Design and theoretical analysis of advanced power based positioning in RF system

Accurate locating and tracking of people and resources has become a fundamental requirement for many applications. The global navigation satellite systems (GNSS) is widely used. But its accuracy suffers from signal obstruction by buildings, multipath fading, and disruption due to jamming and spoof. Hence, it is required to supplement GPS with inertial sensors and indoor localization schemes that make use of WiFi APs or beacon nodes. In the GPS-challenging or fault scenario, radio-frequency (RF) infrastructure based localization schemes can be a fallback solution for robust navigation. For the indoor/outdoor transition scenario, we propose hypothesis test based fusion method to integrate multi-modal localization sensors. In the first paper, a ubiquitous tracking using motion and location sensor (UTMLS) is proposed. As a fallback approach, power-based schemes are cost-effective when compared with the existing ToA or AoA schemes. However, traditional power-based positioning methods suffer from low accuracy and are vulnerable to environmental fading. Also, the expected accuracy of power-based localization is not well understood but is needed to derive the hypothesis test for the fusion scheme. Hence, in paper 2-5, we focus on developing more accurate power-based localization schemes. The second paper improves the power-based range estimation accuracy by estimating the LoS component. The ranging error model in fading channel is derived. The third paper introduces the LoS-based positioning method with corresponding theoretical limits and error models. In the fourth and fifth paper, a novel antenna radiation-pattern-aware power-based positioning (ARPAP) system and power contour circle fitting (PCCF) algorithm are proposed to address antenna directivity effect on power-based localization. Overall, a complete LoS signal power based positioning system has been developed that can be included in the fusion scheme --Abstract, page iv

Asymptotically efficient estimators for geometric shape fitting and source localization

Solving the nonlinear estimation problem is known to be a challenging task because of the implicit relationship between the measurement data and the unknown parameters to be estimated. Iterative methods such as the Taylor-series expansion based ML estimator are presented in this thesis to solve the nonlinear estimation problem. However, they might suffer from the initialization and convergence problems. Other than the iterative methods, this thesis aims to provide a computational effective, asymptotically efficient and closed-form solution to the nonlinear estimation problem. Two kinds of classic nonlinear estimation problems are considered: the geometric shape fitting problem and the source localization problem. For the geometric shape fitting, the research in this thesis focuses on the circle and the ellipse fittings. Three iterative methods for the fitting of a single circle: the ML method, the FLS method and the SDP method, are provided and their performances are analyzed. To overcome the limitations of the iterative methods, asymptotically efficient and closed-form solutions for both the circle and ellipse fittings are derived. The good performances of the proposed solutions are supported by simulations using synthetic data as well as experiments on real images. The localization of a source via a group of sensors is another important nonlinear estimation problem studied in this thesis. Based on the TOA measurements, the CRLB and MSE results of a source location when sensor position errors are present are derived and compared to show the estimation performance loss due to the sensor position errors. A closed-formed estimator that takes into account the sensor position errors is then proposed. To further improve the sensor position and the source location estimates, an algebraic solution that jointly estimates the source and sensor positions is provided, which provides better performance in sensor position estimates at higher noise level comparing to the sequential estimation-refinement technique. The TOA based CRLB and MSE studies are further extended to the TDOA and AOA cases. Through the analysis one interesting result has been found: there are situations exist where taking into account the sensor position errors when estimating the source location will not improve the estimation accuracy. In such cases a calibration emitter with known position is needed to limit the estimation damage caused by the sensor position uncertainties. Investigation has been implemented to find out where would be the optimum position to place the calibration emitter. When the optimum calibration source position may be of theoretical interest only, a practical suboptimum criterion is developed which yields a better calibration emitter position than the closest to the unknown source criterion

Efficient closed-form estimators in multistatic target localization and motion analysis

