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.

• Publication year

  2013

• Venue

  IEEE Transactions on Signal Processing

• Publication date

  2013-12-03

• Fields of study

  Mathematics, Computer Science, Engineering

• Identifiers
  DOI 10.1109/TSP.2014.2385039arXiv 1312.0781
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Rao-Blackwellized particle filter for Markov modulated nonlinear dynamic systems

  2014cited by this paper
• Exact Fast Computation of Optimal Filter in Gaussian Switching Linear Systems

  2013cited by this paper
• An Online Expectation–Maximization Algorithm for Changepoint Models

  2013cited by this paper
• Backward Simulation Methods for Monte Carlo Statistical Inference

  2013cited by this paper
• Online EM algorithm for joint state and mixture measurement noise estimation

  2012cited by this paper
• Online EM algorithm for jump Markov systems

  2012cited by this paper
• Exact filtering in conditionally Markov switching hidden linear models

  2011cited by this paper
• Understanding Human Relations (Kinship Systems)

  2011cited by this paper
• Online Expectation Maximization algorithm to solve the SLAM problem

  2011cited by this paper
• Kalman filtering approximations in triplet Markov Gaussian switching models

  2011cited by this paper
• An explicit variance reduction expression for the Rao-Blackwellised particle filter

  2011cited by this paper
• Forward Smoothing using Sequential Monte Carlo

  2010influential reference
• Particle filter theory and practice with positioning applications

  2010cited by this paper
• Propagation channel impact on LTE positioning accuracy: A study based on real measurements of observed time difference of arrival

  2009cited by this paper
• Online EM Algorithm for Hidden Markov Models

  2009cited by this paper
• ONLINE SEQUENTIAL MONTE CARLO EM ALGORITHM

  2009cited by this paper
• Robust mobile terminal tracking in NLOS environments using interacting multiple model algorithm

  2009cited by this paper
• Chapter 3 Recent Developments in Auxiliary Particle Filtering

  2009cited by this paper
• A Jump Markov Particle Filter for Localization of Moving Terminals in Multipath Indoor Scenarios

  2008cited by this paper
• Online Learning with Hidden Markov Models

  2008cited by this paper
• A Tutorial on Particle Filtering and Smoothing: Fifteen years later

  2008cited by this paper
• Maximum Likelihood Estimation of Transition Probabilities of Jump Markov Linear Systems

  2008influential reference
• Mobility Tracking in Cellular Networks Using Particle Filtering

  2007cited by this paper
• Particle Filtering for Multisensor Data Fusion With Switching Observation Models: Application to Land Vehicle Positioning

  2007cited by this paper
• A general framework for the identification of jump Markov linear systems

  2007cited by this paper
• Simulation-based sequential analysis of Markov switching stochastic volatility models

  2007cited by this paper
• Inference in Hidden Markov Models

  2006cited by this paper
• Robust Mobile Location Estimator with NLOS Mitigation using Interacting Multiple Model Algorithm

  2006cited by this paper
• An online sequential algorithm for the estimation of transition probabilities for jump Markov linear systems

  2006cited by this paper
• A Gaussian Mixture PHD Filter for Nonlinear Jump Markov Models

  2006cited by this paper
• Survey of maneuvering target tracking. Part V. Multiple-model methods

  2005cited by this paper
• Marginalized particle filters for mixed linear/nonlinear state-space models

  2005cited by this paper
• Inference in Hidden Markov Models (Springer Series in Statistics)

  2005cited by this paper
• Efficient particle filter for jump Markov nonlinear systems

  2005cited by this paper
• Central limit theorem for sequential Monte Carlo methods and its application to Bayesian inference

  2004cited by this paper
• Online Bayesian estimation of transition probabilities for Markovian jump systems

  2004cited by this paper
• Efficient particle filtering for jump Markov systems. Application to time-varying autoregressions

  2003cited by this paper
• Efficient particle filtering for Jump Markov Systems

  2002cited by this paper
• Monte Carlo Strategies in Scientific Computing

  2002cited by this paper
• Particle filtering for partially observed Gaussian state space models

  2002cited by this paper
• Following a moving target—Monte Carlo inference for dynamic Bayesian models

  2001cited by this paper
• Particle filters for state estimation of jump Markov linear systems

  2001cited by this paper
• Mixture Kalman filters

  2000cited by this paper
• On sequential Monte Carlo sampling methods for Bayesian filtering

  2000cited by this paper
• Filtering via Simulation: Auxiliary Particle Filters

  1999cited by this paper
• Expectation maximization algorithms for MAP estimation of jump Markov linear systems

  1999cited by this paper
• An equivalence of the EM and ICE algorithm for exponential family

