The manifold particle filter for state estimation on high-dimensional implicit manifolds

Sampling density design for particle filters

Visual tracking is one of the key tasks in computer vision. The particle filter algorithm has been extensively used to tackle this problem due to its flexibility. However the conventional particle filter uses system transition as the proposal distribution, frequently resulting in poor priors for the filtering step. The main reason is that it is difficult, if not impossible, to accurately model the target's motion. Such a proposal distribution does not take into account the current observations. It is not a trivial task to devise a satisfactory proposal distribution for the particle filter. In this paper we advance a general augmented particle filtering framework for designing the optimal proposal distribution. The essential idea is to augment a second filter's estimate into the proposal distribution design. We then show that several existing improved particle filters can be rationalised within this general framework. Based on this framework we further propose variant algorithms for robust and efficient visual tracking. Experiments indicate that the augmented particle filters are more efficient and robust than the conventional particle filter.

Robust particle filter for state estimation in presence of bounded but uncertain parameters based on ellipsoidal set membership approach

The particle filter has attracted considerable attention in visual tracking due to its relaxation of the linear and Gaussian restrictions in the state space model. It is thus more flexible than the Kalman filter. However, the conventional particle filter uses system transition as the proposal distribution, leading to poor sampling efficiency and poor performance in visual tracking. It is not a trivial task to design satisfactory proposal distributions for the particle filter. In this paper, we introduce an improved particle filtering framework into visual tracking, which combines the unscented Kalman filter and the auxiliary particle filter. The efficient unscented auxiliary particle filter (UAPF) uses the unscented transformation to predict one-step ahead likelihood and produces more reasonable proposal distributions, thus reducing the number of particles required and substantially improving the tracking performance. Experiments on real video sequences demonstrate that the UAPF is computationally efficient and outperforms the conventional particle filter and the auxiliary particle filter.KeywordsParticle FilterImportance SamplingObservation ModelVisual TrackingUnscented Kalman FilterThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The human respiratory movement seriously affects the precision of the robotized radiotherapy treatment for lung cancer. In order to reduce the influence of respiratory movement, the most effective method is real-time tracking of respiratory tumor motion, which adopts tracking algorithm to predict the location of the tumor, and adjust the treatment beam to catch the motion of the target. This paper utilizes the particle filter as tracking algorithm to predict the tumor motion trajectory. Firstly, the principle and process of particle filter algorithm are introduced; Secondly, the probability correlation model based on UT transform are proposed as the observation model of the particle filter; Finally, the conventional particle filter and the UT transform modeling are used to predict the location of the tumor with respiratory motion. The effectiveness and accuracy of particle filter algorithm based on UT transform is verified by error analysis. The experiment results show that the particle filter algorithm based on UT transform has stronger robustness and higher prediction precision compared with the linear estimation and the traditional particle filter, so it can meet the requirements of real-time tumor tracking for radiotherapy robots.

We study efficient importance sampling techniques for particle filtering (PF) when either (a) the observation likelihood (OL) is frequently multimodal or heavy-tailed, or (b) the state space dimension is large or both. When the OL is multimodal, but the state transition pdf (STP) is narrow enough, the optimal importance density is usually unimodal. Under this assumption, many techniques have been proposed. But when the STP is broad, this assumption does not hold. We study how existing techniques can be generalized to situations where the optimal importance density is multimodal, but is unimodal conditioned on a part of the state vector. Sufficient conditions to test for the unimodality of this conditional posterior are derived. Our result is directly extendable to testing for unimodality of any posterior. The number of particles N to accurately track using a PF increases with state space dimension, thus making any regular PF impractical for large dimensional tracking problems. But in most such problems, most of the state change occurs in only a few dimensions, while the change in the rest of the dimensions is small. Using this property, we propose to replace importance sampling from a large part of the state space (whose conditional posterior is narrow enough) by just tracking the mode of the conditional posterior. This introduces some extra error, but it also greatly reduces the importance sampling dimension. The net effect is much smaller error for a given N, especially when the available N is small. An important class of large dimensional problems with multimodal OL is tracking spatially varying physical quantities such as temperature or pressure in a large area using a network of sensors which may be nonlinear and/or may have nonnegligible failure probabilities. Improved performance of our proposed algorithms over existing PFs is demonstrated for this problem.

High dimensional pose state space is the main challenge in articulated human pose tracking which makes pose analysis computationally expensive or even infeasible. In this paper, we propose a novel generative approach in the framework of evolutionary computation, by which we try to widen the bottleneck with effective search strategy embedded in the extracted state subspace. Firstly, we use ISOMAP to learn the low-dimensional latent space of pose state in the aim of both reducing dimensionality and extracting the prior knowledge of human motion simultaneously. Then, we propose a manifold reconstruction method to establish smooth mappings between the latent space and original space, which enables us to perform pose analysis in the latent space. In the search strategy, we adopt a new evolutionary approach, clonal selection algorithm (CSA), for pose optimization. We design a CSA based method to estimate human pose from static image, which can be used for initialization of motion tracking. In order to make CSA suitable for motion tracking, we propose a sequential CSA (S-CSA) algorithm by incorporating the temporal continuity information into the traditional CSA. Actually, in a Bayesian inference view, the sequential CSA algorithm is in essence a multilayer importance sampling based particle filter. Our methods are demonstrated in different motion types and different image sequences. Experimental results show that our CSA based pose estimation method can achieve viewpoint invariant 3D pose reconstruction and the S-CSA based motion tracking method can achieve accurate and stable tracking of 3D human motion.

