A review of resampling techniques in particle filtering framework

We present a computationally efficient algorithm for using variations in the ambient magnetic field to compensate for position drift in integrated odometry measurements (dead-reckoning estimates) through simultaneous localization and mapping (SLAM). When the magnetic field map is represented with a reduced-rank Gaussian process (GP) using Laplace basis functions defined in a cubical domain, analytic expressions of the gradient of the learned magnetic field become available. An existing approach for magnetic field SLAM with reduced-rank GP regression uses a Rao-Blackwellized particle filter (RBPF). For each incoming measurement, training of the magnetic field map using an RBPF has a computational complexity per time step of O(NpNm2), where Np is the number of particles, and Nm is the number of basis functions used to approximate the Gaussian process. Contrary to the existing particle filter-based approach, we propose applying an extended Kalman filter based on the gradients of our learned magnetic field map for simultaneous localization and mapping. Our proposed algorithm only requires training a single map. It, therefore, has a computational complexity at each time step of O(Nm2). We demonstrate the workings of the extended Kalman filter for magnetic field SLAM on an open-source data set from a foot-mounted sensor and magnetic field measurements collected onboard a model ship in an indoor pool. We observe that the drift compensating abilities of our algorithm are comparable to what has previously been demonstrated for magnetic field SLAM with an RBPF.

https://www.mdpi.com/1424-8220/22/8/2833/pdf?version=1649411707

An Extended Kalman Filter for Magnetic Field SLAM Using Gaussian Process Regression

Particle Filters (PFs) are Sequential Monte Carlo methods which are widely used to solve filtering problems of dynamic models under Non-Linear Non-Gaussian noise. Modern PF applications have demanding accuracy and run-time constraints that can be addressed through parallel computing. However, an efficient parallelization of PFs can only be achieved by effectively parallelizing the bottleneck: resampling and its constituent redistribution step. A pre-existing implementation of redistribute on Shared Memory Architectures (SMAs) achieves $O(\frac{N}{T}log_2N)$ time complexity over $T$ parallel cores. This redistribute implementation is, however, highly computationally intensive and cannot be effectively parallelized due to the inherently limited number of cores of SMAs. In this paper, we propose a novel parallel redistribute on OpenMP 4.5 which takes $O(\frac{N}{T} + log_2N)$ steps and fully exploits the computational power of SMAs. The proposed approach is up to six times faster than the $O(\frac{N}{T}log_2N)$ one and its implementation on GPU provides a further three-time speed-up vs its equivalent on a 32-core CPU. We also show on an exemplary PF that our redistribution is no longer the bottleneck.

A Fast Parallel Particle Filter for Shared Memory Systems

. Markov Chain Monte Carlo (MCMC) is a well-established family of algorithms primarily used in Bayesian statistics to sample from a target distribution when direct sampling is challenging. Existing work on Bayesian decision trees uses MCMC. Unforunately, this can be slow, especially when considering large volumes of data. It is hard to parallelise the accept-reject component of the MCMC. None-the-less, we propose two methods for exploiting parallelism in the MCMC: in the ﬁrst, we replace the MCMC with another numerical Bayesian approach, the Sequential Monte Carlo (SMC) sampler, which has the appealing property that it is an inherently parallel algorithm; in the second, we consider data partitioning. Both methods use multi-core processing with a High-Performance Computing (HPC) resource. We test the two methods in various study settings to determine which method is the most beneﬁcial for each test case. Experiments show that data partitioning has limited utility in the settings we consider and that the use of the SMC sampler can improve run-time (compared to the sequential implementation) by up to a factor of 343.

Parallel Approaches to Accelerate Bayesian Decision Trees

Markov Chain Monte Carlo (MCMC) is a well-established family of algorithms which are primarily used in Bayesian statistics to sample from a target distribution when direct sampling is challenging. Single instances of MCMC methods are widely considered hard to parallelise in a problem-agnostic fashion and hence, unsuitable to meet both constraints of high accuracy and high throughput. Sequential Monte Carlo (SMC) Samplers can address the same problem, but are parallelisable: they share with Particle Filters the same key tasks and bottleneck. Although a rich literature already exists on MCMC methods, SMC Samplers are relatively underexplored, such that no parallel implementation is currently available. In this paper, we first propose a parallel MPI version of the SMC Sampler, including an optimised implementation of the bottleneck, and then compare it with single-core Metropolis-Hastings. The goal is to show that SMC Samplers may be a promising alternative to MCMC methods with high potential for future improvements. We demonstrate that a basic SMC Sampler with 512 cores is up to 85 times faster or up to 8 times more accurate than Metropolis-Hastings.

A Single SMC Sampler on MPI that Outperforms a Single MCMC Sampler.

Abstract The ever-increasing capability of computational methods has resulted in their general acceptance as a key part of the materials design process. Traditionally this has been achieved using a so-called computational funnel, where increasingly accurate - and expensive – methodologies are used to winnow down a large initial library to a size which can be tackled by experiment. In this paper we present an alternative approach, using a multi-output Gaussian process to fuse the information gained from both experimental and computational methods into a single, dynamically evolving design. Common challenges with computational funnels, such as mis-ordering methods, and the inclusion of non-informative steps are avoided by learning the relationships between methods on the fly. We show this approach reduces overall optimisation cost on average by around a factor of three compared to other commonly used approaches, through evaluation on three challenging materials design problems. 

/pdf/a-multi-fidelity-machine-learning-approach-to-high-356jd1a2.pdf

A multi-fidelity machine learning approach to high throughput materials screening

Parallelising Particle Filters with Deterministic Runtime on Distributed Memory Systems

Resampling is a well-known statistical algorithm that is commonly applied in the context of Particle Filters (PFs) in order to perform state estimation for non-linear non-Gaussian dynamic models. As the models become more complex and accurate, the run-time of PF applications becomes increasingly slow. Parallel computing can help to address this. However, resampling (and, hence, PFs as well) necessarily involves a bottleneck, the redistribution step, which is notoriously challenging to parallelize if using textbook parallel computing techniques. A state-of-the-art redistribution takes O((log2N)2) computations on Distributed Memory (DM) architectures, which most supercomputers adopt, whereas redistribution can be performed in O(log2N) on Shared Memory (SM) architectures, such as GPU or mainstream CPUs. In this paper, we propose a novel parallel redistribution for DM that achieves an O(log2N) time complexity. We also present empirical results that indicate that our novel approach outperforms the O((log2N)2) approach.

Alessandro Varsi

Papers

A Fast Parallel Particle Filter for Shared Memory Systems

A multi-fidelity machine learning approach to high throughput materials screening

Parallelising Particle Filters with Deterministic Runtime on Distributed Memory Systems

A Single SMC Sampler on MPI that Outperforms a Single MCMC Sampler.

An O(log2N) Fully-Balanced Resampling Algorithm for Particle Filters on Distributed Memory Architectures