The iterated auxiliary particle filter

We present an offline, iterated particle filter to facilitate statistical inference in general state space hidden Markov models. Given a model and a sequence of observations, the associated marginal likelihood L is central to likelihood-based inference for unknown statistical parameters. We define a class of "twisted" models: each member is specified by a sequence of positive functions psi and has an associated psi-auxiliary particle filter that provides unbiased estimates of L. We identify a sequence psi* that is optimal in the sense that the psi*-auxiliary particle filter's estimate of L has zero variance. In practical applications, psi* is unknown so the psi*-auxiliary particle filter cannot straightforwardly be implemented. We use an iterative scheme to approximate psi*, and demonstrate empirically that the resulting iterated auxiliary particle filter significantly outperforms the bootstrap particle filter in challenging settings. Applications include parameter estimation using a particle Markov chain Monte Carlo algorithm

The adaptive patched cubature filter and its implementation

There are numerous contexts where one wishes to describe the state of a randomly evolving system. Effective solutions combine models that quantify the underlying uncertainty with available observational data to form scientifically reasonable estimates for the uncertainty in the system state. Stochastic differential equations are often used to mathematically model the underlying system. The Kusuoka-Lyons-Victoir (KLV) approach is a higher order particle method for approximating the weak solution of a stochastic differential equation that uses a weighted set of scenarios to approximate the evolving probability distribution to a high order of accuracy. The algorithm can be performed by integrating along a number of carefully selected bounded variation paths. The iterated application of the KLV method has a tendency for the number of particles to increase. This can be addressed and, together with local dynamic recombination, which simplifies the support of discrete measure without harming the accuracy of the approximation, the KLV method becomes eligible to solve the filtering problem in contexts where one desires to maintain an accurate description of the ever-evolving conditioned measure. In addition to the alternate application of the KLV method and recombination, we make use of the smooth nature of the likelihood function and high order accuracy of the approximations to lead some of the particles immediately to the next observation time and to build into the algorithm a form of automatic high order adaptive importance sampling.Comment: to appear in Communications in Mathematical Sciences. arXiv admin note: substantial text overlap with arXiv:1311.675

Investigating Machine Learning Techniques for Gesture Recognition with Low-Cost Capacitive Sensing Arrays

Machine learning has proven to be an effective tool for forming models to make predictions based on sample data. Supervised learning, a subset of machine learning, can be used to map input data to output labels based on pre-existing paired data. Datasets for machine learning can be created from many different sources and vary in complexity, with popular datasets including the MNIST handwritten dataset and CIFAR10 image dataset. The focus of this thesis is to test and validate multiple machine learning models for accurately classifying gestures performed on a low-cost capacitive sensing array. Multiple neural networks are trained using gesture datasets obtained from the capacitance board. In this paper, I train and compare different machine learning models on recognizing gesture datasets. Learning hyperparameters are also adjusted for results. Two datasets are used for the training: one containing simple gestures and another containing more complicated gestures. Accuracy and loss for the models are calculated and compared to determine which models excel at recognizing performed gestures

Hybrid Filter Scheme for Optimizing Indoor Mobile Cooperative Tracking System

The precise indoor tracking system using Xbee signal strength protocol has become a potential research to the WSN applications. The main aspects for the success tracking system is accuracy performance based on location estimation. The improvement of location estimation is complicated issue, especially using RSSI with low accuracy due to the signal attenuation from multipath effect at indoor propagation. Hence, many existing research typically focused on specific methods for providing improvement schemes at tracking system area. Then, we propose hybrid filter schemes, including extended gradient filter (EGF) for filtering noise signal based distance modification, and modified extended Kalman filter (MIEKF) will be combined with trilateration for filtering the error position estimation. Using mobile cooperative tracking scenario refers to our previous work, the proposed hybrid filter scheme which is called modified iterated extended gradient Kalman filter (MIEGKF) can optimize the error estimation around 41.28% reduction with 0.63 meters MSE (mean square error) value