Partially Linear Estimation with Application to Sparse Signal Recovery From Measurement Pairs

We address the problem of estimating a random vector X from two sets of measurements Y and Z, such that the estimator is linear in Y. We show that the partially linear minimum mean squared error (PLMMSE) estimator does not require knowing the joint distribution of X and Y in full, but rather only its second-order moments. This renders it of potential interest in various applications. We further show that the PLMMSE method is minimax-optimal among all estimators that solely depend on the second-order statistics of X and Y. We demonstrate our approach in the context of recovering a signal, which is sparse in a unitary dictionary, from noisy observations of it and of a filtered version of it. We show that in this setting PLMMSE estimation has a clear computational advantage, while its performance is comparable to state-of-the-art algorithms. We apply our approach both in static and dynamic estimation applications. In the former category, we treat the problem of image enhancement from blurred/noisy image pairs, where we show that PLMMSE estimation performs only slightly worse than state-of-the art algorithms, while running an order of magnitude faster. In the dynamic setting, we provide a recursive implementation of the estimator and demonstrate its utility in the context of tracking maneuvering targets from position and acceleration measurements.Comment: 13 pages, 5 figure

GPS Carrier Tracking Loop Performance in the presence of Ionospheric Scintillations

The performance of several GPS carrier tracking loops is evaluated using wideband GPS data recorded during strong ionospheric scintillations. The aim of this study is to determine the loop structures and parameters that enable good phase tracking during the power fades and phase dynamics induced by scintillations. Constant-bandwidth and variable-bandwidth loops are studied using theoretical models, simulation, and tests with actual GPS signals. Constant-bandwidth loops with loop bandwidths near 15 Hz are shown to lose phase lock during scintillations. Use of the decision-directed discriminator reduces the carrier lock threshold by ∼1 dB relative to the arctangent and conventional Costas discriminators. A proposed variablebandwidth loop based on a Kalman filter reduces the carrier lock threshold by more than 7 dB compared to a 15-Hz constant-bandwidth loop. The Kalman filter-based strategy employs a soft-decision discriminator, explicitly models the effects of receiver clock noise, and optimally adapts the loop bandwidth to the carrier-to-noise ratio. In extensive simulation and in tests using actual wideband GPS data, the Kalman filter PLL demonstrates improved cycle slip immunity relative to constant bandwidth PLLs.Aerospace Engineering and Engineering Mechanic

Helical automatic approaches of helicopters with microwave landing systems

A program is under way to develop a data base for establishing navigation and guidance concepts for all-weather operation of rotorcraft. One of the objectives is to examine the feasibility of conducting simultaneous rotorcraft and conventional fixed-wing, noninterfering, landing operations in instrument meteorological conditions at airports equipped with microwave landing systems (MLSs) for fixed-wing traffic. An initial test program to investigate the feasibility of conducting automatic helical approaches was completed, using the MLS at Crows Landing near Ames. These tests were flown on board a UH-1H helicopter equipped with a digital automatic landing system. A total of 48 automatic approaches and landings were flown along a two-turn helical descent, tangent to the centerline of the MLS-equipped runway to determine helical light performance and to provide a data base for comparison with future flights for which the helical approach path will be located near the edge of the MLS coverage. In addition, 13 straight-in approaches were conducted. The performance with varying levels of state-estimation system sophistication was evaluated as part of the flight tests. The results indicate that helical approaches to MLS-equipped runways are feasible for rotorcraft and that the best position accuracy was obtained using the Kalman-filter state-estimation with inertial navigation systems sensors

Approximate Gaussian conjugacy: parametric recursive filtering under nonlinearity, multimodality, uncertainty, and constraint, and beyond

Since the landmark work of R. E. Kalman in the 1960s, considerable efforts have been devoted to time series state space models for a large variety of dynamic estimation problems. In particular, parametric filters that seek analytical estimates based on a closed-form Markov–Bayes recursion, e.g., recursion from a Gaussian or Gaussian mixture (GM) prior to a Gaussian/GM posterior (termed ‘Gaussian conjugacy’ in this paper), form the backbone for a general time series filter design. Due to challenges arising from nonlinearity, multimodality (including target maneuver), intractable uncertainties (such as unknown inputs and/or non-Gaussian noises) and constraints (including circular quantities), etc., new theories, algorithms, and technologies have been developed continuously to maintain such a conjugacy, or to approximate it as close as possible. They had contributed in large part to the prospective developments of time series parametric filters in the last six decades. In this paper, we review the state of the art in distinctive categories and highlight some insights that may otherwise be easily overlooked. In particular, specific attention is paid to nonlinear systems with an informative observation, multimodal systems including Gaussian mixture posterior and maneuvers, and intractable unknown inputs and constraints, to fill some gaps in existing reviews and surveys. In addition, we provide some new thoughts on alternatives to the first-order Markov transition model and on filter evaluation with regard to computing complexity

