Thomas B. Schön

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.

System identification of nonlinear state-space models

This paper is concerned with the parameter estimation of a general class of nonlinear dynamic systems in state-space form. More specifically, a Maximum Likelihood (ML) framework is employed and an Expectation Maximisation (EM) algorithm is derived to compute these ML estimates. The Expectation (E) step involves solving a nonlinear state estimation problem, where the smoothed estimates of the states are required. This problem lends itself perfectly to the particle smoother, which provides arbitrarily good estimates. The maximisation (M) step is solved using standard techniques from numerical optimisation theory. Simulation examples demonstrate the efficacy of our proposed solution.

On Resampling Algorithms for Particle Filters

In this paper a comparison is made between four frequently encountered resampling algorithms for particle filters. A theoretical framework is introduced to be able to understand and explain the differences between the resampling algorithms. This facilitates a comparison of the algorithms with respect to their resampling quality and computational complexity. Using extensive Monte Carlo simulations the theoretical results are verified. It is found that systematic resampling is favourable, both in terms of resampling quality and computational complexity.

Complexity analysis of the marginalized particle filter

In this paper, the computational complexity of the marginalized particle filter is analyzed and a general method to perform this analysis is given. The key is the introduction of the equivalent flop measure. In an extensive Monte Carlo simulation, different computational aspects are studied and compared with the derived theoretical results.

Identification of Hammerstein-Wiener models

This paper develops and illustrates a new maximum-likelihood based method for the identification of Hammerstein-Wiener model structures. A central aspect is that a very general situation is considered wherein multivariable data, non-invertible Hammerstein and Wiener nonlinearities, and colored stochastic disturbances both before and after the Wiener nonlinearity are all catered for. The method developed here addresses the blind Wiener estimation problem as a special case.

A Basic Convergence Result for Particle Filtering

The basic nonlinear filtering problem for dynamical systems is considered. Approximating the optimal filter estimate by particle filter methods has become perhaps the most common and useful method in recent years. Many variants of particle filters have been suggested, and there is an extensive literature on the theoretical aspects of the quality of the approximation. Still, a clear cut result that the approximate solution, for unbounded functions, converges to the true optimal estimate as the number of particles tends to infinity seems to be lacking. It is the purpose of this contribution to give such a basic convergence result.

Backward Simulation Methods for Monte Carlo Statistical Inference

Monte Carlo methods, in particular those based on Markov chains and on interacting particle systems, are by now tools that are routinely used in machine learning. These methods have had a profound impact on statistical inference in a wide range of application areas where probabilistic models are used. Moreover, there are many algorithms in machine learning which are based on the idea of processing the data sequentially, first in the forward direction and then in the backward direction. In this tutorial, we will review a branch of Monte Carlo methods based on the forward–backward idea, referred to as backward simulators. These methods are useful for learning and inference in probabilistic models containing latent stochastic processes. The theory and practice of backward simulation algorithms have undergone a significant development in recent years and the algorithms keep finding new applications. The foundation for these methods is sequential Monte Carlo (SMC). SMC-based backward simulators are capable of addressing smoothing problems in sequential latent variable models, such as general, nonlinear/non-Gaussian state-space models (SSMs). However, we will also clearly show that the underlying backward simulation idea is by no means restricted to SSMs. Furthermore, backward simulation plays an important role in recent developments of Markov chain Monte Carlo (MCMC) methods. Particle MCMC is a systematic way of using SMC within MCMC. In this framework, backward simulation gives us a way to significantly improve the performance of the samplers. We review and discuss several related backward-simulation-based methods for state inference as well as learning of static parameters, both using a frequentistic and a Bayesian approach.

Tightly coupled UWB/IMU pose estimation

In this paper we propose a 6DOF tracking system combining Ultra-Wideband measurements with low-cost MEMS inertial measurements. A tightly coupled system is developed which estimates position as well as orientation of the sensor-unit while being reliable in case of multipath effects and NLOS conditions. The experimental results show robust and continuous tracking in a realistic indoor positioning scenario.

Evaluation of wild-type MIC distributions as a tool for determination of clinical breakpoints for Mycobacterium tuberculosis

OBJECTIVES The aim of this study was to establish wild-type MIC distributions of first-line drugs for Mycobacterium tuberculosis, as well as to explore the usefulness of such distributions when setting clinical breakpoints. METHODS We determined the MICs of rifampicin, isoniazid and ethambutol for M. tuberculosis using a Middlebrook 7H10 dilution method for 90 consecutive clinical isolates, 8 resistant strains and 16 isolates from the WHO proficiency test panel. M. tuberculosis H37Rv was used for quality control and susceptibility results using 7H10 were compared with the results obtained with BACTEC460. RESULTS The agreement with BACTEC460 was very high for isoniazid (99.1%) and rifampicin (99.1%) but lower for ethambutol (94.7%). Intra- and inter-assay variation was below one MIC dilution. The MIC distributions for isoniazid and rifampicin provided a clear separation between susceptible and resistant strains. Regarding ethambutol, the current breakpoint for 7H10 (5 mg/L) is close to the wild-type and all strains (n = 6) showing a disagreement between BACTEC460 and 7H10 were distributed very close to the breakpoint (MIC 4-8 mg/L). This problematic relation was confirmed by investigating isolates from the WHO panel with an agreement <95% (64%-88% among 26 laboratories, n = 4) for which the MICs were 4-8 mg/L. CONCLUSIONS Utilizing the wild-type MIC distribution was found to be as useful in M. tuberculosis as in other bacteria when setting clinical breakpoints. We suggest that the present clinical breakpoints should be re-evaluated, taking into account wild-type MIC distributions and available pharmacokinetic data.

Challenging a dogma: antimicrobial susceptibility testing breakpoints for Mycobacterium tuberculosis

The rise in multidrug-resistant tuberculosis makes it increasingly important that antimicrobial susceptibility testing of Mycobacterium tuberculosis produce clinically meaningful and technically reproducible results. Unfortunately, this is not always the case because mycobacteriology specialists have not followed generally accepted modern principles for the establishment of susceptibility breakpoints for bacterial and fungal pathogens. These principles specifically call for a definition of the minimum inhibitory concentrations (MICs) applicable to organisms without resistance mechanisms (also known as wild-type MIC distributions), to be used in combination with data on clinical outcomes, pharmacokinetics and pharmacodynamics. In a series of papers the authors have defined tentative wild-type MIC distributions for M. tuberculosis and hope that other researchers will follow their example and provide confirmatory data. They suggest that some breakpoints are in need of revision because they either (i) bisect the wild-type distribution, which leads to poor reproducibility in antimicrobial susceptibility testing, or (ii) are substantially higher than the MICs of wild-type organisms without supporting clinical evidence, which may result in some strains being falsely reported as susceptible. The authors recommend, in short, that susceptibility breakpoints for antituberculosis agents be systematically reviewed and revised, if necessary, using the same modern tools now accepted for all other bacteria and fungi by the scientific community and by the European Medicines Agency and the European Centre for Disease Prevention and Control. For several agents this would greatly improve the accuracy and reproducibility of antimicrobial susceptibility testing of M. tuberculosis.