  1997cited by this paper
• The EM algorithm and extensions

  1996cited by this paper
• Adaptive interacting multiple model algorithm for tracking a manoeuvring target

  1995cited by this paper
• Sequential Imputations and Bayesian Missing Data Problems

  1994cited by this paper
• Dynamic linear models with switching

  1991cited by this paper
• Interacting Multiple Model Methods in Target Tracking: A Survey

  1988cited by this paper
• The interacting multiple model algorithm for systems with Markovian switching coefficients

  1988cited by this paper
• ON THE CONVERGENCE PROPERTIES OF THE EM ALGORITHM

  1983cited by this paper
• Adaptive estimation and identification for discrete systems with Markov jump parameters

  1981cited by this paper
• Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper

  1977cited by this paper

• Mismatch-indicator identification-enabled generalized labeled multi-Bernoulli filter for tracking multi-UAVs in urban environments

  2026cites this paper
• A variational Bayesian marginalized particle filter for jump Markov nonlinear systems with unknown measurement noise parameters

  2025cites this paper
• Recursive Parameter Estimation of Fractional Order Hammerstein Output Error Autoregressive Model

  2025cites this paper
• An interactive prognostics framework for lithium-ion battery remaining useful life based on neural networks and statistical processes

  2025cites this paper
• Joint Vessel Multilateration and Classification Using Coastal Surveillance Cameras

  2025cites this paper
• Context and intent enhanced target tracking

  2025cites this paper
• A distributed randomized method for the identification of switched ARX systems

  2024cites this paper
• Estimation of potential field environments from heterogeneous behaviour of sensing agents

  2023cites this paper
• System identification in presence of undetectable packet losses in the actuation path

  2023cites this paper
• State estimation for one-dimensional agro-hydrological processes with model mismatch

  2023cites this paper
• Tightly Integrated Motion Classification and State Estimation in Foot-Mounted Navigation Systems

  2023cites this paper
• Identification of Nonlinear Multi-Input Multi-Output Systems Based on Maximum Likelihood Principle

  2023cites this paper
• A randomized method for the identification of switched NARX systems

  2023cites this paper
• Laplace Distribution Based Online Identification of Linear Systems With Robust Recursive Expectation–Maximization Algorithm

  2023cites this paper
• Data-Compatibility Analysis Based on Expectation-Maximization Algorithm With Unknown Noise Statistics

  2023cites this paper
• A novel system identification algorithm for nonlinear Markov jump system

  2022cites this paper
• Teaching–Learning-Based Optimization for Parameter Identification of an Activated Sludge Process Model

  2022cites this paper
• Identification of time-delay Markov jumps autoregressive system with recursive expectation maximum and convex optimization algorithm

  2022cites this paper
• Channel tracking of uncoordinated access under uncertain evolution for massive connectivity with massive MIMO

  2021cites this paper
• Online state and inputs identification for stochastic systems using recursive expectation-maximization algorithm

  2021cites this paper
• Near-Optimal Recursive Identification for Markov Switched Systems

  2021cites this paper
• Rating Transitions Forecasting: A filtering Approach

  2021cites this paper
• A variational marginalized particle filter for jump Markov nonlinear systems with unknown transition probabilities

  2021influential citation
• Adaptive Real-Time Filter for Partially-Observed Boolean Dynamical Systems

  2021cites this paper
• A marginalised particle filter with variational inference for non‐linear state‐space models with Gaussian mixture noise

  2021cites this paper
• Failure Prediction of Hard Disk Drives Based on Adaptive Rao–Blackwellized Particle Filter Error Tracking Method

  2021cites this paper
• Online identification of time‐delay jump Markov autoregressive exogenous systems with recursive expectation‐maximization algorithm

  2020cites this paper
• Integrated navigation of GPS/INS based on fusion of recursive maximum likelihood IMM and Square-root Cubature Kalman filter.

  2020cites this paper
• Identification of jump Markov autoregressive exogenous systems with missing measurements

  2020cites this paper
• Estimation of jump Box-Jenkins models

  2020cites this paper
• Mode separability-based state estimation for uncertain constrained dynamic systems

  2020cites this paper
• A Rao-Blackwellized Particle Filter With Variational Inference for State Estimation With Measurement Model Uncertainties

  2020cites this paper
• Robust identification of linear ARX models with recursive EM algorithm based on Student's t-distribution

  2020cites this paper
• Estimation of Switched Markov Polynomial NARX models

  2020cites this paper
• Estimation of JumpBox-JenkinsModels

  2020cites this paper
• Security-Enhanced Filter Design for Stochastic Systems under Malicious Attack via Smoothed Signal Model and Multiobjective Estimation Method

  2020cites this paper
• Sensorimotor learning under switching dynamics

  2020cites this paper
• Event-Triggered Steering Control for Semiautonomous Vehicles with a Stochastic Driver Model