Acoustic underwater target tracking methods using autonomous vehicles

Marine ecological research related to the increasing importance which the fisheries sector has reached so far, new methods and tools to study the biological components of our oceans are needed. The capacity to measure different population and environmental parameters of marine species allows a greater knowledge of the human impact, improving exploitation strategies of these resources. For example, the displacement capacity and mobility patterns are crucial to obtain the required knowledge for a sustainable management of fisheries. However, underwater localisation is one of the main problems which must be addressed in subsea exploration, where no Global Positioning System (GPS) is available. In addition to the traditional underwater localisation systems, such as Long BaseLine (LBL) or Ultra-Short BaseLine (USBL), new methods have been developed to increase navigation performance, flexibility, and to reduce deployment costs. For example, the Range-Only and Single-Beacon (ROSB) is based on an autonomous vehicle which localises and tracks different underwater targets using slant range measurements conducted by acoustic modems. In a moving target tracking scenario, the ROSB target tracking method can be seen as a Hidden Markov Model (HMM) problem. Using Bayes' rule, the probability distribution function of the HMM states can be solved by using different filtering methods. Accordingly, this thesis presents different strategies to improve the ROSB localisation and tracking methods for static and moving targets. Determining the optimal parameters to minimize acoustic energy use and search time, and to maximize the localisation accuracy and precision, is therefore one of the discussed aspects of ROSB. Thus, we present and compare different methods under different scenarios, both evaluated in simulations and field tests. The main mathematical notation and performance of each algorithm are presented, where the best practice has been derived. From a methodology point of view, this work advances the understanding of accuracy that can be achieved by using ROSB target tracking methods with autonomous vehicles. Moreover, whereas most of the work conducted during the last years has been focused on target tracking using acoustic modems, here we also present a novel method called the Area-Only Target Tracking (AOTT). This method works with commercially available acoustic tags, thereby reducing the costs and complexity over other tracking systems. These tags do not have bidirectional communication capabilities, and therefore, the ROSB techniques are not applicable. However, this method can be used to track small targets such as jellyfish due to the reduced tag's size. The methodology behind the area-only technique is shown, and results from the first field tests conducted in Monterey Bay area, California, are also presented.La biologia marina junt amb la importància que ha adquirit el sector pesquer, fa que es requereixin noves eines per a l’estudi dels nostres oceans. La capacitat de mesurar diferents poblacions i paràmetres ambientals d’espècies marines permet millorar el coneixement de l’impacte que l’ésser humà té sobre elles, millorant-ne els mètodes d’explotació. Per exemple, la capacitat de desplaçament i els patrons de moviment són crucials per obtenir el coneixement necessari per a una explotació sostenible de les pescaries involucrades. No obstant, la localització submarina és un dels principals problemes que s’ha de resoldre en l’explotació dels recursos submarins, on el sistema de posició global (GPS) no es pot utilitzar. A part dels mètodes tradicionals de posicionament submarí, com per exemple el Long Base-Line (LBL) o el Ultra-Short Base-Line (USBL), nous mètodes han estat desenvolupats per tal de millorar la navegació, la flexibilitat, i per reduir els costos de desplegament. Per exemple, el Range-Only and Single-Beacon (ROSB) utilitza un vehicle autònom per a localitzar i seguir diferents objectius submarins mitjançant mesures de rang realitzades a partir de mòdems acústics. En un escenari on l’objectiu a seguir és mòbil, el mètode ROSB de seguiment pot ser vist com a un problema de Hidden Markov Model (HMM). Aleshores, utilitzant la regla de Bayes, la funció de distribució de probabilitat dels estats del HMM pot ser solucionat utilitzant diferents mètodes de filtratge. Per tant, s’estudien diferents estratègies per millorar el sistema de localització i seguiment basat en ROSB, tant per objectius estàtics com mòbils. En aquesta tesis, presentem i comparem diferents mètodes utilitzant diferents escenaris, els quals s’han avaluat tant en simulacions com en proves de camp reals. A més, es presenten les principals notacions matemàtiques de cada algoritme i les millors pràctiques a utilitzar. Per tant, des d’un punt de vista metodològic, aquest treball fa un pas endavant en el coneixement de l’exactitud que es pot assolir utilitzant els mètodes de localització i seguiment d’espècies mitjançant algoritmes ROSB i vehicles autònoms. A més a més, mentre molts dels treballs realitzant durant els últims anys es centren en l’ús de mòdems acústics per al seguiment d’objectius submarins, en aquesta tesis es presenta un innovador mètode anomenat Area-Only Target Tracking (AOTT). Aquest sistema utilitza petites etiquetes acústiques comercials (tag), la qual cosa, redueix el cost i la complexitat en comparació amb els altres mètodes. Addicionalment, gràcies a l’ús d’aquests tags de dimensions reduïdes, aquest sistema permet seguir espècies marines com les meduses. La metodologia utilitzada per el mètode AOTT es mostra en aquesta tesis, on també es presenten els primers experiments realitzats a la badia de Monterey a Califòrnia

