## An Optimal Filtering Algorithm for Non-Parametric Observation Models in Robot Localization

Citations: | 3 - 2 self |

### BibTeX

@MISC{Blanco_anoptimal,

author = {Jose-luis Blanco and Javier González and Juan-antonio Fernández-madrigal},

title = {An Optimal Filtering Algorithm for Non-Parametric Observation Models in Robot Localization},

year = {}

}

### OpenURL

### Abstract

Abstract — The lack of a parameterized observation model in robot localization using occupancy grids requires the application of sampling-based methods, or particle filters. This work addresses the problem of optimal Bayesian filtering for dynamic systems with observation models that cannot be approximated properly as any parameterized distribution, which includes localization and SLAM with occupancy grids. By integrating ideas from previous works on adaptive sample size, auxiliary particle filters, and rejection sampling, we derive a new particle filter algorithm that enables the usage of the optimal proposal distribution to estimate the true posterior density of a non-parametric dynamic system. Our solution avoids approximations adopted in previous approaches at the cost of a higher computational burden. We present simulations and experimental results for a real robot showing the suitability of the method for localization. I.

### Citations

8564 |
Elements of Information Theory
- Cover, Thomas
- 2006
(Show Context)
Citation Context ...p t–1: [ i] { xt −1} i= 1... Mt−1 Auxiliary particles [ i, j] [ i, j] { x� t 1 , � − ωt−1 } [ i, j] [ i, j] { x� t , � ωt } [ k ] { xt } k = 1... Mt j= 1... N j= 1... N Particles for time step t: [1] =-=[2]-=- [1,1] [1,N] [2,1] [2,N] … … … … … [M t-1 ] [M t-1 ,1] [M t-1 ,N] … Group 1 Group 2 Group Mt-1 … … … … [1] [2] [3] [Mt] … … … Fig. 1. The theoretic model of our optimal particle filter. An initial set... |

2113 |
A New Approach to Linear Filtering and Prediction Problems
- Kalman
- 1960
(Show Context)
Citation Context ...uentially by applying the Bayes rule: p(xt|z t ,u t ) ∝ Prior Observation likelihood { }} { { }} { p(zt|xt) p(xt|z t−1 ,u t ) (1) Under the assumptions of linearity and Gaussianity, the Kalman filter =-=[13]-=- represents a closed-form, optimal solution to (1). Some improvements have been proposed to overcome the assumption of linearity, where the most widely known is the Extended Kalman Filter (EKF) [12]. ... |

1148 | Tutorial on Particle Filters for Online Nonlinear/Non-Gaussian Bayesian Tracking
- Arulampalam, “A
- 2002
(Show Context)
Citation Context ...ELATED RESEARCH In this section we briefly review the applications of particle filters to robot localization and SLAM. A more comprehensive review of particle filter techniques can be found elsewhere =-=[1]-=-, [5]. The probabilistic approach to localization and SLAM includes the estimation of the posterior distribution of the robot poses up to the current instant of time given the whole history of availab... |

1060 |
Novel approach to nonlinear/non-gaussian bayesian state estimation
- Gordon, Salmond, et al.
- 1993
(Show Context)
Citation Context ...trast to analytical models available for landmark maps [3], [4]. Standard particle filter algorithms like the Sequential Importance Sampling (SIS) filter [20] and the SIS with resampling (SIR) filter =-=[10]-=-, [21] allow us to perform sequential filtering provided only the ability to draw samples according to the system transition model (the robot motion model) and to pointwise evaluate the observation mo... |

892 |
Sequential Monte Carlo methods in practice, volume 1
- Doucet, Freitas, et al.
- 2001
(Show Context)
Citation Context ... as occupancy grid-maps [17], forcing a samplebased representation of the joint probability density. In this case, sequential estimation is carried-out by Monte-Carlo simulations, or particle filters =-=[5]-=-. In this paper we focus on the problem of localization using occupancy grids, although the proposed method can be also applied to other representations, e.g. topological maps. Some advantages of occu... |

780 |
Probalistic Robotics
- Thrun, Burgard, et al.
- 2005
(Show Context)
Citation Context ...CTION Two prominent applications of Bayesian sequential estimation have received a huge attention in robotics research, namely localization and simultaneous localization and map building (SLAM) [22], =-=[23]-=-. The former consists of estimating the pose of a mobile robot within a known environment, whereas in SLAM the map is also estimated while performing self-localization. In both problems the choice for... |

658 | On sequential monte carlo sampling methods for bayesian filtering
- Doucet, Godsill, et al.
- 2000
(Show Context)
Citation Context ...se sensors such as laser range finders. A theoretical solution that enables the efficient representation of probability densities through perfectly distributed particles was proposed by Doucet et al. =-=[7]-=-, consisting of an optimal proposal distribution from which to draw samples at each time step. However, a direct application of this approach requires an observation model with a parametric distributi... |

513 | Filtering via simulation: Auxiliary particle
- Pitt, Shephard
- 1999
(Show Context)
Citation Context ...models can perform optimal filtering due the approximate nature of Monte-Carlo methods. Our method is grounded on previous works related to optimal sampling [6], [7], auxiliary particle filters (APF) =-=[19]-=-, rejection sampling [14], and adaptive sample size for robot localization [8]. In the context of mobile robots, the proposed algorithm represents an important contribution since no Gaussian approxima... |

454 | Sequential monte carlo methods for dynamic systems
- Liu, Chen
- 1998
(Show Context)
Citation Context ...l filtering due the approximate nature of Monte-Carlo methods. Our method is grounded on previous works related to optimal sampling [6], [7], auxiliary particle filters (APF) [19], rejection sampling =-=[14]-=-, and adaptive sample size for robot localization [8]. In the context of mobile robots, the proposed algorithm represents an important contribution since no Gaussian approximations are assumed while g... |

