Estimation theory is a branch of statistics and probability that derives information about random variables based on known information. In process engineering, state estimation is used for a variety of purposes, such as: soft sensing, digital filter design, model predictive control and performance monitoring. In literature, there exist numerous estimation algorithms. In this study, we provide guidelines for choosing the appropriate estimator for a system under consideration. Various estimators are compared and their advantages and disadvantages are highlighted. This has been done through case studies which use examples from process engineering. We also address certain robustness issues of application of estimation techniques to chemical processes. Choice of estimator in case of high plant-model mismatch has also been discussed. The study is restricted to unconstrained nonlinear estimators. / Process Control

The effects of wind farm installation on the conventional monostatic radar operation have been investigated in previous studies. The interference on radar operation is due to the complex scattering characteristics from the wind turbine structure. This research considers alternative approach for studying and potentially mitigating these negative impacts by adapting the multistatic radar system technique. This radar principle is well known and it is attracting research interest recently, but has not been applied in modelling the wind farm interference on multistatic radar detection and tracking of multiple targets. The research proposes two areas of novelties. The first area includes the simulation tool development of multistatic radar operation near a wind farm environment. The second area includes the adaptation of Range-Only target detection approach based on mathematical and/or statistical methods for target detection and tracking, such as Interval Analysis and Particle Filter. These methods have not been applied against such complex detection scenario of large number of targets within a wind farm environment. Range-Only target detection approach is often considered to achieve flexibility in design and reduction in cost and complexity of the radar system. However, this approach may require advanced signal processing techniques to effectively associate measurements from multiple sensors to estimate targets positions. This issue proved to be more challenging for the complex detection environment of a wind farm due to the increase in number of measurements from the complex radar scattering of each turbine. The research conducts a comparison between Interval Analysis and Particle Filter. The comparison is based on the performance of the two methods according to three aspects; number of real targets detected, number of ghost targets detected and the accuracy of the estimated detections. Different detection scenarios are considered for this comparison, such as single target detection, wind farm detection, and ultimately multiple targets at various elevations within a wind farm environment.

This dissertation describes the development of a method for simultaneous localization and mapping (SLAM)algorithm which is suitable for high dimensional vehicle and map states. The goal of SLAM is to be able to navigate autonomously without the use of external aiding sources for vehicles. SLAM's combination of the localization and mapping problems makes it especially difficult to solve accurately and efficiently, due to the shear size of the unknown state vector. The vehicle states are typically constant in number while the map states increase with time. The increasing number of unknowns in the map state makes it impossible to use traditional Kalman filters to solve the problem- the covariance matrix grows too large and the computational complexity becomes too overwhelming. Particle filters have proved beneficial for alleviating the complexity of the SLAM problem for low dimensional vehicle states, but there is little work done for higher dimensional states. This research provides an Gaussian Mixture Model based alternative to the particle filtering SLAM methods, and provides a further partition that alleviates the vehicle state dimensionality problem with the standard particle filter. A SLAM background and basic theory is provided in the early chapters. A description of the new algorithm is provided in detail. Simulations are run demonstrating the performance of the algorithm, and then an aerial SLAM platform is developed for further testing. The aerial SLAM system uses a RGBD camera as well as an inertial measurement unit to collect SLAM data, and the ground truth is captured using an indoor optical motion capture system. Details on image processing and specifics on the inertial integration are provided. The performance of the algorithm is compared to a state of the art particle filtering based SLAM algorithm, and the results are discussed. Further work performed while working in the industry is described, which involves SLAM for adding transponders onto long-baseline acoustic arrays and stereo-inertial SLAM for 3D reconstruction of deep-water sub-sea structures. Finally, a neatly packaged production line version of the stereo-inertial SLAM system presented.

