In this paper we study continuous tracking of airplanes using object detection models, namely YOLOv7, combined with a Kalman filter. The tracking should be able to be done in real-time. The idea of combining Kalman filters with an object detection model comes from the lack of time-dependent context in models such as YOLOv7. The model analyzes each frame independently and outputs airplane detections for the analyzed frame. Therefore, if an airplane flies behind a tree or a cloud, the object detection model will say that there is no object there. The Kalman filter is used to construct an object with a state consisting of position and velocity for every airplane. As such if an airplane flies behind a tree, it is possible to extrapolate the trajectory and resume tracking once the airplane is visible again, much like a human would extrapolate the trajectory naturally. In the report I describe the implementation and training of a YOLOv7 model, I further describe the construction and implementation of a Kalman filter as well as how observations are mapped on to objects in the Kalman filter. During this I introduce a parameter called cumulative confidence. This describes how long something is being tracked after observations cease. After losing sight of an object, the cumulative confidence starts to drop. When it reaches zero and the object is removed. This can take anywhere between 100 ms to 6 seconds depending on how much confidence the object has accumulated. Objects accumulate confidence by being observed and detected by the object detection model. In the results section I describe how the performance of the program changed when using a Kalman filter or when not using a Kalman filter. The results showed that continuous tracking of airborne airplanes was superior when using a Kalman filter as opposed to only using the YOLOv7 model. Continuous tracking was never lost in these 2 airborne cases when using the integrated Kalman filter. Continuous tracking was lost 5 respectively 11 times on the same cases when not using the Kalman filter. The last case in the results section, an airplane on a runway, showed the same performance with and without the Kalman filter. I go into detail why this is in both the results section and in Section 5.1 (Interpreting the results). / I detta pappret studeras kontinuerlig spårning av flygplan med hjälp av objektdetekterings-modeller, mer specifikt YOLOv7 modellen i kombination med Kalman filter. Spårningen ska kunna göras i realtid. Idén att kombinera Kalman filter med modeller för objektdetektering kommer från avsaknaden på tidsberoende kontext i modeller som YOLOv7. Modellen analyserar varje bild i en dataström oberoende och ger en utmatning med positioner av flygplan i den analyserade bilden. Därmed, om ett flygplan flyger in bakom ett träd eller ett moln så kommer modellen konstatera att det inte är ett objekt där. Kalman filtret används för att konstruera ett objekt med ett tillstånd som består av position och hastigheten av varje flygplan. På så vis om ett flygplan flyger in bakom ett träd är det möjligt att extrapolera vägen planet kommer flyga samt återuppta spårning när flygplanet blir synligt igen, på samma vis som en människa extrapolerar planets bana naturligt. I rapporten beskriver jag en implementering och träning av en YOLOv7 modell. Vidare beskriver jag konstruktionen och implementationen av ett Kalman filter, samt hur observationer mappas till objekt i Kalman filtret. Jag introducerar även en parameter som kallas “kumulativt förtroende”. Denna beskriver hur länge något spåras även efter att observationer upphör. När ett objekt ej får observationer längre så börjar det kumulativa förtroendet minska. När det når noll så tas objektet bort. Detta kan ta mellan 100 ms och sex sekunder, beroende på hur mycket förtroende objektet har ackumulerat. Objekt ackumulerar förtroende genom att bli observerade och detekterade av YOLOv7 modellen. I resultatdelen beskriver jag hur prestandan skiljer sig om programmet använder ett Kalman filter eller inte ett Kalman filter. Resultaten visar att kontinuerlig spårning av flygplan i luften var bättre när man använder ett Kalman filter. Spårningen av flygplan upphörde aldrig i de 2 fallen då flygplan var i luften. På dessa fallen så tappade modellen spårningen 5 respektive 11 gånger när den inte använde Kalman filtret. Det tredje och sista fallet i resultatdelen, ett flygplan på banan, visade samma prestanda med eller utan Kalman filtret. Jag går in i detalj kring varför det var så i resultatdelen och i diskussionen.

