Pose Graph Optimisation is a technique that is used to solve the Simultaneous Localisation and Mapping problem by relying on least-square minimisation techniques to find the most likely set of robot poses (i.e., location and orientation) given the set of measurements. It formalises the maximum likelihood formulation using a pose graph, where poses are represented as nodes, and measurements are represented as edges. Each measurement is paired with a measurement model that maps the related poses to an expected measurement value. PGO tries to find the set of poses that minimises the difference between the expected measurement values and the true measurement values. An accurate solution requires accurate measurement models. Models can be dependent on knowledge of specific robot parameters, or may fail to account for unknown systematic measurement deviations. By identifying the dependency of the unknown parameter within the measurement model, the parameter can be added as a graph node, thereby creating a pose-parameter graph and the accompanying Pose-Parameter Graph Optimisation problem.
In this thesis, a generalised approach to PPGO is proposed that is based on the implementation of two generally applicable parameters (a bias and scaling factor). Each parameter implementation defines modified measurement models that relate the newly defined parameter-nodes. Connectivity strategies are proposed that connect the set of parameter-nodes within the pose-parameter graph based on the nature of the parameter fluctuation.
For this thesis, a framework was developed in python that uses g2o to solve the PPGO problem. A GUI was designed to intuitively visualise graph components and evaluate performance metrics. The estimation of the bias parameter is found to be reliable over all measurement components, whereas the scaling factor only allows for reliable estimation over measurement components that exhibit consistent non-zero values. The static connectivity strategy can be reliably utilised to estimate an unknown constant parameter value. The sliding window and timely batch strategies are able to reconstruct a sinusoidal parameter with time, with the former offering an accurate instantaneous estimate with a slight delay, and the latter offering higher accuracy when applied as a post-processing step. The spatial batch strategy is able to reconstruct a sinusoidal parameter with space by creating a matching parameter heat map.