Object localization is fast becoming an important research topic because of its wide applications. Often of the time, object localization is accomplished in two steps. The first step exploits the characteristics of the received signals and extracts certain localization information i.e. measurements. Some typical measurements include timeof-arrival (TOA), time-difference-of-arrival (TDOA), received signal strength (RSS) and angle-of-arrival (AOA). Together with the known receiver position information, the object location is then estimated in the second step from the obtained measurements. The localization of an object using a number of sensors is often challenged due to the highly nonlinear relationship between the measurements and the object location. This thesis focuses on the second step and considers designing novel and efficient localization algorithms to solve such a problem. This thesis first derives a new algebraic positioning solution using a minimum number of measurements, and from which to develop an object location estimator. Two measurements are sufficient in 2-D and three in 3-D to yield a solution if they are consistent. The derived minimum measurement solution is exact and reduces the computation to the roots of a quadratic equation. The solution derivation also leads to simple criteria to ascertain if the line of positions from two measurements intersects. By partitioning the overdetermined set of measurements first to obtain the individual minimum measurement solutions, we propose a best linear unbiased estimator to form the final location estimate. The analysis supports the proposed estimator in reaching the Cramer-Rao Lower Bound (CRLB) accuracy under Gaussian noise. A measurement partitioning scheme is developed to improve performance when the noise level becomes large. We mainly use elliptic time delay measurements for presentation, and the derived results apply to the hyperbolic time difference measurements as well. Both the 2-D and 3-D scenarios are considered. A multistatic system uses a transmitter to illuminate the object of interest and collects the reflected signal by several receivers to determine its location. In some scenarios such as passive coherent localization or for gaining flexibility, the position of the transmitter is not known. In this thesis, we investigate the use of the indirect path measurements reflected off the object alone, or together with the direct path measurements from the transmitter to receiver for locating the object in the absence of the transmitter position. We show that joint estimation of the object and transmitter positions from both the indirect and direct measurements can yield better object location estimate than using the indirect measurements only by eliminating the dependency of the transmitter position. An algebraic closed-form solution is developed for the nonlinear problem of joint estimation and is shown analytically to achieve the CRLB performance under Gaussian noise over the small error region. To complete the study and gain insight, the optimum receiver placement in the absence of transmitter position is derived, by minimizing the estimation confidence region or the estimation variance for the object location. The performance lost due to unknown transmitter position under the optimum geometries is quantified. Simulations confirm well with the theoretical developments. In practice, a more realistic localization scenario with the unknown transmitter is that the transmitter works non-cooperatively. In this situation, no timestamp is available in the transmitted signal so that the signal sent time is often not known. This thesis next considers the extension of the localization scenario to such a case. More generally, the motion potential of the unknown object and transmitter is considered in the analysis. When the transmitted signal has a well-defined pattern such as some standard synchronization or pilot sequence, it would still be able to estimate the indirect and direct time delays and Doppler frequency shifts but with unknown constant time delay and frequency offset added. In this thesis, we would like to estimate the object and transmitter positions and velocities, and the time and frequency offsets jointly. Both dynamic and partial dynamic localization scenarios based on the motion status of the object and the transmitter are considered in this thesis. By investigating the CRLB of the object location estimate, the improvement in position and velocity estimate accuracy through joint estimation comparing with the differencing approach using TDOA/FDOA measurements is evaluated. The degradation due to time and frequency offsets is also analyzed. Algebraic closed-form solutions to solve the highly nonlinear joint estimation problems are then proposed in this thesis, followed by the analysis showing that the CRLB performance can be achieved under Gaussian noise over the small error region. When the transmitted signal is not time-stamped and does not have a well-defined pattern such as some standard synchronization or pilot sequence, it is often impossible to obtain the indirect and direct measurements separately. Instead, a self-calculated TDOA between the indirect- and direct-path TOAs shall be considered which does not require any synchronization between the transmitter and a receiver, or among the receivers. A refinement method is developed to locate the object in the presence of the unknown transmitter position, where a hypothesized solution is needed for initialization. Analysis shows that the refinement method is able to achieve the CRLB performance under Gaussian noise. Three realizations of the hypothesized solution applying multistage processing to simplify the nonlinear estimation problem are derived. Simulations validate the effectiveness in initializing the refinement estimator

Fast Numerical and Machine Learning Algorithms for Spatial Audio Reproduction

Audio reproduction technologies have underwent several revolutions from a purely mechanical, to electromagnetic, and into a digital process. These changes have resulted in steady improvements in the objective qualities of sound capture/playback on increasingly portable devices. However, most mobile playback devices remove important spatial-directional components of externalized sound which are natural to the subjective experience of human hearing. Fortunately, the missing spatial-directional parts can be integrated back into audio through a combination of computational methods and physical knowledge of how sound scatters off of the listener's anthropometry in the sound-field. The former employs signal processing techniques for rendering the sound-field. The latter employs approximations of the sound-field through the measurement of so-called Head-Related Impulse Responses/Transfer Functions (HRIRs/HRTFs). This dissertation develops several numerical and machine learning algorithms for accelerating and personalizing spatial audio reproduction in light of available mobile computing power. First, spatial audio synthesis between a sound-source and sound-field requires fast convolution algorithms between the audio-stream and the HRIRs. We introduce a novel sparse decomposition algorithm for HRIRs based on non-negative matrix factorization that allows for faster time-domain convolution than frequency-domain fast-Fourier-transform variants. Second, the full sound-field over the spherical coordinate domain must be efficiently approximated from a finite collection of HRTFs. We develop a joint spatial-frequency covariance model for Gaussian process regression (GPR) and sparse-GPR methods that supports the fast interpolation and data fusion of HRTFs across multiple data-sets. Third, the direct measurement of HRTFs requires specialized equipment that is unsuited for widespread acquisition. We ``bootstrap'' the human ability to localize sound in listening tests with Gaussian process active-learning techniques over graphical user interfaces that allows the listener to infer his/her own HRTFs. Experiments are conducted on publicly available HRTF datasets and human listeners