A parallel hypothesis method of autonomous underwater vehicle navigation

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution June 2009This research presents a parallel hypothesis method for autonomous underwater vehicle navigation that enables a vehicle to expand the operating envelope of existing long baseline acoustic navigation systems by incorporating information that is not normally used. The parallel hypothesis method allows the in-situ identification of acoustic multipath time-of-flight measurements between a vehicle and an external transponder and uses them in real-time to augment the navigation algorithm during periods when direct-path time-of-flight measurements are not available. A proof of concept was conducted using real-world data obtained by the Woods Hole Oceanographic Institution Deep Submergence Lab's Autonomous Benthic Explorer (ABE) and Sentry autonomous underwater vehicles during operations on the Juan de Fuca Ridge. This algorithm uses a nested architecture to break the navigation solution down into basic building blocks for each type of available external information. The algorithm classifies external information as either line of position or gridded observations. For any line of position observation, the algorithm generates a multi-modal block of parallel position estimate hypotheses. The multimodal hypotheses are input into an arbiter which produces a single unimodal output. If a priori maps of gridded information are available, they are used within the arbiter structure to aid in the elimination of false hypotheses. For the proof of concept, this research uses ranges from a single external acoustic transponder in the hypothesis generation process and grids of low-resolution bathymetric data from a ship-based multibeam sonar in the arbitration process. The major contributions of this research include the in-situ identification of acoustic multipath time-of-flight measurements, the multiscale utilization of a priori low-resolution bathymetric data in a high-resolution navigation algorithm, and the design of a navigation algorithm with a exible architecture. This flexible architecture allows the incorporation of multimodal beliefs without requiring a complex mechanism for real-time hypothesis generation and culling, and it allows the real-time incorporation of multiple types of external information as they become available in situ into the overall navigation solution

Aircraft state estimation using cameras and passive radar

Multiple target tracking (MTT) is a fundamental task in many application domains. It is a difficult problem to solve in general, so applications make use of domain specific and problem-specific knowledge to approach the problem by solving subtasks separately. This work puts forward a MTT framework (MTTF) which is based on the Bayesian recursive estimator (BRE). The MTTF extends a particle filter (PF) to handle the multiple targets and adds a probabilistic graphical model (PGM) data association stage to compute the mapping from detections to trackers. The MTTF was applied to the problem of passively monitoring airspace. Two applications were built: a passive radar MTT module and a comprehensive visual object tracking (VOT) system. Both applications require a solution to the MTT problem, for which the MTTF was utilized. The VOT system performed well on real data recorded at the University of Cape Town (UCT) as part of this investigation. The system was able to detect and track aircraft flying within the region of interest (ROI). The VOT system consisted of a single camera, an image processing module, the MTTF module and an evaluation module. The world coordinate frame target localization was within ±3.2 km and these results are presented on Google Earth. The image plane target localization has an average reprojection error of ±17.3 pixels. The VOT system achieved an average area under the curve value of 0.77 for all receiver operating characteristic curves. These performance figures are typical over the ±1 hr of video recordings taken from the UCT site. The passive radar application was tested on simulated data. The MTTF module was designed to connect to an existing passive radar system developed by Peralex Electronics Pty Ltd. The MTTF module estimated the number of targets in the scene and localized them within a 2D local world Cartesian coordinate system. The investigations encompass numerous areas of research as well as practical aspects of software engineering and systems design