High Dimensional Statistical Estimation under Uniformly Dithered One-bit Quantization

In this paper, we propose a uniformly dithered 1-bit quantization scheme for high-dimensional statistical estimation. The scheme contains truncation, dithering, and quantization as typical steps. As canonical examples, the quantization scheme is applied to the estimation problems of sparse covariance matrix estimation, sparse linear regression (i.e., compressed sensing), and matrix completion. We study both sub-Gaussian and heavy-tailed regimes, where the underlying distribution of heavy-tailed data is assumed to have bounded moments of some order. We propose new estimators based on 1-bit quantized data. In sub-Gaussian regime, our estimators achieve near minimax rates, indicating that our quantization scheme costs very little. In heavy-tailed regime, while the rates of our estimators become essentially slower, these results are either the first ones in an 1-bit quantized and heavy-tailed setting, or already improve on existing comparable results from some respect. Under the observations in our setting, the rates are almost tight in compressed sensing and matrix completion. Our 1-bit compressed sensing results feature general sensing vector that is sub-Gaussian or even heavy-tailed. We also first investigate a novel setting where both the covariate and response are quantized. In addition, our approach to 1-bit matrix completion does not rely on likelihood and represent the first method robust to pre-quantization noise with unknown distribution. Experimental results on synthetic data are presented to support our theoretical analysis.Comment: We add lower bounds for 1-bit quantization of heavy-tailed data (Theorems 11, 14

Real-Time Localization Using Software Defined Radio

Service providers make use of cost-effective wireless solutions to identify, localize, and possibly track users using their carried MDs to support added services, such as geo-advertisement, security, and management. Indoor and outdoor hotspot areas play a significant role for such services. However, GPS does not work in many of these areas. To solve this problem, service providers leverage available indoor radio technologies, such as WiFi, GSM, and LTE, to identify and localize users. We focus our research on passive services provided by third parties, which are responsible for (i) data acquisition and (ii) processing, and network-based services, where (i) and (ii) are done inside the serving network. For better understanding of parameters that affect indoor localization, we investigate several factors that affect indoor signal propagation for both Bluetooth and WiFi technologies. For GSM-based passive services, we developed first a data acquisition module: a GSM receiver that can overhear GSM uplink messages transmitted by MDs while being invisible. A set of optimizations were made for the receiver components to support wideband capturing of the GSM spectrum while operating in real-time. Processing the wide-spectrum of the GSM is possible using a proposed distributed processing approach over an IP network. Then, to overcome the lack of information about tracked devices’ radio settings, we developed two novel localization algorithms that rely on proximity-based solutions to estimate in real environments devices’ locations. Given the challenging indoor environment on radio signals, such as NLOS reception and multipath propagation, we developed an original algorithm to detect and remove contaminated radio signals before being fed to the localization algorithm. To improve the localization algorithm, we extended our work with a hybrid based approach that uses both WiFi and GSM interfaces to localize users. For network-based services, we used a software implementation of a LTE base station to develop our algorithms, which characterize the indoor environment before applying the localization algorithm. Experiments were conducted without any special hardware, any prior knowledge of the indoor layout or any offline calibration of the system

Adaptive Discrete Second Order Sliding Mode Control with Application to Nonlinear Automotive Systems

Sliding mode control (SMC) is a robust and computationally efficient model-based controller design technique for highly nonlinear systems, in the presence of model and external uncertainties. However, the implementation of the conventional continuous-time SMC on digital computers is limited, due to the imprecisions caused by data sampling and quantization, and the chattering phenomena, which results in high frequency oscillations. One effective solution to minimize the effects of data sampling and quantization imprecisions is the use of higher order sliding modes. To this end, in this paper, a new formulation of an adaptive second order discrete sliding mode control (DSMC) is presented for a general class of multi-input multi-output (MIMO) uncertain nonlinear systems. Based on a Lyapunov stability argument and by invoking the new Invariance Principle, not only the asymptotic stability of the controller is guaranteed, but also the adaptation law is derived to remove the uncertainties within the nonlinear plant dynamics. The proposed adaptive tracking controller is designed and tested in real-time for a highly nonlinear control problem in spark ignition combustion engine during transient operating conditions. The simulation and real-time processor-in-the-loop (PIL) test results show that the second order single-input single-output (SISO) DSMC can improve the tracking performances up to 90%, compared to a first order SISO DSMC under sampling and quantization imprecisions, in the presence of modeling uncertainties. Moreover, it is observed that by converting the engine SISO controllers to a MIMO structure, the overall controller performance can be enhanced by 25%, compared to the SISO second order DSMC, because of the dynamics coupling consideration within the MIMO DSMC formulation.Comment: 12 pages, 7 figures, 1 tabl