Robust particle filtering with enhanced outlier resilience and real-time disturbance compensation

The implicit particle filter is a sequential Monte Carlo method for data assimilation. The idea is to focus the particles onto the high probability regions of the target probability density function (pdf) so that the number of particles required for a good approximation of this pdf remains manageable, even if the dimension of the state space is large. We explain how this idea is implemented, discuss special cases of practical importance, and work out the relations of the implicit particle filter with other data assimilation methods. We illustrate the theory with six examples.

To localize mobile target timely and improve the accuracy of the target state estimation in wireless sensor networks, this paper presents a novel mobile target localization algorithm. By using the mean shift algorithm to construct the proposal distribution to make use of the current measurements, and weighting particles according to the virtual hamming distances in the particle filter, this proposed algorithm improves the accuracy of the target state estimation and reduces the necessary number of samples. It has lower computation and communication cost than the conventional particle filter because of more accurate state estimate of samples. Extensive simulation results confirm that this localization scheme outperforms conventional particle filter and its localization accuracy is comparable to the unscented particle filter, but its computation cost is 50% less than that of UPF.

This paper addresses the filtering problem in large-dimensional systems, in which conventional particle filters (PFs) remain computationally prohibitive owing to the large number of particles needed to obtain reasonable performances. To overcome this drawback, a class of multiple particle filters (MPFs) has been recently introduced in which the state-space is split into low-dimensional subspaces, and then a separate PF is applied to each subspace. In this paper, we adopt the variational Bayesian (VB) approach to propose a new MPF, the VBMPF. The proposed filter is computationally more efficient since the propagation of each particle requires generating one (new) particle only, while in the standard MPFs a set of (children) particles needs to be generated. In a numerical test, the proposed VBMPF behaves better than the PF and MPF.

Solutions to real world robotic tasks often require complex behaviors in high dimensional continuous state and action spaces. Reinforcement Learning (RL) is aimed at learning such behaviors but often fails for lack of scalability. To address this issue, Hierarchical RL (HRL) algorithms leverage hierarchical policies to exploit the structure of a task. However, many HRL algorithms rely on task specific knowledge such as a set of predefined sub-policies or sub-goals. In this paper we propose a new HRL algorithm based on information theoretic principles to autonomously uncover a diverse set of sub-policies and their activation policies. Moreover, the learning process mirrors the policys structure and is thus also hierarchical, consisting of a set of independent optimization problems. The hierarchical structure of the learning process allows us to control the learning rate of the sub-policies and the gating individually and add specific information theoretic constraints to each layer to ensure the diversification of the sub-policies. We evaluate our algorithm on two high dimensional continuous tasks and experimentally demonstrate its ability to autonomously discover a rich set of sub-policies.

This paper introduces a new recursive dialogue game framework for personalized computer-assisted language learning. A series of sub-dialogue trees are cascaded into a loop as the script for the game. At each dialogue turn there are a number of training sentences to be selected. The dialogue policy is optimized to offer the most appropriate training sentence for an individual learner at each dialogue turn considering the learning status, such that the learner can have the scores for all pronunciation units exceeding a pre-defined threshold in minimum number of turns. The policy is modeled as a Markov Decision Process (MDP) with high dimensional continuous state space. Experiments demonstrate promising results for the approach.

In this work we address the problem of inferring the height of atmospheric boundary layer from lidar data. From one hand the problem to reconstruct the boundary layer dynamics is addressed using a Bayesian statistical inference method. Both parameter estimation and classification to mixed/residual layer, are studied. Probabilistic specification of the unknown variables is deduced from measurements. Hierarchical Bayesian models are adopted to relax the prior assumptions on the unknowns. Markov chain Monte Carlo (MCMC) simulations are conducted to explore the high dimensional posterior state space. On the other hand a novel neuro-fuzzy model (Fuzzy Relational Neural Network) is used to obtain an IF-THEN reasoning scheme able to classify future observations. Experiments on real data are introduced.

Most methods for multiple object tracking in video represent the state of multi-object in a high dimensional joint state space. This leads to high computational complexity. This paper presents a method using the probability hypothesis density (PHD) filter to estimate the state of multiple objects in video. The method operates on the single object state space instead of the joint state space. A PHD recursion for visual observations with color measurements is proposed. Our method can track varying number of objects.