Gradient-free maximum likelihood parameter estimation with particle filters

Poyiadjis, George; Singh, Sumeetpal S.; Doucet, Arnaud

doi:10.1109/acc.2006.1657187

Cited by 22 publications

(39 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This is wasteful and statistically harmful. See Figure 1 of [21] for a beautiful depiction of this problem.…”

Section: And Is Known As Sequential Importance Sampling (Sis)mentioning

confidence: 99%

“…To eliminate the problems discussed in the previous section, we will perform particle filtering directly on the marginal distribution p(x t |y 1:t ) instead of on the joint space [20], [25], [21]. To do so, we begin by noting that the predictive density can be obtained by marginalization: p θ (x t |y 1:t−1 ) = p(x t |x t−1 )p θ (x t−1 |y 1:t−1 )dx t−1 (3) To simplify the exposition later on, we introduce the following notation [21]:…”

Section: B the Marginal Space Approach 1) Marginal Filtering And Filmentioning

confidence: 99%

“…To do so, we begin by noting that the predictive density can be obtained by marginalization: p θ (x t |y 1:t−1 ) = p(x t |x t−1 )p θ (x t−1 |y 1:t−1 )dx t−1 (3) To simplify the exposition later on, we introduce the following notation [21]:…”

Section: B the Marginal Space Approach 1) Marginal Filtering And Filmentioning

confidence: 99%

“…2) Monte Carlo Implementation: We are now ready to present the particle algorithm of [21] for approximating the filter derivative efficiently. Assume that at time t − 1, we have a Monte Carlo approximations of the filter and its gradient.…”

Section: B the Marginal Space Approach 1) Marginal Filtering And Filmentioning

confidence: 99%

“…This has only become possible very recently following new advances in particle simulation [20], [21], which will be presented in Section III.B. Static parameter estimation in nonlinear, non-Gaussian dynamic models is a formidable challenge, so it comes as no surprise that probabilistic SLAM has proved to be so demanding.…”

mentioning

confidence: 99%

See 4 more Smart Citations

Analysis of Particle Methods for Simultaneous Robot Localization and Mapping and a New Algorithm: Marginal-SLAM

Martínez-Cantín

Freitas

Castellanos

2007

Proceedings 2007 IEEE International Conference on Robotics and Automation

View full text Add to dashboard Cite

Abstract-This paper presents a new particle method, with stochastic parameter estimation, to solve the SLAM problem. The underlying algorithm is rooted on a solid probabilistic foundation and is guaranteed to converge asymptotically, unlike many existing popular approaches. Moreover, it is efficient in storage and computation. The new algorithm carries out filtering only in the marginal filtering space, thereby allowing for the recursive computation of low variance estimates of the map. The paper provides mathematical arguments and empirical evidence to substantiate the fact that the new method represents an improvement over the existing particle filtering approaches for SLAM, which work on the joint path state space.

show abstract

“…This is wasteful and statistically harmful. See Figure 1 of [21] for a beautiful depiction of this problem.…”

Section: And Is Known As Sequential Importance Sampling (Sis)mentioning

confidence: 99%

Section: B the Marginal Space Approach 1) Marginal Filtering And Filmentioning

confidence: 99%

Section: B the Marginal Space Approach 1) Marginal Filtering And Filmentioning

confidence: 99%

Section: B the Marginal Space Approach 1) Marginal Filtering And Filmentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

Analysis of Particle Methods for Simultaneous Robot Localization and Mapping and a New Algorithm: Marginal-SLAM

Martínez-Cantín

Freitas

Castellanos

2007

Proceedings 2007 IEEE International Conference on Robotics and Automation

View full text Add to dashboard Cite

show abstract

Simultaneous Perturbation and Finite Difference Methods

Bhatnagar

2011

Wiley Encyclopedia of Operations Research and Management Science

View full text Add to dashboard Cite

This article presents a survey of simultaneous perturbation and finite difference algorithms. One of the most important in this category of algorithms is the simultaneous perturbation stochastic approximation (SPSA) algorithm that has been used in a wide range of settings. The article presents an overview of the theory behind SPSA as well as the recent development of other finite‐difference algorithms along the lines of SPSA. The article also gives an overview of the applications of SPSA and SPSA‐type algorithms in various disciplines of engineering and science.

show abstract

Particle filtering and marginalization for parameter identification in structural systems

Olivier

Smyth

2016

Struct. Control Health Monit.

View full text Add to dashboard Cite

In structural health monitoring, one wishes to use available measurements from a structure to assess structural condition, localize damage if present, and quantify remaining life. Nonlinear system identification methods are considered that use a parametric, nonlinear, physics-based model of the system, cast in the state-space framework. Various nonlinear filters and parameter learning algorithms can then be used to recover the parameters and quantify uncertainty. This paper focuses on the particle filter (PF), which shows the advantage of not assuming Gaussianity of the posterior densities. However, the PF is known to behave poorly in high dimensional spaces, especially when static parameters are added to the state vector. To improve the efficiency of the PF, the concept of Rao-Blackwellisation is applied, that is, we use conditional linearities present in the equations to marginalize out some of the states/parameters and infer their conditional posterior pdf using the Kalman filtering equations. This method has been studied extensively in the particle filtering literature, and we start our discussion by improving upon and applying two well-known algorithms on a benchmark structural system. Then, noticing that in structural systems, high nonlinearities are often localized while the remaining equations are bilinear in the states and parameters, a novel algorithm is proposed, which combines this marginalization approach with a second-order extended Kalman filter. This new approach enables us to marginalize out all the states/parameters, which do not contribute to any high nonlinearity in the equations and, thus, improve identification of the unknown parameters.The idea is then to use a parametric model of the structure (using the equations of motion) that can be discretized in time and cast in state-space form. In the event that there is uncertainty in the excitation, environmental disturbance, or modeling error, some process noise may exist in the system equation. The response of structural systems is assumed to be measured at (or between) certain degrees of freedom. Because of real-life imperfections and sensor noise, one must also consider a potential measurement noise in the measurement equations. Nonlinear system identification tools are then used to recover the parameters of the model (stiffness, damping, and possible nonlinear parameters) and thus identify possible damage.For state filtering, that is, inference of the hidden (non-measured) states, the unscented Kalman filter (UKF) and the particle filter (PF) are both extensively studied in the literature. For parameter estimation, many different algorithms can be used: point estimates can be obtained via optimization algorithms (minimization of an error function, maximization of the likelihood, and expectation-maximization algorithm), or one can perform Bayesian inference, that is, infer the whole posterior density function (pdf) of the parameters knowing the measurements (Markov Chain Monte Carlo methods, joint state/parameter filters).However, learning al...

show abstract

Gradient-free maximum likelihood parameter estimation with particle filters

Cited by 22 publications

References 18 publications

Analysis of Particle Methods for Simultaneous Robot Localization and Mapping and a New Algorithm: Marginal-SLAM

Analysis of Particle Methods for Simultaneous Robot Localization and Mapping and a New Algorithm: Marginal-SLAM

Simultaneous Perturbation and Finite Difference Methods

Particle filtering and marginalization for parameter identification in structural systems

Contact Info

Product

Resources

About