Planetary rovers are robots that need to perform autonomous navigation, because of the long delay communication and no human assistance. Furthermore, they need to perform the optimal estimation of its position in order to have a good performance on its navigation system. The need for good performance filters for estimating the actual position of mobile robots of this kind is needed, due to the fact that sensors are noisy and that information is of vital importance for a planetary rover’s mission. Besides, good accurate sensors for the matter, are not easy to find for space application. Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) were implemented to analyze a data set of a 4-wheel robot, and later used for comparison on accuracy in the estimation of its pose. The analysis will give the possibility to know the right combination of sensors, recognize some issues during the trajectory. Furthermore, this study has been made with aims to give the reader knowledge of state of the art in planetary rovers, their constraints and consideration while developing them. The robot used for the research has been developed for an international competition of field robot automation. The main goal is to navigate autonomously through flowerpots performing different tasks as flowerpot collection, distance traveled and robustness on localization and navigation algorithms. / <p>Validerat; 20120822 (anonymous)</p>

The low latitude tropical ionosphere has been investigated by various researchers using Global Positioning System (GPS). Presently for many civil aviation applications, the ionospheric modeling of the tropical region has gained importance, in particular for flight safety. Since ionosphere is dispersive in nature, dual frequency (L1 = 1575.42 MHz and L2 = 1227.60 MHz) GPS observations can be used to obtain Ionospheric Total Electron Content (TEC). Since TEC varies with local time and geomagnetic latitude, an Ionospheric Modeling Technique using spatial linear approximation of vertical TEC over receiver station has been implemented following Sardon et al. The effects of all the systematic errors due to the satellite plus the receiver (SPR) instrumental biases can reach upto several nanoseconds. (1 TEC is 1016 electrons/m2, 1 ns = 2.86 TEC and 1 TEC = 0.16 m). Hence, to have an accurate estimation of ionospheric TEC, the instrumental biases must also be estimated. This thesis describes a heuristic adaptive Kalman Filtering scheme developed to estimate the TEC, the constants in the linearisation scheme, as well as the above total instrumental biases. The Kalman filter implementation is basically an optimization problem of minimizing the Cost Function J based on the difference between the model output and the measurement, called as the ‘innovation’, scaled by its covariance. In order to obtain the best possible results using the Kalman Filter approach, it is essential to provide appropriate values for the initial state, process and measurement noise covariances (P0, Q and R) respectively, which in general may not be known. Usually manual tuning of the filter parameter is carried out without using the above cost function J! The filter estimates can be highly sensitive to the above chosen statistics and thus these will have to be estimated carefully. Hence, we have utilized the Adaptive Kalman Filtering procedure of Myers and Tapley extended by Gemson and Ananthasayanam. The minimization is carried out by simultaneously estimating the above statistics and the unknown parameters, which include the TEC and the instrumental bias. In addition, A Constant Gain Kalman Filter approach using Genetic Algorithm (GA) has also been developed for the above requirement. It is observed that the steady state gains in KF and AKF approaches are in good match with the constant gains obtained from Genetic Algorithm. Using the above Adaptive Kalman Filtering technique and Constant Gain Kalman Filter approach, vertical TEC values and SPR biases have been estimated from the IGS receiver observations stationed at ISTRAC/ISRO, Bangalore, India. A diurnal TEC variation over Bangalore for a period of one year for 2003 and January 2004 is estimated and reported in this thesis. This approach has also been applied to study the behaviour of the ionosphere over low latitude IGS station at Fortaleza, Brazil data during the great magnetic storm on the 15th July 2000 and the results were found to be consistent with the results of Basu et al. In addition, Using Constant Kalman filter, the TEC enhancement over Indian region has been estimated for the October 2003 Ionospheric storm, and the results were found to be consistent with the reported results in the literature.

