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We consider the filtering problem in linear state space models with heavy tailed process and measurement noise. Our work is based on Student's t distribution, for which we give a number of useful results. The derived filtering algorithm is a generalization of the ubiquitous Kalman filter, and reduces to it as special case. Both Kalman filter and the new algorithm are compared on a challenging tracking example where a maneuvering target is observed in clutter. / MC Impulse

A model-based estimation process is implemented in simulation of a water transmission line for the purpose of leak detection. The objective of this thesis is aimed at determining, through simulation results, the effectiveness of the Extended Kalman Filter for leak detection. Water distribution systems often contain large amounts of unknown losses. The range in magnitude of losses varies from 10 to over 50 percent of the total volume of water pumped. The result is a loss of product, including water and the chemicals used to treat it, environmental damage, demand shortfalls, increased energy usage and unneeded pump capacity expansions. It is clear that more control efforts need to be implemented on these systems to reduce losses and increase energy efficiencies. The problems of demand shortfalls, resulting from lost product, are worsened by the limited availability of water resources and a growing population and economy. The repair of leakage zones as they occur is not a simple problem since the vast majority of leaks, not considered to be major faults, go undetected. The leak detection process described in the work of this thesis is model based. A transient model of a transmission line is developed using the Method of Characteristics. This method provides the most accurate results of all finite-difference solutions to the two partial differential equations of continuity and momentum that describe pipe flow. Simulations are run with leakage within the system and small transients are added as random perturbations in the upstream reservoir head. The head measurements at the two pipe extremes are used as inputs into the filter estimation process. The Extended Kalman Filter is used for state estimation of leakage within the transmission line. The filter model places two artificial leakage states within the system. The estimates of these fictitious leakage states are then used to locate the actual position and magnitude of leakage within the transmission line. This method is capable of locating one leak within the line. The results of the Extended Kalman Filter (EKF) process show that it is capable of locating the position and magnitude of small leaks within the line. It was concluded that the EKF could be used for leak detection, but field tests need to be done to better quantify the ability of these methods. It is recommended that a multiple filtering method be implemented that may be able to locate the occurrence of multiple leakage.

A model based algorithm of pipeline flow is developed and tested to determine if the model is capable of detecting a leak in a pipeline. The overall objective of this research is to determine the feasibility of applying the Extended Kalman Filter and a new technique defined as the Extended Boundary Approach to the detection of leakages in a physical water distribution system. <p>The demands on the water supply system increase as the human population grows and expands throughout the world. Water conservation is required to ensure an adequate supply of water remains for future generations. One way to conserve this water is by reducing the leakages in underground water distribution systems. Currently between 10 to 50 percent of the pumped water is lost due to unrecognized leakages. This results in a huge revenue loss of water, chemicals and energy that is required for transporting the water. The detection of underground leakages is a very complex problem because many leakages are small and go unnoticed by todays leak detection technology. <p>A model based leak detection technique is developed and tested in this thesis. The Method of Characteristics is used to develop a model of a single pipeline. This method is extensively used and provides the most accurate results of the two partial differential equations of continuity and momentum that describe pipe flow. The Extended Kalman Filter is used to estimate two fictitious leakages at known locations along the pipeline. In order to ensure the model is observable four pressure measurements are needed at equally spaced nodes along the pipeline. With the development of the Extended Boundary Approach only the upstream and downstream pressure measurements are required, however; the upstream and downstream flow measurements are also required. Using the information from the two fictitious leaks the actual leak location and magnitude can be determined. This method is only capable of detecting one leak in a single pipeline. <p>The results of the developed model show that the approach is capable of theoretically determining the leak location and magnitude in a pipeline. However, at this time, the feasibility of implementing the proposed leak detection method is limited by the required level of accuracy of the sensors which is beyond that found in todays technology. It was also found that the EKF used primarily steady state information to predict the leakage. It is recommended that further research explore alternate models which might better enhance the EKF approach using transient information from the pipeline. This may allow implementation on a real pipeline.

