Browsing by Subject "Adaptive estimation"

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    Exploiting Inherent Magnetic Signatures of Ferromagnetic Objects for Detection, Identification, and Position Estimation Applications
    (2014-09-12) Taghvaeeyan, Saber
    Many creatures in nature, such as butterflies, newts and mole rats, use the Earth's inherent magnetic field for navigation. They use magnetic field lines and magnetic field intensity variations to determine their geographical position. In this thesis, similar techniques are developed to measure the positions of individual ferromagnetic objects found all around us in everyday life. Ferromagnetic objects have inherent magnetic fields around them. It is shown here that the magnetic field variation around a ferromagnetic object can be modeled using purely the geometry of the object under consideration. Exploiting this model of the inherent magnetic field, the position of the object can be measured accurately using a small inexpensive magnetic sensor. Further, the use of one or more additional (redundant) sensors and adaptive estimation algorithms eliminates the need for pre-calibration of the measurement system. The significance and applicability of this new sensing principle is shown through three major applications: 1) Imminent automotive crash detection, 2) Non-intrusive piston position estimation, and 3) Portable road-side sensor for vehicle counting, speed measurement, and classification. The work on imminent automotive crash detection is motivated by the need to develop an inexpensive sensor system for an automobile that can predict an imminent collision with another vehicle just before the collision occurs. The prediction needs to occur at least 100 milliseconds before the collision so that there is adequate time to initiate active occupant protection measures during the crash. A vehicle is made of many metallic parts (such as chassis, engine, and body) which have a residual magnetic field and/or get magnetized in the Earth's magnetic field. These magnetic fields create a net magnetic field for the whole vehicle which can be analytically modeled as a function of 2-D position around the vehicle. While this model can be used to estimate position and orientation, a challenge is posed by the fact that the parameters in the analytical function vary with the type and model of the encountered car. Since the type of vehicle encountered is not known a priori, the parameters in the magnetic field function are unknown. The use of both sonar and magnetic sensors and an adaptive estimator is shown to address this problem. While the sonar sensors do not work at very small inter-vehicle distance and have low refresh rates, their use during a short initial time period leads to a reliable estimator. Extensive experimental results are presented using a laboratory wheeled car door and full scale passenger sedans. The results show that planar position and orientation can be accurately estimated for a range of relative motions at different oblique angles. A video showing a real-time demo of the system is included both in the thesis and supplementary files. Next, the proposed sensing principle is adopted to develop a sensor system for non-intrusive measurement of piston position inside a cylinder. Piston position measurement is required for many applications in a number of industrial domains. Examples include piston position estimation for engine performance optimization, automatic earth excavation, and seeding depth control for precision farming. By modeling the magnetic field of the piston as a function of its position and using sensors to measure magnetic field intensity, the position of the piston can be estimated. A challenge arises from the fact that the parameters of the model vary from one piston to another piston and it would be cumbersome to calibrate for each piston. This challenge is addressed by utilizing two magnetic field sensors with known longitudinal separation between them. A number of estimation methods are proposed that identify and update magnetic field parameters in real time without requiring any additional reference sensor for calibration. Results of experiments with a free piston engine and a pneumatic actuator are presented showing a maximum absolute error of 0.4 mm in both applications. A video showing a real-time demo of the system is included both in the thesis and supplementary files. A serious challenge in the usage of magnetic sensors is the influence of disturbances caused by other ferromagnetic objects brought close to the sensors. External ferromagnetic objects can disturb the sensors signals causing large errors in position estimation. To address this issue, a method based on redundant sensors is developed to eliminate the influence of external magnetic disturbances. Experimental results demonstrate that sub-millimeter accuracies in position measurement can be obtained with such a system in spite of disturbances from external ferromagnetic objects. Finally, the proposed sensing principle is adopted to develop a portable roadside sensor system for vehicle counting, classification and speed measurement. The sensor system can be placed next to the road to measure traffic in the adjacent lane. The detection rate accuracy of the system is shown to be 99%. An algorithm based on a magnetic field model is proposed to make the system robust to the errors created by larger vehicles driving in the nonadjacent lane of the road. These false calls cause 8% error if uncorrected. Use of the proposed algorithm reduces this error to only 1%. A speed measurement algorithm is developed that is based on calculation of cross-correlation between longitudinally spaced sensors. Fast computation of cross-correlation is enabled by using frequency domain signal processing techniques. An algorithm to automatically correct for any small misalignment of the sensors is utilized. Using an accurate differential GPS as a reference, it is shown that maximum absolute error of the speed estimates is less than 2.5% over the entire speed range of 5-27 m/s (11-60 mph). Vehicle classification is done based on the magnetic length and an estimate of the average vertical magnetic height of the vehicle. Vehicle length is estimated from the product of occupancy and estimated speed. Average vertical magnetic height is estimated by using two magnetic sensors vertically spaced by 0.3 m. Also, it is shown that the sensor system can be used to reliably count the number of right turns at an intersection with an accuracy of 95%. The developed sensor system is compact, portable, wireless and inexpensive. Data is presented from a large number of vehicles on a regular busy urban road in the Twin Cities in Minnesota. The fundamental contribution of this thesis is the development of a new sensing principle that has a large number of applications in a number of different engineering domains.
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    Minimax estimation and model identification for high-dimensional regression.
    (2012-08) Wang, Zhan
    This dissertation consists of two parts. In Part I, adaptive minimax estimation over sparse `q-hulls is studied. Given a dictionary of Mn initial estimates of the unknown regression function, we aim to construct linearly aggregated estimators that target the best performance among all linear combinations under a sparse q-norm (0 <_ q <_ 1) constraint. Besides identifying the optimal rates of aggregation for these `q-aggregation problems, our multi-directional (or adaptive) strategies by model mixing or model selection achieve the optimal rates simultaneously over the full range of 0 <_ q <_ 1 for general Mn and upper bound tn of the q-norm. Both random and fixed designs, with known or unknown error variance, are handled, and the `q-aggregations examined in this work cover major types of aggregation problems previously studied in the literature. Consequences on minimax-rate adaptive regression under `q- constrained coefficients are also provided. In Part II, the relationship between consistency and minimax-rate optimality in possibly high-dimensional regression estimation is investigated. In model selection where the true model is fixed, it is now well-known that if a model selection method is consistent, it cannot be minimax-rate optimal at the same time. We investigate this con ict in a high-dimensional regression setting where the true model is a changing target, and show that consistency and minimaxrate optimality may co-exist in a single model selection method. Our results provide a comprehensive guideline for characteristics of a model selection method which can be consistent and minimax-rate optimality at the same time.