This is true even if the targets under consideration are only allowed to move onroad due to the possibility of imperfect roadmap information and drivers violating the traffic rules. The particle filters currently used struggles during sharp mode transitions, with poor estimation quality as a result. This is due to the fact the number of particles allocated to each motion mode is varying according to the mode probabilities. A recently proposed interacting multiple model (IMM) particle filtering algorithm, which keeps