Coupling conditionally independent submaps for large-scale 2.5D mapping with Gaussian Markov Random Fields

© 2017 IEEE. Building large-scale 2.5D maps when spatial correlations are considered can be quite expensive, but there are clear advantages when fusing data. While optimal submapping strategies have been explored previously in covariance-form using Gaussian Process for large-scale mapping, this paper focuses on transferring such concepts into information form. By exploiting the conditional independence property of the Gaussian Markov Random Field (GMRF) models, we propose a submapping approach to build a nearly optimal global 2.5D map. In the proposed approach data is fused by first fitting a GMRF to one sensor dataset; then conditional independent submaps are inferred using this model and updated individually with new data arrives. Finally, the information is propagated from submap to submap to later recover the fully updated map. This is efficiently achieved by exploiting the inherent structure of the GMRF, fusion and propagation all in information form. The key contribution of this paper is the derivation of the algorithm to optimally propagate information through submaps by only updating the common parts between submaps. Our results show the proposed method reduces the computational complexity of the full mapping process while maintaining the accuracy. The performance is evaluated on synthetic data from the Canadian Digital Elevation Data

Adaptive Sampling For Efficient Online Modelling

This thesis examines methods enabling autonomous systems to make active sampling and planning decisions in real time. Gaussian Process (GP) regression is chosen as a framework for its non-parametric approach allowing flexibility in unknown environments. The first part of the thesis focuses on depth constrained full coverage bathymetric surveys in unknown environments. Algorithms are developed to find and follow a depth contour, modelled with a GP, and produce a depth constrained boundary. An extension to the Boustrophedon Cellular Decomposition, Discrete Monotone Polygonal Partitioning is developed allowing efficient planning for coverage within this boundary. Efficient computational methods such as incremental Cholesky updates are implemented to allow online Hyper Parameter optimisation and fitting of the GP's. This is demonstrated in simulation and the field on a platform built for the purpose. The second part of this thesis focuses on modelling the surface salinity profiles of estuarine tidal fronts. The standard GP model assumes evenly distributed noise, which does not always hold. This can be handled with Heteroscedastic noise. An efficient new method, Parametric Heteroscedastic Gaussian Process regression, is proposed. This is applied to active sample selection on stationary fronts and adaptive planning on moving fronts where a number of information theoretic methods are compared. The use of a mean function is shown to increase the accuracy of predictions whilst reducing optimisation time. These algorithms are validated in simulation. Algorithmic development is focused on efficient methods allowing deployment on platforms with constrained computational resources. Whilst the application of this thesis is Autonomous Surface Vessels, it is hoped the issues discussed and solutions provided have relevance to other applications in robotics and wider fields such as spatial statistics and machine learning in general

Gaussian Processes for Uncertainty Visualization

Data is virtually always uncertain in one way or another. Yet, uncertainty information is not routinely included in visualizations and, outside of simple 1D diagrams, there is no established way to do it. One big issue is to find a method that shows the uncertainty without completely cluttering the display. A second important question that needs to be solved, is how uncertainty and interpolation interact. Interpolated values are inherently uncertain, because they are heuristically estimated values – not measurements. But how much more uncertain are they? How can this effect be modeled? In this thesis, we introduce Gaussian processes, a statistical framework that allows for the smooth interpolation of data with heteroscedastic uncertainty through regression. Its theoretical background makes it a convincing method to analyze uncertain data and create a model of the underlying phenomenon and, most importantly, the uncertainty at and in-between the data points. For this reason, it is already popular in the GIS community where it is known as Kriging but has applications in machine learning too. In contrast to traditional interpolation methods, Gaussian processes do not merely create a surface that runs through the data points, but respect the uncertainty in them. This way, noise, errors or outliers in the data do not disturb the model inappropriately. Most importantly, the model shows the variance in the interpolated values, which can be higher but also lower than that of its neighboring data points, providing us with a lot more insight into the quality of our data and how it influences our uncertainty! This enables us to use uncertainty information in algorithms that need to interpolate between data points, which includes almost all visualization algorithms

APPLYING MACHINE LEARNING FOR COP/CTP DATA FILTERING

Student Thesis (NPS NRP Project Related)Accurate tracks and targeting are key to providing decision-makers with the confidence to execute their missions. Increasingly, multiple intelligence, surveillance, and reconnaissance (ISR) assets across different intelligence sources are being used to increase the accuracy of track location, resulting in the need to develop methods to exploit heterogeneous sensor data streams for better target state estimation. One of the algorithms commonly used for target state estimation is the Kalman Filter (KF) algorithm. This algorithm performs well if its covariance matrices are accurate approximations of the uncertainty in sensor measurements. Our research complements the artificial intelligence/machine learning (AI/ML) efforts the U.S. Navy is conducting by quantitatively assessing the potential of using an ML model to predict sensor measurement noise for KF state estimation. We used a computer simulation to generate sensor tracks of a single target and trained a neural network to predict sensor error. The hybrid model (ML-KF) was able to outperform our baseline KF model that uses normalized sensor errors by approximately 20% in target position estimation. Further research in enhancing the ML model with external environment variables as inputs could potentially create an adaptive state estimation system that is capable of operating in varied environment settings.NPS Naval Research ProgramThis project was funded in part by the NPS Naval Research Program.Outstanding ThesisCaptain, Singapore ArmyApproved for public release. Distribution is unlimited