<p>En patenterad metod [11] ligger till grund för utförandet av det här examensarbetet där målet var att beskriva metoden i reglertekniska termer. En lösning för att kompensera för gyrodrifter var också önskvärd. En olinjär modell som beskriver flygplanets dynamik har tagits fram och simulerats. Modellen har linjäriserats kring en trajektoria och diskretiserats för att undersöka observerbarheten för systemet. Huruvida ett system är observerbart eller inte avgör om det är möjligt eller inte att applicera ett extended kalmanfilter (EKF) på för att skatta systemets tillstånd. Kalmanfiltret används för att man inte har tillgång till mätningar på systemets alla tillstånd och måste därför skatta dem. Olika tester har gjorts för att undersöka kalmanfiltrets prestanda. Trots att kalmanfiltret är ett optimalt filter kan man inte garantera tillfredsställande resultat eftersom antalet tillgängliga mätbara tillstånd påverkar hur bra skattningar man får.</p>

<p>In angle-only target tracking the aim is to estimate the state of a target with use of measurement of elevation and azimuth. The state consists of relative position and velocity between the target and the platform. The platform is an Unmanned Aerial Vehicle (UAV) and the tracking system is meant to be a part of the platform’s anti-collision system. In the case where both the target and the platform travel with constant velocity the angle measurements do not provide any information of the range between the target and the platform. The platform has to maneuver to be able to estimate the range to the target.</p><p>Two filters are implemented and tested on simulated data. The first filter is based on a Extended Kalman Filter (EKF) and is designed for tracking nonmaneuvering targets. Different platform maneuvers are studied and the influence of initial errors and the geometry of the simulation scenario is investigated. The filter is able to estimate the position of the target if the platform maneuvers and the target travels with constant velocity. Maneuvering targets on the other hand can not be tracked by the filter.</p><p>The second filter is an interacting multiple model (IMM) filter, designed for tracking maneuvering targets. The filter performance is highly dependent of the geometry of the scenario. The filter has been tuned for a scenario where the target approaches the platform from the front. In this scenario the filter is able to track both maneuvering and non-maneuvering targets. If the target approaches the platform from the side on the other hand, the filter has problems with distinguish target maneuvers from measurement noise.</p>

Starting from Maxwell’s equations, we derive a sensor model for three-axis magnetometerssuitable for localization and tracking applications. The model dependson the relative position between the sensor and the target, orientation of the targetand its magnetic signature. Both point targets and extended target modelsare provided. The models are validated on data taken from various road vehicles.The suitability of magnetometers for tracking is analyzed in terms of local observabilityand Cramér Rao lower bound as a function of the sensor positions in atwo sensor scenario. Also the signal to noise ratio is computed to determine theeffective range of the magnetometer. Results from field test data indicate excellenttracking of position and velocity of the target, as well as identification of themagnetic target model suitable for target classification.

This thesis aims the problem of underwater vehicle positioning. The vehicle usedwas a Saab Seaeye Falcon which was equipped with a Doppler Velocity Log(DVL)manufactured by RD Instruments and an inertial measurement unit (IMU) fromXsense. During the work several different Extended Kalman Filter (EKF) havebeen tested both with a hydrodynamic model of the vehicle and a model withconstant acceleration and constant angular velocity. The filters were tested withdata from test runs in lake Vättern. The EKF with constant acceleration andconstant angular velocity appeared to be the better one. The misalignment of thesensors were also tried to be estimated but with poor result.

The first loudspeaker was invented almost 150 years ago and even though much has changed regarding the manufacturing, the main idea is still the same. To produce clean sound, modern loudspeaker consist of expensive materials that often need advanced manufacturing equipment. The relatively newly established company Actiwave AB uses digital signal processing to enhance the audio for loudspeakers with poor acoustic properties. Their algorithms concentrate on attenuating the linear distortion but there is no compensation for the loudspeakers' non-linear distortion, such as harmonic distortion. To attenuate the harmonic distortion, this thesis presents controllers based on exact input-output linearisation. This type of controller needs an accurate model of the system. A loudspeaker model has been derived based on the LR-2 model, an extension of the more common Thiele-Small model. A controller based on exact input-output linearisation also needs full state feedback, but since feedback risk being expensive, state estimators were used. The state estimators were based on feed-forward or observers using the extended Kalman filter or the unscented Kalman filter. A combination of feed-forward state estimation and a PID controller were designed as well. In simulations, the total harmonic distortion was attenuated for all controllers up to 180 Hz. The simulations also showed that the controllers are sensitive to inaccurate parameter values in the loudspeaker model. During real-life experiments, the controllers needed to be extended with a model of the used amplifier to function properly. The controllers that were able to attenuate the harmonic distortion were the two methods using feed-forward state estimation. Both controllers showed improvement compared to the uncontrolled case for frequencies up to 40 Hz.