The global Positioning System (GPS) provides location and time information as long as there are unobstructed lines of sight to four or more GPS satellites. However, when this is not the case the signal may be inaccurate or sometimes even completely blocked. In these situations the Inertial Navigation System (INS) is an appropriate choice for positioning.  An INS has already been proposed in a previous thesis by Erik Andersson and the objective of this thesis is to fuse the GPS with the INS in a proper way. A part of this project is to decide the reliability of the GPS.Three methods for GPS reliability detection have been proposed. One method based on the statistical properties of each of the separate systems, and two methods based on the statistical properties of the residuals between the GPS and INS. Two methods for GPS/INS integration have been proposed. One method based on a bank of parallel running Kalman filters and one method based on an adaptive observer.The method based on Kalman filter diverged. By adding a state that was suppose to represent the bias of the noise an attempt was to fix this problem made. The filter still diverged and was not examined any further. Among the other two algorithms did the one that uses both magnetometer and gyroscope presents a better result than the one that uses only gyroscope. However, the result differences between the two algorithms were not big and the result may change if a better INS is used.

Renewable power sources with a relatively uneven or constant DC power production require synchronization methods to work with the current utility power grid. The solution to this synchronization problem has been solved with semiconductor based converters and advanced switching algorithms. To enable switching algorithms that work well with the grids amplitude, phase-shift and frequency, the current waveform has to be measured and estimated.    There are many sources of noise that will add distortion of the current waveform, making its appearance less similar to the grids. The distorted measurement affects the accuracy of the converters negatively. Therefore, using a filter algorithm to attenuate the grid noise is required.  This project uses a Kalman filter with the aim to decrease the noise and estimate the current phase shift for a three phase power-grid.  To achieve reliable and fast calculation, implementing the Kalman filter within a FPGA were done.The project contains results from both simulated MATLAB data and the FPGAs real time data. The method was able to estimate the grid within a few Hz frequency deviation and enable some noise reduction. For larger degree of harmonic distortion during steady state operation, the Kalman filter could remove more of the harmonic distortion. Limits and differences with MATLAB are discussed for the FPGA implemented Kalman filter.

The aim of platooning is to enable several Heavy Duty Vehicles (HDVs) to drive in a convoy and act as one unit to decrease the fuel consumption. By introducing wireless communication and tight control, the distance between the HDVs can be decreased significantly. This implies a reduction of the air drag and consequently the fuel consumption for all the HDVs in the platoon. The challenge in platooning is to keep the HDVs as close as possible to each other without endangering safety. Therefore, sensor fusion is necessary to get an accurate estimate of the relative distance and velocity, which is a pre-requisite for the controller. This master thesis aims at developing a sensor fusion framework from on-board sensor information as well as other vehicles’ sensor information communicated over a WiFi link. The most important sensors are GPS, that gives a rough position of each HDV, and radar that provides relative distance for each pair of HDV’s in the platoon. A distributed solution is developed, where an Extended Kalman Filter (EKF) estimates the state of the whole platoon. The state vector includes position, velocity and length of each HDV, which is used in a Model Predictive Control (MPC). Furthermore, a method is discussed on how to handle vehicles outside the platoon and how various road surfaces can be managed. This master thesis is a part of a project consisting of three parallel master’s theses. The other two master’s theses investigate and implement rough pre-processing of data, time synchronization and MPC associated with platooning. It was found that the three implemented systems could reduce the average fuel consumption by 11.1 %.

A model-based estimation process is implemented in simulation of a water transmission line for the purpose of leak detection. The objective of this thesis is aimed at determining, through simulation results, the effectiveness of the Extended Kalman Filter for leak detection. Water distribution systems often contain large amounts of unknown losses. The range in magnitude of losses varies from 10 to over 50 percent of the total volume of water pumped. The result is a loss of product, including water and the chemicals used to treat it, environmental damage, demand shortfalls, increased energy usage and unneeded pump capacity expansions. It is clear that more control efforts need to be implemented on these systems to reduce losses and increase energy efficiencies. The problems of demand shortfalls, resulting from lost product, are worsened by the limited availability of water resources and a growing population and economy. The repair of leakage zones as they occur is not a simple problem since the vast majority of leaks, not considered to be major faults, go undetected. The leak detection process described in the work of this thesis is model based. A transient model of a transmission line is developed using the Method of Characteristics. This method provides the most accurate results of all finite-difference solutions to the two partial differential equations of continuity and momentum that describe pipe flow. Simulations are run with leakage within the system and small transients are added as random perturbations in the upstream reservoir head. The head measurements at the two pipe extremes are used as inputs into the filter estimation process. The Extended Kalman Filter is used for state estimation of leakage within the transmission line. The filter model places two artificial leakage states within the system. The estimates of these fictitious leakage states are then used to locate the actual position and magnitude of leakage within the transmission line. This method is capable of locating one leak within the line. The results of the Extended Kalman Filter (EKF) process show that it is capable of locating the position and magnitude of small leaks within the line. It was concluded that the EKF could be used for leak detection, but field tests need to be done to better quantify the ability of these methods. It is recommended that a multiple filtering method be implemented that may be able to locate the occurrence of multiple leakage.

