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Filtering has been shown successful in prediction from dynamically changing data. In this thesis, we perform case studies and comparison among three filters: Kalman filter, unscented Kalman filter and particle flow filter. We consider Kalman filter in the first chapter where we focus on studying the S&P model in a time-discrete dynamics with time-discrete observations for dividend yield and S&P returns. For this filtering problem, Kalman filter performs well only in the first few time steps. Since the S&P model we consider is nonlinear, we are motivated to apply nonlinear filters and use unscented Kalman filter. The key technique is to approximate non-Gaussian processes (non-linear models) by assigning the so-called sigma points (nonrandom) around the priori mean. We implement it on the S&P model in Chapter 2. We also implement unscented Kalman filter for a two-dimensional tumor growth model. Unscented Kalman filter works reasonably well for both models with capturing the trend and predicting the values. We consider the recently-developed particle flow filter in Chapter 3. Particle flow filter is a method of moving the particles by partial differential equations generated from proper chosen likelihood functions via the Bayes rule. By solving partial differential equations, one can construct an explicit dynamic model on how to move particles.In this chapter, we implement two models as in Chapter 2. One is the S&P model and the other is perturbed tumor growth model. We compare performance of particle flow filter and unscented Kalman filter for these two models.

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The thesis focuses on resource management or sensor allocation when we use bearings-only measurements to track targets in an unattended ground sensor (UGS) network. Intelligent resource management is necessary because each UGS sensor node has limited power and it is desirable that estimation performance not degrade very much when only a few nodes are active to maximize the effective tracking lifetime. For scheduling to prolong the tracking lifetime, a new energy-based (EB) metric is proposed to model the number of snapshots remaining for a hypothesized node set, i.e., the remaining battery energy divided by the energy to sense and share information amongst the node set. Unlike other methods that use the total energy consumed for the given snapshot as the energy-based metric, the new EB metric can achieve load balancing of the nodes without resorting to computationally demanding non-myopic optimization. The metrics to choose nodes at a given snapshot could be geometry-based (GB) to minimize the estimation error, EB, or multiobjective. In determining the active set, each node only knows the existence of itself, the active set of nodes from the previous snapshot and the node's neighbors, i.e., the set of nodes within a distance of r_nei. When measuring the tracking lifetime of the system, we propose an adaptive transmission range control, known as the knowledge pool (KP) where the transmission range is determined by the knowledge of the network and the currently remaining battery level. The KP saves more energy usage than another adaptive transmission range control bounded with the GB metric when the global location information is available. We also provide practical search algorithms to optimize a constraint metric (multiobjective function) using one metric as the optimization metric under the constraint of the other. We also demonstrate the resource management schemes for multitarget tracking with the field data.

<p>Sensor fusion deals with the merging of several signals into one, extracting a better and more reliable result. Traditionally the Kalmanfilter is used for this purpose and the aircraft navigation has benefited tremendously from its use. This thesis considers the merge of two navigation systems, the GPS positioning system and the Saab developed Synthetic Attitude and Heading Reference System (SAHRS). The purpose is to find a model for such a fusion and to investigate whether the fusion will improve the overall navigation performance. The non-linear nature of the navigation equations will lead to the use of the extended Kalman filter and the model is evaluated against both simulated and real data. The results show that this strategy indeed works but problems will arise when the GPS signal falls away.</p>

Sensor fusion deals with the merging of several signals into one, extracting a better and more reliable result. Traditionally the Kalmanfilter is used for this purpose and the aircraft navigation has benefited tremendously from its use. This thesis considers the merge of two navigation systems, the GPS positioning system and the Saab developed Synthetic Attitude and Heading Reference System (SAHRS). The purpose is to find a model for such a fusion and to investigate whether the fusion will improve the overall navigation performance. The non-linear nature of the navigation equations will lead to the use of the extended Kalman filter and the model is evaluated against both simulated and real data. The results show that this strategy indeed works but problems will arise when the GPS signal falls away.

Time series analysis of Synthetic Aperture Radar Interferometry (InSAR) data has become an important scientific tool for monitoring and measuring the displacement of Earth’s surface due to a wide range of phenomena, including earthquakes, volcanoes,landslides, changes in ground water levels, and wetlands. Time series analysis is a product of interferometric phase measurements, which become ambiguous when the observed motion is larger than half of the radar wavelength. Thus, phase observations must first be unwrapped in order to obtain physically meaningful results. Persistent Scatterer Interferometry (PSI), Stanford Method for Persistent Scatterers (StaMPS), Short Baselines Interferometry (SBAS) and Small Temporal Baseline Subset (STBAS)algorithms solve for this ambiguity using a series of spatio-temporal unwrapping algorithms and filters. In this dissertation, I improve upon current phase unwrapping algorithms, and apply the PSI method to study subsidence in Mexico City. PSI was used to obtain unwrapped deformation rates in Mexico City (Chapter 3),where ground water withdrawal in excess of natural recharge causes subsurface, clay-rich sediments to compact. This study is based on 23 satellite SAR scenes acquired between January 2004 and July 2006. Time series analysis of the data reveals a maximum line-of-sight subsidence rate of 300mm/yr at a high enough resolution that individual subsidence rates for large buildings can be determined. Differential motion and related structural damage along an elevated metro rail was evident from the results. Comparison of PSI subsidence rates with data from permanent GPS stations indicate root mean square(RMS) agreement of 6.9 mm/yr, about the level expected based on joint data uncertainty.The Mexico City results suggest negligible recharge, implying continuing degradation and loss of the aquifer in the third largest metropolitan area in the world. Chapters 4 and 5 illustrate the link between time series analysis and three-dimensional (3-D) phase unwrapping. Chapter 4 focuses on the unwrapping path.Unwrapping algorithms can be divided into two groups, path-dependent and path-independent algorithms. Path-dependent algorithms use local unwrapping functions applied pixel-by-pixel to the dataset. In contrast, path-independent algorithms use global optimization methods such as least squares, and return a unique solution. However, when aliasing and noise are present, path-independent algorithms can underestimate the signal in some areas due to global fitting criteria. Path-dependent algorithms do not underestimate the signal, but, as the name implies, the unwrapping path can affect the result. Comparison between existing path algorithms and a newly developed algorithm based on Fisher information theory was conducted. Results indicate that Fisher information theory does indeed produce lower misfit results for most tested cases. Chapter 5 presents a new time series analysis method based on 3-D unwrapping of SAR data using extended Kalman filters. Existing methods for time series generation using InSAR data employ special filters to combine two-dimensional (2-D) spatial unwrapping with one-dimensional (1-D) temporal unwrapping results. The new method,however, combines observations in azimuth, range and time for repeat pass interferometry. Due to the pixel-by-pixel characteristic of the filter, the unwrapping path is selected based on a quality map. This unwrapping algorithm is the first application of extended Kalman filters to the 3-D unwrapping problem. Time series analyses of InSAR data are used in a variety of applications with different characteristics. Consequently, it is difficult to develop a single algorithm that can provide optimal results in all cases, given that different algorithms possess a unique set of strengths and weaknesses. Nonetheless, filter-based unwrapping algorithms such as the one presented in this dissertation have the capability of joining multiple observations into a uniform solution, which is becoming an important feature with continuously growing datasets.