High-dimensional Linear Problems Research Articles

GOI: A Novel Design for Vehicle Positioning and Trajectory Prediction Under Urban Environments

In this paper, we propose a new paradigm of GPS and OBD Integration (GOI) based on GPS receiver and on-board diagnostics (OBD) reader, which offers a feasible way for large-scale trajectory collection especially suitable for private cars. With GOI, we adopt GPS receiver to obtain vehicle location and design a low-cost OBD reader to retrieve the driving information, such as vehicle velocity and steering direction from the in-vehicle motion sensors through the OBD interface. In order to deal with the inherent errors of the motion sensors and the GPS outage issue, we propose a vehicle positioning approach by employing supporting vector machine for regression (SVR) to achieve accurate and reliable vehicle position and trajectory prediction based on GOI. The low-dimensional non-linear GOI trajectory data is transferred into high-dimensional linear problems by using kernel function so that it reduces the computational complexity and overcomes the problem of dimension disaster. Furthermore, we design a local shrinking particle swarm optimization algorithm to cope with the parameter selection for SVR-based GOI approach. Experiments from real urban environment demonstrate the effectiveness of our approach, which outperforms the existing methods in terms of prediction accuracy under various GPS outages and road conditions.

An algorithm for total variation regularization in high-dimensional linear problems

This paper describes an iterative algorithm for high-dimensional linear inverse problems, which is regularized by a differentiable discrete approximation of the total variation (TV) penalty. The algorithm is an interlaced iterative method based on optimization transfer with a separable quadratic surrogate for the TV penalty. The surrogate cost function is optimized using the block iterative regularized algebraic reconstruction technique (RSART). A proof of convergence is given and convergence is illustrated by numerical experiments with simulated parallel-beam computerized tomography (CT) data. The proposed method provides a block-iterative and convergent, hence efficient and reliable, algorithm to investigate the effects of TV regularization in applications such as CT.