A model based algorithm of pipeline flow is developed and tested to determine if the model is capable of detecting a leak in a pipeline. The overall objective of this research is to determine the feasibility of applying the Extended Kalman Filter and a new technique defined as the Extended Boundary Approach to the detection of leakages in a physical water distribution system. <p>The demands on the water supply system increase as the human population grows and expands throughout the world. Water conservation is required to ensure an adequate supply of water remains for future generations. One way to conserve this water is by reducing the leakages in underground water distribution systems. Currently between 10 to 50 percent of the pumped water is lost due to unrecognized leakages. This results in a huge revenue loss of water, chemicals and energy that is required for transporting the water. The detection of underground leakages is a very complex problem because many leakages are small and go unnoticed by todays leak detection technology. <p>A model based leak detection technique is developed and tested in this thesis. The Method of Characteristics is used to develop a model of a single pipeline. This method is extensively used and provides the most accurate results of the two partial differential equations of continuity and momentum that describe pipe flow. The Extended Kalman Filter is used to estimate two fictitious leakages at known locations along the pipeline. In order to ensure the model is observable four pressure measurements are needed at equally spaced nodes along the pipeline. With the development of the Extended Boundary Approach only the upstream and downstream pressure measurements are required, however; the upstream and downstream flow measurements are also required. Using the information from the two fictitious leaks the actual leak location and magnitude can be determined. This method is only capable of detecting one leak in a single pipeline. <p>The results of the developed model show that the approach is capable of theoretically determining the leak location and magnitude in a pipeline. However, at this time, the feasibility of implementing the proposed leak detection method is limited by the required level of accuracy of the sensors which is beyond that found in todays technology. It was also found that the EKF used primarily steady state information to predict the leakage. It is recommended that further research explore alternate models which might better enhance the EKF approach using transient information from the pipeline. This may allow implementation on a real pipeline.

The major problems encountered in wireless location are the effects caused by non-line of sight (NLOS) propagation and multipath interference. In the thesis, we propose an approach to mitigate NLOS error. First of all, we use improved biased Kalman filter (IBKF) based on time of arrival (TOA) measurement to identify and mitigate NLOS error. Applying the statistic characteristic that the standard deviation of the NLOS propagation errors is generally much larger than that of measurement noises in the LOS condition, we combine hypothesis test and sliding window to identify NLOS error. According to the feedback identification and the calculated standard deviation, IBKF switches biased or unbiased to process TOA measurement. Nevertheless, the performance of IBKF-TOA is still affected slightly by NLOS error. Since extended Kalman filter (EKF) based on received signal strength (RSS) measurement is designed for prespecified environments, the effect of NLOS mitigation is more obvious. Moreover, EKF-RSS not only exists higher error probability in NLOS identification, but also needs longer time to converge in the cases that start with NLOS. Comparing IBKF-TOA with EKF-RSS, we adopt interacting multiple model (IMM) in the proposed data fusion structure for processing TOA and RSS measurements. In the proposed scheme, we reserve the basic IMM structure and add the step of NLOS identification into basic IMM structure. By accurate NLOS identification results and soft decision of IMM, the proposed scheme will switch to adequate filter mode and obtain better estimation. With simulation in UWB channel, the analysis and performance evaluation show advantages and disadvantages of using IBKF-TOA, EKF-RSS, and proposed scheme. Simulation results reveal that NLOS error can be mitigated effectively by data fusion of TOA and RSS measurements and can achieve high accuracy in positioning and tracking.