448 | Fast SLAM: A Factored Solution to the Simultaneous Localization and Mapping
- erlo, Thrun, et al.
- 2002
(Show Context)
Citation Context ...tion from which to draw samples at each time step. However, a direct application of this approach requires an observation model with a parametric distribution from which to draw random samples (as in =-=[15]-=-), whereas for grid maps we can evaluate it only pointwise [23]. The contribution of this work is a new particle filter algorithm that, given the same requirements as the original SIS and SIR algorith... |

426 | New Extension of the Kalman Filter to Nonlinear Systems - Julier, Uhlmann - 1997 |

406 |
High Resolution Maps from Wide Angle Sonar
- Moravec, Elfes
- 1985
(Show Context)
Citation Context ..., SLAM with landmark maps can be approached well through Gaussian filters such as the EKF [12]. However, these methods are not applicable to other types of map representations, as occupancy grid-maps =-=[17]-=-, forcing a samplebased representation of the joint probability density. In this case, sequential estimation is carried-out by Monte-Carlo simulations, or particle filters [5]. In this paper we focus ... |

347 | A solution to the simultaneous localization and map building (slam) problem
- Gamini, Newman, et al.
- 2001
(Show Context)
Citation Context ...thod that can be applied. In the case of landmarks, the map can be modeled by multivariate Gaussian distributions with Gaussian observation models, obtained by solving the problem of association [3], =-=[4]-=-. Thus, SLAM with landmark maps can be approached well through Gaussian filters such as the EKF [12]. However, these methods are not applicable to other types of map representations, as occupancy grid... |

288 | Robotic mapping: A survey
- Thrun
(Show Context)
Citation Context ...NTRODUCTION Two prominent applications of Bayesian sequential estimation have received a huge attention in robotics research, namely localization and simultaneous localization and map building (SLAM) =-=[22]-=-, [23]. The former consists of estimating the pose of a mobile robot within a known environment, whereas in SLAM the map is also estimated while performing self-localization. In both problems the choi... |

277 | Monte Carlo Localization: Efficient position estimation for mobile robots - Fox, Burgard, et al. - 1999 |

263 | MonoSLAM: Real-Time Single Camera SLAM
- Davison, Reid, et al.
(Show Context)
Citation Context ...on method that can be applied. In the case of landmarks, the map can be modeled by multivariate Gaussian distributions with Gaussian observation models, obtained by solving the problem of association =-=[3]-=-, [4]. Thus, SLAM with landmark maps can be approached well through Gaussian filters such as the EKF [12]. However, these methods are not applicable to other types of map representations, as occupancy... |

253 | Raoblackwellised particle filtering for dynamic bayesian networks
- Doucet, Freitas, et al.
- 2000
(Show Context)
Citation Context ...lly, no particle filter without parametric models can perform optimal filtering due the approximate nature of Monte-Carlo methods. Our method is grounded on previous works related to optimal sampling =-=[6]-=-, [7], auxiliary particle filters (APF) [19], rejection sampling [14], and adaptive sample size for robot localization [8]. In the context of mobile robots, the proposed algorithm represents an import... |

135 | Bayesian Map Learning in Dynamic Environments
- Murphy
- 1999
(Show Context)
Citation Context ...ND SLAM System models Linear Gaussian Non-Linear Gaussian Non-Linear Non-Gaussian Non-Linear Gaussian Non-Linear Non-Gaussian Algorithms Kalman Filter [13] EKF [12], UKF [24] SIR [10], APF [19], RBPF =-=[18]-=-, FastSLAM [16] FastSLAM 2.0 [15], Grisetti et al. [11] This work with the evaluation, at each particle, of the observation model p(zt|x t,[i] ,z t−1 ,u t ). Note how the SIS filter requires only the ... |

126 |
der Merwe. The unscented kalman filter for nonlinear estimation
- Wan, van
- 2000
(Show Context)
Citation Context ...Optimal Optimal LOCALIZATION AND SLAM System models Linear Gaussian Non-Linear Gaussian Non-Linear Non-Gaussian Non-Linear Gaussian Non-Linear Non-Gaussian Algorithms Kalman Filter [13] EKF [12], UKF =-=[24]-=- SIR [10], APF [19], RBPF [18], FastSLAM [16] FastSLAM 2.0 [15], Grisetti et al. [11] This work with the evaluation, at each particle, of the observation model p(zt|x t,[i] ,z t−1 ,u t ). Note how the... |

97 | Adapting the sample size in particle filters through KLD-sampling
- Fox
- 2003
(Show Context)
Citation Context ...methods. Our method is grounded on previous works related to optimal sampling [6], [7], auxiliary particle filters (APF) [19], rejection sampling [14], and adaptive sample size for robot localization =-=[8]-=-. In the context of mobile robots, the proposed algorithm represents an important contribution since no Gaussian approximations are assumed while generating new particles, which is the case of previou... |

97 | Improved techniques for grid mapping with rao-blackwellized particle filters
- Grisetti, Stachniss, et al.
- 2007
(Show Context)
Citation Context ... context of mobile robots, the proposed algorithm represents an important contribution since no Gaussian approximations are assumed while generating new particles, which is the case of previous works =-=[11]-=-, [15]. Moreover, our method is based on the formulation of a general particle filter, thus it does not depend on the reliability of scan matching as previous works and can be applied to a wider varie... |

37 | A noniterative sampling/importance resampling alternative to the data augmentation algorithm for creating a few imputations when the fraction of missing information is modest: the SIR algorithm. Discussion of - Rubin - 1987 |