The Defence, Peace, Safety and Security (DPSS) competency area within the Council for Scientific and Industrial Research (CSIR) has identified the need for the development of a robot that can operate in almost any land-based environment. Legged robots, especially hexapod (six-legged) robots present a wide variety of advantages that can be utilised in this environment and is identified as a feasible solution. The biggest advantage and main reason for the development of legged robots over mobile (wheeled) robots, is their ability to navigate in uneven, unstructured terrain. However, due to the complicated control algorithms needed by a legged robot, most literature only focus on navigation in even or relatively even terrains. This is seen as the main limitation with regards to the development of legged robot applications. For navigation in unstructured terrain, postural controllers of legged robots need fast and precise knowledge about the state of the robot they are regulating. The speed and accuracy of the state estimation of a legged robot is therefore very important. Even though state estimation for mobile robots has been studied thoroughly, limited research is available on state estimation with regards to legged robots. Compared to mobile robots, locomotion of legged robots make use of intermitted ground contacts. Therefore, stability is a main concern when navigating in unstructured terrain. In order to control the stability of a legged robot, six degrees of freedom information is needed about the base of the robot platform. This information needs to be estimated using measurements from the robot’s sensory system. A sensory system of a robot usually consist of multiple sensory devices on board of the robot. However, legged robots have limited payload capacities and therefore the amount of sensory devices on a legged robot platform should be kept to a minimum. Furthermore, exteroceptive sensory devices commonly used in state estimation, such as a GPS or cameras, are not suitable when navigating in unstructured and unknown terrain. The control and localisation of a legged robot should therefore only depend on proprioceptive sensors. The need for the development of a reliable state estimation framework (that only relies on proprioceptive information) for a low-cost, commonly available hexapod robot is identified. This will accelerate the process for control algorithm development. In this study this need is addressed. Common proprioceptive sensors are integrated on a commercial low-cost hexapod robot to develop the robot platform used in this study. A state estimation framework for legged robots is used to develop a state estimation methodology for the hexapod platform. A kinematic model is also derived and verified for the platform, and measurement models are derived to address possible errors and noise in sensor measurements. The state estimation methodology makes use of an Extended Kalman filter to fuse the robots kinematics with measurements from an IMU. The needed state estimation equations are also derived and implemented in Matlab®. The state estimation methodology developed is then tested with multiple experiments using the robot platform. In these experiments the robot platform captures the sensory data with a data acquisition method developed while it is being tracked with a Vicon motion capturing system. The sensor data is then used as an input to the state estimation equations in Matlab® and the results are compared to the ground-truth measurement outputs of the Vicon system. The results of these experiments show very accurate estimation of the robot and therefore validate the state estimation methodology and this study. / MIng (Computer and Electronic Engineering), North-West University, Potchefstroom Campus, 2015

The Defence, Peace, Safety and Security (DPSS) competency area within the Council for Scientific and Industrial Research (CSIR) has identified the need for the development of a robot that can operate in almost any land-based environment. Legged robots, especially hexapod (six-legged) robots present a wide variety of advantages that can be utilised in this environment and is identified as a feasible solution. The biggest advantage and main reason for the development of legged robots over mobile (wheeled) robots, is their ability to navigate in uneven, unstructured terrain. However, due to the complicated control algorithms needed by a legged robot, most literature only focus on navigation in even or relatively even terrains. This is seen as the main limitation with regards to the development of legged robot applications. For navigation in unstructured terrain, postural controllers of legged robots need fast and precise knowledge about the state of the robot they are regulating. The speed and accuracy of the state estimation of a legged robot is therefore very important. Even though state estimation for mobile robots has been studied thoroughly, limited research is available on state estimation with regards to legged robots. Compared to mobile robots, locomotion of legged robots make use of intermitted ground contacts. Therefore, stability is a main concern when navigating in unstructured terrain. In order to control the stability of a legged robot, six degrees of freedom information is needed about the base of the robot platform. This information needs to be estimated using measurements from the robot’s sensory system. A sensory system of a robot usually consist of multiple sensory devices on board of the robot. However, legged robots have limited payload capacities and therefore the amount of sensory devices on a legged robot platform should be kept to a minimum. Furthermore, exteroceptive sensory devices commonly used in state estimation, such as a GPS or cameras, are not suitable when navigating in unstructured and unknown terrain. The control and localisation of a legged robot should therefore only depend on proprioceptive sensors. The need for the development of a reliable state estimation framework (that only relies on proprioceptive information) for a low-cost, commonly available hexapod robot is identified. This will accelerate the process for control algorithm development. In this study this need is addressed. Common proprioceptive sensors are integrated on a commercial low-cost hexapod robot to develop the robot platform used in this study. A state estimation framework for legged robots is used to develop a state estimation methodology for the hexapod platform. A kinematic model is also derived and verified for the platform, and measurement models are derived to address possible errors and noise in sensor measurements. The state estimation methodology makes use of an Extended Kalman filter to fuse the robots kinematics with measurements from an IMU. The needed state estimation equations are also derived and implemented in Matlab®. The state estimation methodology developed is then tested with multiple experiments using the robot platform. In these experiments the robot platform captures the sensory data with a data acquisition method developed while it is being tracked with a Vicon motion capturing system. The sensor data is then used as an input to the state estimation equations in Matlab® and the results are compared to the ground-truth measurement outputs of the Vicon system. The results of these experiments show very accurate estimation of the robot and therefore validate the state estimation methodology and this study. / MIng (Computer and Electronic Engineering), North-West University, Potchefstroom Campus, 2015