  2019cites this paper
• Switching State-Space Degradation Model With Recursive Filter/Smoother for Prognostics of Remaining Useful Life

  2019cites this paper
• Parameter Estimation in Switching Markov Systems and Unsupervised Smoothing

  2019cites this paper
• Multiellipsoidal extended target tracking with known extent using sequential Monte Carlo framework

  2019cites this paper
• Performance Criteria for the Identification of Inertial Sensor Error Models

  2019cites this paper
• An EM-based multipath interference mitigation in GNSS receivers

  2019cites this paper
• A Variational Bayesian Approach for Identification of Time-Delay Markov Jump Autoregressive Exogenous Systems

  2019cites this paper
• Jump Markov Nonlinear System Identification for Behavior Classification in Multi-Sensor Target Tracking

  2019cites this paper
• Rao-Blackwellized Particle Gibbs Kernels for Smoothing in Jump Markov Nonlinear Models

  2018cites this paper
• Maximum Likelihood Recursive Extended Least Squares Estimation for Multivariate Equation-Error Moving Average Systems

  2018cites this paper
• Recursive identification for multivariate autoregressive equation-error systems with autoregressive noise

  2018cites this paper
• Variational Bayesian Inference for Jump Markov Linear Systems with Unknown Transition Probabilities

  2018cites this paper
• A Projection-Based Rao-Blackwellized Particle Filter to Estimate Parameters in Conditionally Conjugate State-Space Models

  2018cites this paper
• A Particle Stochastic Approximation EM Algorithm to Identify Jump Markov Nonlinear Models

  2018cites this paper
• Exactly Decoupled Kalman Filtering for Multitarget State Estimation With Sensor Bias

  2018cites this paper
• Rapid System Identi fi cation for Jump Markov Non-Linear Systems

  2018cites this paper
• Estimation of Random Mobility Models using the Expectation-Maximization Method

  2018cites this paper
• Jump Markov Nonlinear System Identification in Multi-Sensor Target Tracking: A Novel Approach for Multiple Model Joint Tracking and Behavior Classification

  2018influential citation
• Multiple motor memories are learned to control different points on a tool

  2018cites this paper
• Fast Filtering in Switching Approximations of Nonlinear Markov Systems With Applications to Stochastic Volatility

  2017cites this paper
• A Kalman Estimation Based Rao-Blackwellized Particle Filtering for Radar Tracking

  2017cites this paper
• Learning and Smoothing in Switching Markov Models with Copulas. (Apprentissage et Lissage dans Les Modèles de Markov à Sauts et à Copules)

  2017cites this paper
• Identification of time‐delay Markov jump autoregressive exogenous systems with expectation‐maximization algorithm

  2017cites this paper
• An indoor gas leakage source localization algorithm using distributed maximum likelihood estimation in sensor networks

  2017cites this paper
• Multiplex Decomposition of Non-Markovian Dynamics and the Hidden Layer Reconstruction Problem

  2017cites this paper
• The maximum likelihood least squares based iterative estimation algorithm for bilinear systems with autoregressive moving average noise

  2017cites this paper
• Gradient-based recursive maximum likelihood identification of Jump Markov Non-Linear Systems

  2017cites this paper
• LMMSE estimation of Markovian jump linear systems with random parameters and estimate feedback

  2017cites this paper
• Mode-dependent filter design for Markov jump systems with sensor nonlinearities in finite frequency domain

  2017cites this paper
• Rapid system identification for jump Markov non-linear systems

  2017cites this paper
• The Marginal Bayesian Cramér–Rao Bound for Jump Markov Systems

  2016cites this paper
• Cooperative navigation and coverage identification with random gossip and sensor fusion

  2016influential citation
• Markov Nonlinear System Estimation for Engine Performance Tracking

  2016cites this paper
• Technical report from Automatic Control at Linköpings universitet Supplementary Material for “ Recent results on Bayesian Cramér-Rao bounds for jump Markov systems ”

  2016cites this paper
• Online Nonparametric Bayesian Activity Mining and Analysis From Surveillance Video

  2016cites this paper
• A survey on joint tracking using expectation-maximization based techniques

  2016cites this paper
• Incremental Nonlinear System Identification and Adaptive Particle Filtering Using Gaussian Process

  2016cites this paper
• A NLOS-robust TOA positioning filter based on a skew-t measurement noise model

  2015cites this paper
• Cooperative Terrain Based Navigation and coverage identification using consensus

  2015influential citation
• A particle filter based sequential trajectory classifier for behavior analysis in video surveillance

  2015cites this paper
• Rao-Blackwellized particle filter for Markov modulated nonlinear dynamic systems

  2014cites this paper