Efficient Bayesian Estimation for Localization and Mapping

Abstract

This thesis addresses the theoretical and practical development of efficient Bayesian filtering algorithms for use in robotic localization and mapping. Full Bayesian filters generally require an infinite number of parameters to maintain the full conditional probability density function (PDF), which is computationally intractable. The extended Kalman filter, Gaussian sum and particle filter are commonly used to address the above problem. The limitations of these methods are the inherent trade-off between accuracy and computational complexity, and difficulty in ensuring consistent estimation. This thesis investigates the use of degenerate Gaussian density functions to approximate the nonlinear measurement densities arising in various sensing systems, such as conical density in bearing sensors, or spherical density in ranging sensors. There are four main contributions:

First, we propose the Minimal Iterative Gaussian Estimator (MIGE), which utilizes a degenerate Gaussian density to approximate the nonlinear measurement likelihood. A degenerate Gaussian allows uncertainty to be infinite along some directions, allowing the representation of cylindrical and planar likelihood functions. A minimal parametric representation of the Gaussian likelihood function is developed, which allows for simple measurement likelihood update. Through Monte Carlo simulation, we show improved accuracy and consistency for bearing-only localization, while using the least amount of memory and computational time, when compared to existing popular filters.

Second, the MIGE algorithm is applied to improve the performance of Time Difference of Arrival (TDOA) and Frequency Difference of Arrival (FDOA) localization. TDOA is a differenced range measurement forming a hyperboloid distribution. FDOA is a pseudo bearing measurement forming conical distributions for a stationary emitter. Existing methods typically utilize linearization methods by computing Jacobians. The MIGE-based method is shown to better approximate the measurement density. Outliers may also be present in real-data experiments, which may degrade estimator's performance. It is shown that MIGE can effectively handle the outliers by utilizing a bounding box method. Simulations and experiments using real data collected from sensors (receivers) and a target (radio-station) demonstrate the improved localization accuracy.

Third, the MIGE algorithm is applied to improve the performance of visual simultaneous localization and mapping (SLAM). The visual mapping process requires three-dimensional triangulation of scene points. We apply MIGE by utilizing the cylindrical degenerate Gaussian for the triangulation with minimal parametric representation. Next, the Bayes Dense Flow (BDF) algorithm is proposed for a SLAM front-end module to address the difficulty of feature-limited scenes in a probabilistic framework. A new Mahalanobis eight-point algorithm is also proposed, which minimises the Mahalanobis distance of the epipolar line to each optical flow estimate. By combining the BDF, Mahalanobis eight-point algorithm and MIGE, a robust visual odometry is designed. The visual odometry is then combined with an existing SLAM back-end, called robust linear pose-graph. The resulting visual SLAM is shown to be more accurate for a standard dataset and our own UAV dataset, effectively handling feature-limited scenes, pure rotational motion and large camera height variations.

Lastly, with the robustly estimated camera pose from our visual SLAM method, it is possible to estimate a smooth camera trajectory for digital video stabilization. We propose a method using window-based weighted pair-wise rotation average to obtain a smooth rotational motion. Improved video stabilization performance is shown with the proposed method.