This paper presents a new method for constructing 2D maps of enclosed un- derwater structures using an underwater robot equipped with only a 2D scanning sonar, compass and depth sensor. In particular, no motion model or odometry is used. To accomplish this, a two step offline SLAM method is applied to a set of stationary sonar scans. In the first step, the change in position of the robot between each consecutive pair of stationary sonar scans is estimated using a particle filter. This set of pair wise relative scan positions is used to create an estimate of each scan’s position within a global coordinate frame using a weighted least squares fit that optimizes consistency between the relative positions of the entire set of scans. In the second step of the method, scans and their estimated positions act as inputs to a mapping algorithm that constructs 2D octree-based evidence grid maps of the site. This work is motivated by a multi-year archaeological project that aims to construct maps of ancient water storage systems, i.e. cisterns, on the islands of Malta and Gozo. Cisterns, wells, and water galleries within fortresses, churches and homes operated as water storage systems as far back as 2000 B.C. Using a Remotely Operated Vehicle (ROV) these water storage systems located around the islands were explored while collecting video, still images, sonar, depth, and compass measurements. Data gathered from 5 different expeditions has produced maps of over 90 sites. Presented are results from applying the new mapping method to both a swimming pool of known size and to several of the previously unexplored water storage systems.

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<p> Particle filters are being used in a number of state estimation applications because of their capability to effectively solve nonlinear and non-Gaussian problems. However, they have high computational requirements and this becomes even more so in the case of multitarget tracking, where data association is the bottleneck. In order to perform data association and estimation jointly, typically an augmented state vector, whose dimensions depend on the number of targets, is used in particle filters. As the number of targets increases, the corresponding computational load increases exponentially. In this case, parallelization is a possibility for achieving real-time feasibility in large-scale multitarget tracking applications. In this paper, we present an optimization-based scheduling algorithm that minimizes the total computation time for the bus-connected heterogeneous primary-secondary architecture. This scheduler is capable of selecting the optimal number of processors from a large pool of secondary processors and mapping the particles among the selected ones. A new distributed resampling algorithm suitable for parallel computing is also proposed. Furthermore, a less communication intensive parallel implementation of the particle filter without sacrificing tracking accuracy using an efficient load balancing technique, in which optimal particle migration among secondary processors is ensured, is presented. Simulation results demonstrate the tracking effectiveness of the new parallel particle filter and the speedup achieved using parallelization.</p> / Thesis / Master of Applied Science (MASc)

<p> Detection and estimation of multiple unresolved targets with a monopulse radar is a challenging problem. For ideal single bin processing, it was shown in the literature that at most two unresolved targets can be extracted from the complex matched filter output signal. In this thesis, a new algorithm is developed to jointly detect and track more than two targets from a single detection. This method involves the use of tracking data in the detection process. For this purpose, target states are transformed into the detection parameter space, which involves high nonlinearity. In order to handle this, the sequential Monte Carlo (SMC) method, which has proven to be effective in nonlinear non-Gaussian estimation problems, is used as the basis of the closed loop system for tracking multiple unresolved targets. In addition to the standard SMC steps, the detection parameters corresponding to the predicted particles are evaluated using the nonlinear monopulse radar beam model. This in turn enables the evaluation of the likelihood of the monopulse signal given tracking data. Hypothesis testing is then used to find the correct detection event. The particles are updated and resampled according to the hypothesis that has the highest likelihood (score). A simulated amplitude comparison monopulse radar is used to generate the data and to validate the extraction and tracking of more than two unresolved targets.</p> / Thesis / Master of Applied Science (MASc)

