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

An autonomous, real-time orbit determination system was developed within thiswork for the next iteration of the University of W¨urzburg’s CubeSat programme.The algorithm only made use of magnetometer and sun sensors, which already wereimplemented on UWE-3, the third satellite in the programme. Previous developedsystems used the same approach, however the unique aspect in this work is thatthe algorithm was implemented using equinoctial elements.A Runge-Kutta-4 integrator propagated the orbit position using the orbit dynamicsunder the consideration of J2-perturbations. Afterwards, an Extended KalmanFilter corrected the position through processing the two measurements.The algorithm was then tested under multiple conditions. At first, a two weekstability test was conducted using simulated data, followed by a test with recordedsatellite data. These have shown a mean error of 13.2 km and 12.6 km respectively.Lastly, the algorithm was translated in to C and evaluated on a micro-controller.

In this thesis, the impact of false information injection is investigated for linear dynamic systems with multiple sensors. It is assumed that the Kalman filter system is unaware of the existence of false information and the adversary is trying to maximize the negative effect of the false information on the Kalman filter's estimation performance. First, a brief introduction to the Kalman filter is shown in the thesis. We mathematically characterize the false information attack under different conditions. For the adversary, many closed-form results for the optimal attack strategies that maximize the Kalman filter's estimation error are theoretically derived. It is shown that by choosing the optimal correlation coefficients among the bias noises and allocating power optimally among sensors, the adversary could significantly increase the Kalman filter's estimation errors. To be concrete, a target tracking system is used as an example in the thesis. From the adversary's point of view, the best attack strategies are obtained under different scenarios, including a single-sensor system with both position and velocity measurements, and a multi-sensor system with position and velocity measurements. Under a constraint on the total power of the injected bias noises, the optimal solutions are solved from two perspectives: trace and determinant of the mean squared error matrix. Numerical results are also provided in order to illustrate the negative effect which the proposed attack strategies could inflict on the Kalman filter.

The objective of this research is to study various methods for censoring state estimate updates generated from radar measurements. The generated 2-D radar data are sent to a fusion center using the J-Divergence metric as the means to assess the quality of the data. Three different distributed sensor network architectures are considered which include different levels of feedback. The Extended Kalman Filter (EKF) and the Gaussian Particle Filter (GPF) were used in order to test the censoring methods in scenarios which vary in their degrees of non-linearity. A derivation for the direct calculation of the J-Divergence using a particle filter is provided. Results show that state estimate updates can be censored using the J-Divergence as a metric controlled via feedback, with higher J-Divergence thresholds leading to a larger covariance at the fusion center.

The ensemble Kalman filter (EnKF) is a reliable data assimilation tool for high-dimensional meteorological problems. On the other hand, the EnKF can be interpreted as a particle filter, and particle filters (PF) collapse in high-dimensional problems. We explain that these seemingly contradictory statements offer insights about how PF function in certain high-dimensional problems, and in particular support recent efforts in meteorology to 'localize' particle filters, i.e. to restrict the influence of an observation to its neighbourhood.

Structural health monitoring (SHM) is a quickly advancing field of study in civil engineering and recent advances in the field are in stark contrast to where the field started. For example modern technology of wireless sensing systems allowed for easier monitoring of structures, but the challenge of limiting the number of instrumented locations has not been overcome with traditional methods. The potential of alternative methods has only been realized in recent years with the increase of model based approaches. In particular, the use of limited measurements to estimate structural response at all locations is appealing. To accomplish this goal, this work approaches SHM by using a numerical model combined with a linear recursive state estimation algorithm, known as the Kalman Filter, to update the model-based prediction with a limited number of real time measurements taken on the structure. A thorough overview of the contents is given here. The first section introduces the topic of SHM and the goal of SHM. Then the challenges and limitation that face SHM are discussed along with the recent advances that can be used to overcome them. In Section 2, the proposed framework, a Kalman filter approach, is established. First, a finite element model is formulated for plate structures using the Mindlin-Reissner plate theory and then this finite element code is verified by a comparison with a commercial FEA software. Then the state space model of the system is defined for use with the Augmented Kalman Filter (AKF); the AKF approach overcomes the intrinsic challenge of unknown excitations for civil structures. The AKF is then formulated and discussed. For Section 3, using the AKF in numerical simulations are conducted for 5 different cases. The first three cases study the advantages of multi-metric measurements, i.e. strain and acceleration measurements combined, versus single metric measurement, i.e. strain measurement only or acceleration measurement only. Following that, the next two cases explore the question of whether multi-metric measurements will always provide the best results. Based on the conclusions from the previous section, Section 4 investigates the application of a genetic algorithm, a search algorithm based of Darwinian principles, to find the optimal sensor placement to use as the input to the AKF. Here the developed search algorithm is used in two cases, the first is to find the optimal placement for the strain measurement only case. Next, the improvements in accuracy that are gained by placing taking more measurements is investigated to determine if the gain in accuracy per added measurement decreases for large numbers of measurements. Section 5 contains the final conclusions about the use of the AKF for SHM of plate structures then the potential opportunities of future work regarding plate structures are discussed.