Getting Started with Particle Metropolis-Hastings for Inference in Nonlinear Dynamical Models

This tutorial provides a gentle introduction to the particle Metropolis-Hastings (PMH) algorithm for parameter inference in nonlinear state-space models together with a software implementation in the statistical programming language R. We employ a step-by-step approach to develop an implementation of the PMH algorithm (and the particle filter within) together with the reader. This final implementation is also available as the package pmhtutorial in the CRAN repository. Throughout the tutorial, we provide some intuition as to how the algorithm operates and discuss some solutions to problems that might occur in practice. To illustrate the use of PMH, we consider parameter inference in a linear Gaussian state-space model with synthetic data and a nonlinear stochastic volatility model with real-world data.Comment: 41 pages, 7 figures. In press for Journal of Statistical Software. Source code for R, Python and MATLAB available at: https://github.com/compops/pmh-tutoria

Evaluating Data Assimilation Algorithms

Data assimilation leads naturally to a Bayesian formulation in which the posterior probability distribution of the system state, given the observations, plays a central conceptual role. The aim of this paper is to use this Bayesian posterior probability distribution as a gold standard against which to evaluate various commonly used data assimilation algorithms. A key aspect of geophysical data assimilation is the high dimensionality and low predictability of the computational model. With this in mind, yet with the goal of allowing an explicit and accurate computation of the posterior distribution, we study the 2D Navier-Stokes equations in a periodic geometry. We compute the posterior probability distribution by state-of-the-art statistical sampling techniques. The commonly used algorithms that we evaluate against this accurate gold standard, as quantified by comparing the relative error in reproducing its moments, are 4DVAR and a variety of sequential filtering approximations based on 3DVAR and on extended and ensemble Kalman filters. The primary conclusions are that: (i) with appropriate parameter choices, approximate filters can perform well in reproducing the mean of the desired probability distribution; (ii) however they typically perform poorly when attempting to reproduce the covariance; (iii) this poor performance is compounded by the need to modify the covariance, in order to induce stability. Thus, whilst filters can be a useful tool in predicting mean behavior, they should be viewed with caution as predictors of uncertainty. These conclusions are intrinsic to the algorithms and will not change if the model complexity is increased, for example by employing a smaller viscosity, or by using a detailed NWP model

Model-based multirate Kalman filtering approach for optimal two-dimensional signal reconstruction from noisy subband systems

Conventional synthesis filters in subband systems lose their optimality when additive noise (due, for example, to signal quantization) disturbs the subband components. The multichannel representation of subband signals is combined with the statistical model of input signal to derive the multirate state-space model for the filter bank system with additive subband noises. Thus the signal reconstruction problem in subband systems can be formulated as the process of optimal state estimation in the equivalent multirate state-space model. Incorporated with the vector dynamical model, a 2-D multirate state-space model suitable for 2-D Kalman filtering is developed. The performance of the proposed 2-D multirate Kalman filter can be further improved through adaptive segmentation of the object plane. The object plane is partitioned into disjoint regions based on their spatial activity, and different vector dynamical models are used to characterize the nonstationary object-plane distributions. Finally, computer simulations with the proposed 2-D multirate Kalman filter give favorable results. ©1998 Society of Photo-Optical instrumentation Engineers.published_or_final_versio

GPU Accelerated Prognostics

Prognostic methods enable operators and maintainers to predict the future performance for critical systems. However, these methods can be computationally expensive and may need to be performed each time new information about the system becomes available. In light of these computational requirements, we have investigated the application of graphics processing units (GPUs) as a computational platform for real-time prognostics. Recent advances in GPU technology have reduced cost and increased the computational capability of these highly parallel processing units, making them more attractive for the deployment of prognostic software. We present a survey of model-based prognostic algorithms with considerations for leveraging the parallel architecture of the GPU and a case study of GPU-accelerated battery prognostics with computational performance results

Metropolis-Hastings prefetching algorithms

Prefetching is a simple and general method for single-chain parallelisation of the Metropolis-Hastings algorithm based on the idea of evaluating the posterior in parallel and ahead of time. In this paper improved Metropolis-Hastings prefetching algorithms are presented and evaluated. It is shown how to use available information to make better predictions of the future states of the chain and increase the efficiency of prefetching considerably. The optimal acceptance rate for the prefetching random walk Metropolis-Hastings algorithm is obtained for a special case and it is shown to decrease in the number of processors employed. The performance of the algorithms is illustrated using a well-known macroeconomic model. Bayesian estimation of DSGE models, linearly or nonlinearly approximated, is identified as a potential area of application for prefetching methods. The generality of the proposed method, however, suggests that it could be applied in many other contexts as well.Prefetching; Metropolis-Hastings; Parallel Computing; DSGE models; Optimal acceptance rate

Detection-assisted Object Tracking by Mobile Cameras

Tracking-by-detection is a class of new tracking approaches that utilizes recent development of object detection algorithms. This type of approach performs object detection for each frame and uses data association algorithms to associate new observations to existing targets. Inspired by the core idea of the tracking-by-detection framework, we propose a new framework called detection-assisted tracking where object detection algorithm provides help to the tracking algorithm when such help is necessary; thus object detection, a very time consuming task, is performed only when needed. The proposed framework is also able to handle complicated scenarios where cameras are allowed to move, and occlusion or multiple similar objects exist. We also port the core component of the proposed framework, the detector, onto embedded smart cameras. Contrary to traditional scenarios where the smart cameras are assumed to be static, we allow the smart cameras to move around in the scene. Our approach employs histogram of oriented gradients (HOG) object detector for foreground detection, to enable more robust detection on mobile platform. Traditional background subtraction methods are not suitable for mobile platforms where the background changes constantly. Adviser: Senem Velipasalar and Mustafa Cenk Gurso

Drone Obstacle Avoidance and Navigation Using Artificial Intelligence

This thesis presents an implementation and integration of a robust obstacle avoidance and navigation module with ardupilot. It explores the problems in the current solution of obstacle avoidance and tries to mitigate it with a new design. With the recent innovation in artificial intelligence, it also explores opportunities to enable and improve the functionalities of obstacle avoidance and navigation using AI techniques. Understanding different types of sensors for both navigation and obstacle avoidance is required for the implementation of the design and a study of the same is presented as a background. A research on an autonomous car is done for better understanding autonomy and learning how it is solving the problem of obstacle avoidance and navigation. The implementation part of the thesis is focused on the design of a robust obstacle avoidance module and is tested with obstacle avoidance sensors such as Garmin lidar and Realsense r200. Image segmentation is used to verify the possibility of using the convolutional neural network for better understanding the nature of obstacles. Similarly, the end to end control with a single camera input using a deep neural network is used for verifying the possibility of using AI for navigation. In the end, a robust obstacle avoidance library is developed and tested both in the simulator and real drone. Image segmentation is implemented, deployed and tested. A possibility of an end to end control is also verified by obtaining a proof of concept