This master thesis investigates the performance of a car navigation system using lateral accelerometers, yaw rate and bearings relative three known radio beacons. Accelerometer, gyroscope and position data has been collected by an IMU combined with a GPS receiver, where the IMU was installed in the approximate motion center of a car. The bearing measurements are simulated using GPS data and the measurement noise model is derived from an experiment where the direction of arrival to one transmitter was estimated by an antenna array and the signal processing algorithm MUSIC. The measurements are fused in a multi-rate extended Kalman filter which assumes that all measurement noise is Gaussian distributed. This is not the case for the bearing measurement noise which contains outliers and therefore is modelled as a Gaussian uniform noise mixture. Different methods to deal with this have been investigated where the main focus is on the principle to use the Kalman filter’s innovation for each bearing measurement as an indication of its quality and discarding measurements with a quality above a certain threshold.

The object of this thesis is to provide a MATLAB framework for nonlinear filtering in general, and particle filtering in particular. This is done by using the object-oriented programming paradigm, resulting in truly expandable code. Three types of discrete and nonlinear state-space models are supported by default, as well as three filter algorithms: the Extended Kalman Filter and the SIS and SIR particle filters. Symbolic expressions are differentiated automatically, which allows for comfortable EKF filtering. A graphical user interface is also provided to make the process of filtering even more convenient. By implementing a specified interface, programming new classes for use within the framework is easy and guidelines for this are presented.

En patenterad metod [11] ligger till grund för utförandet av det här examensarbetet där målet var att beskriva metoden i reglertekniska termer. En lösning för att kompensera för gyrodrifter var också önskvärd. En olinjär modell som beskriver flygplanets dynamik har tagits fram och simulerats. Modellen har linjäriserats kring en trajektoria och diskretiserats för att undersöka observerbarheten för systemet. Huruvida ett system är observerbart eller inte avgör om det är möjligt eller inte att applicera ett extended kalmanfilter (EKF) på för att skatta systemets tillstånd. Kalmanfiltret används för att man inte har tillgång till mätningar på systemets alla tillstånd och måste därför skatta dem. Olika tester har gjorts för att undersöka kalmanfiltrets prestanda. Trots att kalmanfiltret är ett optimalt filter kan man inte garantera tillfredsställande resultat eftersom antalet tillgängliga mätbara tillstånd påverkar hur bra skattningar man får.

In angle-only target tracking the aim is to estimate the state of a target with use of measurement of elevation and azimuth. The state consists of relative position and velocity between the target and the platform. The platform is an Unmanned Aerial Vehicle (UAV) and the tracking system is meant to be a part of the platform’s anti-collision system. In the case where both the target and the platform travel with constant velocity the angle measurements do not provide any information of the range between the target and the platform. The platform has to maneuver to be able to estimate the range to the target. Two filters are implemented and tested on simulated data. The first filter is based on a Extended Kalman Filter (EKF) and is designed for tracking nonmaneuvering targets. Different platform maneuvers are studied and the influence of initial errors and the geometry of the simulation scenario is investigated. The filter is able to estimate the position of the target if the platform maneuvers and the target travels with constant velocity. Maneuvering targets on the other hand can not be tracked by the filter. The second filter is an interacting multiple model (IMM) filter, designed for tracking maneuvering targets. The filter performance is highly dependent of the geometry of the scenario. The filter has been tuned for a scenario where the target approaches the platform from the front. In this scenario the filter is able to track both maneuvering and non-maneuvering targets. If the target approaches the platform from the side on the other hand, the filter has problems with distinguish target maneuvers from measurement noise.

The scope of this report is the development of a mathematical model and a control system for a three degrees of freedom (3DOF) helicopter rig. This 3DOF-system offers a good simplification of a real world tandem helicopter for evaluating performanceof different automatic control principles. A mathematical model of the system is developed using free-body diagrams. This mathematical model is then linearized and a controller is developed by decoupling the system. Due to model imperfections external disturbances and similar effects integral action is added as well as feed-forward compensation to reduce nonlinear effects. After the controller has been decoupled the two different controllers are tuned. The Linear-Quadratic Regulator, described in section 3.6, is used for selectingstate-feedback gains. Due to the highly nonlinear nature of the system an Extended Kalman Filter is developed to estimate unmeasurable states. The model and controller is then implemented on the actual rig and evaluated. The results displayed that the elevation controller had good performance. The travel controller also showed good performance but not as good as the elevation controller. The main goal of this thesis was to develop a controller for the 3DOF helicopter system. The results clearly show that an LQR-controller is able to successfully control a system like this with decent performance characteristics despite the highly nonlinear system.