Stochastic optimization refers to the minimization/maximization of an objective function in the presence of randomness. The randomness may appear in objective functions, constraints, or optimization methods. It has the advantage of dealing with uncertainties that deterministic optimizers cannot solve or cannot solve efficiently. In this work, we discuss the implementation of stochastic optimization methods in solving target positioning problems and tackling key issues in location-based applications.
Firstly, the direction of arrival (DOA) estimation problem is studied in this work. Grid search is useful in on-grid algorithms such as maximum likelihood estimator (MLE), MUltiple SIgnal Classification (MUSIC), and so on. Although robust performance could be obtained, the computational cost is the main drawback. To speed up the search procedure, we implement a machine learning algorithm, namely, random ferns, to extract the features from the beampatterns of different DOAs and use these features to identify potential angle candidates.
Then, we propose an ultrasonic air-writing system based on DOA estimation. In this application, stochastic optimization methods are implemented to solve gesture classification problems. This work shows that stochastic optimization methods are effective tools to address and benchmark practical positioning-related problems.
Next, we discuss how to place antennas/sensors appropriately to reduce the expectation of DOA estimation error. This is useful for layout optimization in designing a receiver array to allocate a limited number of antennas in a limited space or antenna selection in a switch-based multiple-input-multiple-output (MIMO) system. Cramer Rao lower bound (CRLB) expresses a lower bound on the variance of an unbiased estimator, but it does not work well for low SNR scenarios. We proposed a threshold-region approximation-based sensor selection algorithm. A greedy algorithm and a neural network-based algorithm are proposed to enable the system with better DOA performance.
Finally, we propose a joint time difference of arrival (TDOA) and phase difference of arrival (PDOA) localization method. It is shown that the phase difference, which is also widely used in DOA estimation, can improve the performance of the well-established TDOA technique. Although the joint TDOA/PDOA cost function has a lot of local minima, by choosing an appropriate initial estimation and using particle swarm optimization (PSO), accurate estimates can be obtained effectively.
Hui Chen received his B.S. degree in electrical engineering from Beijing Forestry University, Beijing, China, in 2013, and the M.S. degree in computer application technology from the University of Chinese Academy of Sciences (UCAS), Beijing, China, in 2016. He is a PhD candidate in the Electrical and Computer Engineering department, KAUST working with Professor Tareq Al-Naffouri in the Information System Lab (ISL). His research interests include localization and tracking, stochastic optimization, and machine learning for signal processing.