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This thesis contributes to non-linear continuous-discrete Kalman filtering of multiplex systems through the development of two main ideas, namely, integration of the unscented transforms with linearly implicit methods and incorporation of simulation errors in the state estimation problem. The newly developed techniques are then applied to the technically relevant problem of state estimation on the main components of a utility boiler. State estimators in industrial systems are used as soft-sensors in monitoring and control applications as the most cost effective and practical alternative to telemetering all variables of interest. One such example is in utility boilers where reliable and real-time data characterising its behaviour is used to detect faults and optimise performance. With respect to the state-of-the-art, state estimators display limitations in real-time applications to large-scale systems. This motivates theoretical developments in state estimation as a first part in this thesis. These developments are aimed at producing more practical and efficient algorithms in non-linear continuous discrete Kalman filtering for stiff large-scale industrial systems. This is achieved using two novel ideas. The first is to exploit the similarities between the extended and unscented Kalman filter in order to estimate the Jacobian required for linearly implicit schemes, thereby tightly coupling state propagation and continuous-time simulation. The second is to account for numerical integration error by appending a stochastic local error model to the system's stochastic differential equation. This allows for coarser integration time steps in systems that are otherwise only suited to relatively small step sizes, making the filter more computationally efficient without lowering its potential to construct accurate estimates. The second part of this thesis uses these algorithms to demonstrate the feasibility of on-line state estimation on the main components of a once-through utility power boiler that require in excess of a hundred state variables to capture its behaviour with adequate fidelity. Two separate models of the boiler are developed, a MATLAB® and a Flownex® model, comprising the economiser, evaporators, reheaters, superheaters and furnace. The mathematical MATLAB® model is better suited to real-time execution and is used in the filter. The more sophisticated model is based on a commercial thermal-hydraulic simulation environment, Flownex® , and is used to validate the mathematical modelling philosophies and construct filter observation data. After validating the performance of the filter against ground-truth data provided by the Flownex® model, the filter is demonstrated on historical plant data to illustrate its utility.

Over the past five decades, Autonomous Mobile Robots (AMRs) have been an active research field. Maps of high accuracy are required for AMRs to operate successfully. In addition to this, AMRs needs to localise themselves reliably relative to the map. Simultaneous Localisation and Mapping (SLAM) address the problem of both map building and robot localisation. When exploring large areas, Multi-Robot SLAM (MRSLAM) has the potential to be far more efficient and robust, while sharing the computational burden across robots. However, MRSLAM encounters issues such as difficulty in map fusion of multi-resolution maps, and unknown relative positions of the robots. This thesis describes a distributed multi-resolution map merging algorithm for MRSLAM. HectorSLAM, which is one of many single robot SLAM implementations, has demonstrated exceptional results and was selected as the basis for the MRSLAM implementation in this project. We consider the environment to be three-dimensional with the maps being constrained to a two-dimensional plane. Each robot is equipped with a laser range sensor for perception and has no information regarding the relative positioning of the other robots. The experiments were conducted both in simulation and a real-world environment. Up-to three robots were placed in the same environment with Hector-SLAM running, the local maps and localisation were then sent to a central node, which attempted to find map overlaps and merge the resulting maps. When evaluating the success of the map merging algorithm, the quality of the map from each robot was interrogated. Experiments conducted on up to three AMRs show the effectiveness of the proposed algorithms in an indoor environment.