Optimal Precoders for Tracking the AoD and AoA of a mm-Wave Path

In millimeter-wave channels, most of the received energy is carried by a few paths. Traditional precoders sweep the angle-of-departure (AoD) and angle-of-arrival (AoA) space with directional precoders to identify directions with largest power. Such precoders are heuristic and lead to sub-optimal AoD/AoA estimation. We derive optimal precoders, minimizing the Cram\'{e}r-Rao bound (CRB) of the AoD/AoA, assuming a fully digital architecture at the transmitter and spatial filtering of a single path. The precoders are found by solving a suitable convex optimization problem. We demonstrate that the accuracy can be improved by at least a factor of two over traditional precoders, and show that there is an optimal number of distinct precoders beyond which the CRB does not improve.Comment: Resubmission to IEEE Trans. on Signal Processing. 12 pages and 9 figure

Analysis of A Nonsmooth Optimization Approach to Robust Estimation

In this paper, we consider the problem of identifying a linear map from measurements which are subject to intermittent and arbitarily large errors. This is a fundamental problem in many estimation-related applications such as fault detection, state estimation in lossy networks, hybrid system identification, robust estimation, etc. The problem is hard because it exhibits some intrinsic combinatorial features. Therefore, obtaining an effective solution necessitates relaxations that are both solvable at a reasonable cost and effective in the sense that they can return the true parameter vector. The current paper discusses a nonsmooth convex optimization approach and provides a new analysis of its behavior. In particular, it is shown that under appropriate conditions on the data, an exact estimate can be recovered from data corrupted by a large (even infinite) number of gross errors.Comment: 17 pages, 9 figure

Fitting Jump Models

We describe a new framework for fitting jump models to a sequence of data. The key idea is to alternate between minimizing a loss function to fit multiple model parameters, and minimizing a discrete loss function to determine which set of model parameters is active at each data point. The framework is quite general and encompasses popular classes of models, such as hidden Markov models and piecewise affine models. The shape of the chosen loss functions to minimize determine the shape of the resulting jump model.Comment: Accepted for publication in Automatic

Physiological Control of Human Heart Rate and Oxygen Consumption during Rhythmic Exercises

Physical exercise has significant benefits for humans in improving the health and quality of their lives, by improving the functional performance of their cardiovascular and respiratory systems. However, it is very important to control the workload, e.g. the frequency of body movements, within the capability of the individual to maximise the efficiency of the exercise. The workload is generally represented in terms of heart rate (HR) and oxygen consumption VO2. We focus particularly on the control of HR and VO2 using the workload of an individual body movement, also known as the exercise rate (ER), in this research. The first part of this report deals with the modelling and control of HR during an unknown type of rhythmic exercise. A novel feature of the developed system is to control HR via manipulating ER as a control input. The relation between ER and HR is modelled using a simple autoregressive model with unknown parameters. The parameters of the model are estimated using a Kalman filter and an indirect adaptive H1 controller is designed. The performance of the system is tested and validated on six subjects during rowing and cycling exercise. The results demonstrate that the designed control system can regulate HR to a predefined profile. The second part of this report deals with the problem of estimating VO2 during rhythmic exercise, as the direct measurement of VO2 is not realisable in these environments. Therefore, non-invasive sensors are used to measure HR, RespR, and ER to estimate VO2. The developed approach for cycling and rowing exercise predicts the percentage change in maximum VO2 from the resting to the exercising phases, using a Hammerstein model.. Results show that the average quality of fit in both exercises is improved as the intensity of exercise is increased

A New Path Planning Guidance Law For Improved Impact Time Control of Missiles and Precision Munitions

A new missile guidance law is proposed for the control of impact time which provides an improved time-to-go calculation by removing error due to trajectory curvature and also provides a family of trajectories for trajectory planning purposes. Unlike conventional optimal guidance laws, the proposed law is non explicit in time-to-go and the linearization of the engagement kinematics in order to gain a closed form solution is not necessary

Regularized System Identification

This open access book provides a comprehensive treatment of recent developments in kernel-based identification that are of interest to anyone engaged in learning dynamic systems from data. The reader is led step by step into understanding of a novel paradigm that leverages the power of machine learning without losing sight of the system-theoretical principles of black-box identification. The authors’ reformulation of the identification problem in the light of regularization theory not only offers new insight on classical questions, but paves the way to new and powerful algorithms for a variety of linear and nonlinear problems. Regression methods such as regularization networks and support vector machines are the basis of techniques that extend the function-estimation problem to the estimation of dynamic models. Many examples, also from real-world applications, illustrate the comparative advantages of the new nonparametric approach with respect to classic parametric prediction error methods. The challenges it addresses lie at the intersection of several disciplines so Regularized System Identification will be of interest to a variety of researchers and practitioners in the areas of control systems, machine learning, statistics, and data science. This is an open access book