Accurate hydrologic forecasting is vital for proper water resource management. Practices that are impacted by these forecasts include power generation, reservoir management, agricultural water use, and flood early warning systems. Despite these needs, the models largely used are simplifications of the real world and are therefore imperfect. The forecasters face other challenges in addition to the model uncertainty, which includes imperfect observations used for model calibration and validation, imperfect meteorological forecasts, and the ability to effectively communicate forecast results to decision-makers. Bayesian methods are commonly used to address some of these issues, and this thesis will be focused on improving methods related to recursive Bayesian estimation, more commonly known as data assimilation. Data assimilation is a means to optimally account for the uncertainties in observations, models, and forcing data. In the literature, data assimilation for urban hydrologic and flood forecasting is rare; therefore the main areas of study in this thesis are urban and semi-urban watersheds. By providing improvements to data assimilation methods, both hydrologic and flood forecasting can be enhanced in these areas. This work explored the use of alternative data products as a type of observation that can be assimilated to improve hydrologic forecasting in an urban watershed. The impact of impervious surfaces in urban and semi-urban watersheds was also evaluated in regards to its impact on remotely sensed soil moisture assimilation. Lack of observations is another issue when it comes to data assimilation, particularly in semi- or fully-distributed models; because of this, an improved method for updating locations which do not have observations was developed which utilizes information theory’s mutual information. Finally, we explored extending data assimilation into the short-term forecast by using prior knowledge of how a model will respond to forecasted forcing data. Results from this work found that using alternative data products such as those from the Snow Data Assimilation System or the Soil Moisture and Ocean Salinity mission, can be effective at improving hydrologic forecasting in urban watersheds. They also were effective at identifying a limiting imperviousness threshold for soil moisture assimilation into urban and semi-urban watersheds. Additionally, the inclusion of mutual information between gauged and ungauged locations in a semi-distributed hydrologic model was able to provide better state updates in models. Finally, by extending data assimilation into the short-term forecast, the reliability of the forecasts could be improved substantially. / Dissertation / Doctor of Philosophy (PhD) / The ability to accurately model hydrological systems is essential, as that allows for better planning and decision making in water resources management. The better we can forecast the hydrologic response to rain and snowmelt events, the better we can plan and manage our water resources. This includes better planning and usage of water for agricultural purposes, better planning and management of reservoirs for power generation, and better preparing for flood events. Unfortunately, hydrologic models primarily used are simplifications of the real world and are therefore imperfect. Additionally, our measurements of the physical system responses to atmospheric forcing can be prone to both systematic and random errors that need to be accounted for. To address these limitations, data assimilation can be used to improve hydrologic forecasts by optimally accounting for both model and observation uncertainties. The work in this thesis helps to further advance and improve data assimilation, with a focus on enhancing hydrologic forecasting in urban and semi-urban watersheds. The research presented herein can be used to provide better forecasts, which allow for better planning and decision making.

The focus of this thesis is to implement factor graphs into the problem of detection, classification, and localization (DCL) of underwater objects using active SOund Navigation And Ranging (SONAR). A factor graph is a bipartite graphical representation of the decomposition of a particular function. Messages are passed along the edges connecting factor and variable nodes, on which, a message passing algorithm is applied to compute the posterior probabilities at a particular node. This thesis addresses two issues. In the first section, the formulation of factor graphs for each section of the DCL chain required followed by their closed-form solutions. For the detector, the factor graph determines if the signal is a detection or simply noise. In the classifier, it outputs the probability for the elements in the class. Last, when using a factor graph for the tracker, it gives the estimated state of the object being tracked. The second part concentrates on the application to Continuous Active SONAR (CAS). When using CAS, a bistatic configuration is used allowing for a more rapid update rate where two unmanned underwater vehicles (UUVs) are used as the receiver and transmitter. The goal is to evaluate CAS's effectiveness to determine if the tracking accuracy improves as the transmit interval decreases. If CAS proves to be more efficient in target tracking, the next objective is to determine which messages sent between the two UUVs are most beneficial. To test this, a particle filter simulation is used. / Master of Science

In this thesis, we consider some popular stochastic differential equation models used in finance, such as the Vasicek Interest Rate model, the Heston model and a new fractional Heston model. We discuss how to perform inference about unknown quantities associated with these models in the Bayesian framework. We describe sequential importance sampling, the particle filter and the auxiliary particle filter. We apply these inference methods to the Vasicek Interest Rate model and the standard stochastic volatility model, both to sample from the posterior distribution of the underlying processes and to update the posterior distribution of the parameters sequentially, as data arrive over time. We discuss the sensitivity of our results to prior assumptions. We then consider the use of Markov chain Monte Carlo (MCMC) methodology to sample from the posterior distribution of the underlying volatility process and of the unknown model parameters in the Heston model. The particle filter and the auxiliary particle filter are also employed to perform sequential inference. Next we extend the Heston model to the fractional Heston model, by replacing the Brownian motions that drive the underlying stochastic differential equations by fractional Brownian motions, so allowing a richer dependence structure across time. Again, we use a variety of methods to perform inference. We apply our methodology to simulated and real financial data with success. We then discuss how to make forecasts using both the Heston and the fractional Heston model. We make comparisons between the models and show that using our new fractional Heston model can lead to improve forecasts for real financial data.