Master of Science / Department of Electrical and Computer Engineering / Balasubramaniam Natarajan / In this thesis, we investigate two carrier tracking loops. We provide a basic overview of phase-lock loops. We derive a two-state EKF tracking loop. The two-state EKF estimates phase error and frequency error. The estimate of frequency error is fed back to an NCO to complete the tracking loop.

International Telemetering Conference Proceedings / October 18-21, 2004 / Town & Country Resort, San Diego, California / FLL’s are extensively used for fast carrier synchronization. A common approach to meet the wide acquisition range and sufficiently small tracking error requirements is to adopt the wide or narrow band FLL loop in the acquisition and tracking modes and direct switching the loop. The paper analyze the influence of direct switching on performance, including the narrow band loop convergence, transition time etc. and propose applying the Kalman filtering theory to realize the seamless switching (SS) with time-varying loop gains between the two different loop tracking state. The SS control gains for the high dynamic digital spread spectrum receiver is derived. Simulation results for the SS compared to the direct switching demonstrate the improved performance.

International Telemetering Conference Proceedings / October 23-26, 2000 / Town & Country Hotel and Conference Center, San Diego, California / Pseudolites have been proposed for augmentation/replacement of the GPS system in radiolocation applications. However, a terrestrial pseudolite system suffers from the near-far effect due to received power disparities. Conventional code tracking loops as employed in GPS receivers are unable to suppress near-far interference. Here, a multiuser code tracking algorithm is presented based on the extended Kalman filter (EKF.) The EKF jointly tracks the delays and amplitudes of multiple received pseudolite waveforms. A modified EKF based on an approximate Bayesian estimator (BEKF) is also developed, which can in principle both acquire and track code delays, as well as detect loss-of-lock. Representative simulation results for the BEKF are presented for code tracking with 2 and 5 users.

A Discrete Extended Kalman Filter has been designed to process measurements from a magnetometer, sun sensor, IMU, and GPS receiver to provide the relative position, velocity, attitude, and gyro bias of a chaser spacecraft relative to a target spacecraft. An Extended Kalman Filter with Uncompensated Bias has also been developed for the implementation of well known biases and errors that are not directly observable. A detailed explanation of the algorithms, models, and derivations that go into both filters is presented. With this simulation and specific sensor selection the position of the chaser spacecraft relative to the target can be estimated to within about 5 m, the velocity to within .1 m/s, and the attitude to within 2 degrees for both filters. If a thrust is applied to the IMU measurements, it takes about 1.5 minutes to get a good position estimate, using the Extended Kalman Filter with Uncompensated Bias. The error settles almost immediately using the general Extended Kalman Filter. These filters have been designed for and can be implemented on almost any small, low cost, low power satellite with this inexpensive set of sensors. / text

Seasonal influenza epidemics are a major public health concern, causing three to five million cases of severe illness and about 250,000 to 500,000 deaths worldwide. Given the unpredictability of these epidemics, hospitals and health authorities are often left unprepared to handle the sudden surge in demand. Hence early detection of disease activity is fundamental to reduce the burden on the healthcare system, to provide the most effective care for infected patients and to optimize the timing of control efforts. Early detection requires reliable forecasting methods that make efficient use of surveillance data. We developed a dynamic Bayesian estimator to predict weekly hospitalizations due to influenza related illnesses in the state of Texas. The prediction of peak hospitalizations using our model is accurate both in terms of number of hospitalizations and the time at which the peak occurs. For 1-to 8 week predictions, the predicted number of hospitalizations was within 8% of actual value and the predicted time of occurrence was within a week of actual peak. / text