Quantitative Optical Imaging and Sensing by Joint Design of Point Spread Functions and Estimation Algorithms

The joint application of tailored optical Point Spread Functions (PSF) and estimation methods is an important tool for designing quantitative imaging and sensing solutions. By enhancing the information transfer encoded by the optical waves into an image, matched post-processing algorithms are able to complete tasks with improved performance relative to conventional designs. In this thesis, new engineered PSF solutions with image processing algorithms are introduced and demonstrated for quantitative imaging using information-efficient signal processing tools and/or optical-efficient experimental implementations. The use of a 3D engineered PSF, the Double-Helix (DH-PSF), is applied as one solution for three-dimensional, super-resolution fluorescence microscopy. The DH-PSF is a tailored PSF which was engineered to have enhanced information transfer for the task of localizing point sources in three dimensions. Both an information- and optical-efficient implementation of the DH-PSF microscope are demonstrated here for the first time. This microscope is applied to image single-molecules and micro-tubules located within a biological sample. A joint imaging/axial-ranging modality is demonstrated for application to quantifying sources of extended transverse and axial extent. The proposed implementation has improved optical-efficiency relative to prior designs due to the use of serialized cycling through select engineered PSFs. This system is demonstrated for passive-ranging, extended Depth-of-Field imaging and digital refocusing of random objects under broadband illumination. Although the serialized engineered PSF solution is an improvement over prior designs for the joint imaging/passive-ranging modality, it requires the use of multiple PSFs - a potentially significant constraint. Therefore an alternative design is proposed, the Single-Helix PSF, where only one engineered PSF is necessary and the chromatic behavior of objects under broadband illumination provides the necessary information transfer. The matched estimation algorithms are introduced along with an optically-efficient experimental system to image and passively estimate the distance to a test object. An engineered PSF solution is proposed for improving the sensitivity of optical wave-front sensing using a Shack-Hartmann Wave-front Sensor (SHWFS). The performance limits of the classical SHWFS design are evaluated and the engineered PSF system design is demonstrated to enhance performance. This system is fabricated and the mechanism for additional information transfer is identified

Collaborative Information Processing in Wireless Sensor Networks for Diffusive Source Estimation

In this dissertation, we address the issue of collaborative information processing for diffusive source parameter estimation using wireless sensor networks (WSNs) capable of sensing in dispersive medium/environment, from signal processing perspective. We begin the dissertation by focusing on the mathematical formulation of a special diffusion phenomenon, i.e., an underwater oil spill, along with statistical algorithms for meaningful analysis of sensor data leading to efficient estimation of desired parameters of interest. The objective is to obtain an analytical solution to the problem, rather than using non-model based sophisticated numerical techniques. We tried to make the physical diffusion model as much appropriate as possible, while maintaining some pragmatic and reasonable assumptions for the simplicity of exposition and analytical derivation. The dissertation studies both source localization and tracking for static and moving diffusive sources respectively. For static diffusive source localization, we investigate two parametric estimation techniques based on the maximum-likelihood (ML) and the best linear unbiased estimator (BLUE) for a special case of our obtained physical dispersion model. We prove the consistency and asymptotic normality of the obtained ML solution when the number of sensor nodes and samples approach infinity, and derive the Cramer-Rao lower bound (CRLB) on its performance. In case of a moving diffusive source, we propose a particle filter (PF) based target tracking scheme for moving diffusive source, and analytically derive the posterior Cramer-Rao lower bound (PCRLB) for the moving source state estimates as a theoretical performance bound. Further, we explore nonparametric, machine learning based estimation technique for diffusive source parameter estimation using Dirichlet process mixture model (DPMM). Since real data are often complicated, no parametric model is suitable. As an alternative, we exploit the rich tools of nonparametric Bayesian methods, in particular the DPMM, which provides us with a flexible and data-driven estimation process. We propose DPMM based static diffusive source localization algorithm and provide analytical proof of convergence. The proposed algorithm is also extended to the scenario when multiple diffusive sources of same kind are present in the diffusive field of interest. Efficient power allocation can play an important role in extending the lifetime of a resource constrained WSN. Resource-constrained WSNs rely on collaborative signal and information processing for efficient handling of large volumes of data collected by the sensor nodes. In this dissertation, the problem of collaborative information processing for sequential parameter estimation in a WSN is formulated in a cooperative game-theoretic framework, which addresses the issue of fair resource allocation for estimation task at the Fusion center (FC). The framework allows addressing either resource allocation or commitment for information processing as solutions of cooperative games with underlying theoretical justifications. Different solution concepts found in cooperative games, namely, the Shapley function and Nash bargaining are used to enforce certain kinds of fairness among the nodes in a WSN