Introduction to Kalman Filtering

This document is an introduction to Kalman optimal Filtering applied to linear systems. It is assumed that the reader is already aware of linear servo-loop theory, frequency-domain Filtering (continuous and discrete-time) and state-space approach to represent linear systems. Generally, Filtering consists in estimating a useful information (signal) from a measurement (of this information) perturbed by a noise. Frequency-domain Filtering assumes that a frequency-domain separation exists between the frequency response of the useful signal and the frequency response of the noise. Then, frequency-domain Filtering consists in seeking a transfer function fitting a template on its magnitude response (and too much rarely, on its phase response). Kalman optimal filtering aims to estimate the state vector of a linear system (thus, this state is the useful information) and this estimate is optimal w.r.t. an index performance: the sum of estimation error variances for all state vector components. First of all, some backgrounds on random variables and signals are required then, the assumptions, the structure and the computation Kalman Filter could be introduced. In the first chapter, we remind the reader how a random signal can be characterized from a mathematical point of view. The response of a linear system to a random signal will be investigated in an additional way to the more well-known response of a linear system to a deterministic signal (impulse, step, ramp, ... responses). In the second chapter, the assumptions, the structure, the main parameters and properties of Kalman Filter will be defined. The reader who wish to learn tuning methodology of the Kalman filtering can directly start the reading at chapter 2. But the reading of chapter 1, which is more cumbersome from a theoritical point of view, is required if one wishes to learn basic principles in random signal processing, on which is based Kalman Filtering. There are many applications of Kalman Filtering in aeronautics and aerospace engineering. As Kalman filter provides an estimate of plant states from an a priori information of the plant behaviour (model) and from real measurement, Kalman Filter will be used to estimate initial conditions (ballistics), to predict vehicle position and trajectory (navigation) and also to implement control laws based on a state feedback and a state estimator (LQG: Linear Quadratic Gaussian control). The signal processing principles on which is based Kalman Filter will be also very useful to study and perform test protocols, experimental data processing and also parametric identification, that is the experimental determination of some plant dynamic parameters

A survey of uncertainty principles and some signal processing applications

The goal of this paper is to review the main trends in the domain of uncertainty principles and localization, emphasize their mutual connections and investigate practical consequences. The discussion is strongly oriented towards, and motivated by signal processing problems, from which significant advances have been made recently. Relations with sparse approximation and coding problems are emphasized

Roadmap on optical security

Postprint (author's final draft

End-to-End Privacy for Open Big Data Markets

The idea of an open data market envisions the creation of a data trading model to facilitate exchange of data between different parties in the Internet of Things (IoT) domain. The data collected by IoT products and solutions are expected to be traded in these markets. Data owners will collect data using IoT products and solutions. Data consumers who are interested will negotiate with the data owners to get access to such data. Data captured by IoT products will allow data consumers to further understand the preferences and behaviours of data owners and to generate additional business value using different techniques ranging from waste reduction to personalized service offerings. In open data markets, data consumers will be able to give back part of the additional value generated to the data owners. However, privacy becomes a significant issue when data that can be used to derive extremely personal information is being traded. This paper discusses why privacy matters in the IoT domain in general and especially in open data markets and surveys existing privacy-preserving strategies and design techniques that can be used to facilitate end to end privacy for open data markets. We also highlight some of the major research challenges that need to be address in order to make the vision of open data markets a reality through ensuring the privacy of stakeholders.Comment: Accepted to be published in IEEE Cloud Computing Magazine: Special Issue Cloud Computing and the La

Learning to Extract Motion from Videos in Convolutional Neural Networks

This paper shows how to extract dense optical flow from videos with a convolutional neural network (CNN). The proposed model constitutes a potential building block for deeper architectures to allow using motion without resorting to an external algorithm, \eg for recognition in videos. We derive our network architecture from signal processing principles to provide desired invariances to image contrast, phase and texture. We constrain weights within the network to enforce strict rotation invariance and substantially reduce the number of parameters to learn. We demonstrate end-to-end training on only 8 sequences of the Middlebury dataset, orders of magnitude less than competing CNN-based motion estimation methods, and obtain comparable performance to classical methods on the Middlebury benchmark. Importantly, our method outputs a distributed representation of motion that allows representing multiple, transparent motions, and dynamic textures. Our contributions on network design and rotation invariance offer insights nonspecific to motion estimation

Automation and schema acquisition in learning elementary computer programming: Implications for the design of practice

Two complementary processes may be distinguished in learning a complex cognitive skill such as computer programming. First, automation offers task-specific procedures that may directly control programming behavior, second, schema acquisition offers cognitive structures that provide analogies in new problem situations. The goal of this paper is to explore what the nature of these processes can teach us for a more effective design of practice. The authors argue that conventional training strategies in elementary programming provide little guidance to the learner and offer little opportunities for mindful abstraction, which results in suboptimal automation and schema acquisition. Practice is considered to be most beneficial to learning outcomes and transfer under strict conditions, in particular, a heavy emphasis on the use of worked examples during practice and the assignment of programming tasks that demand mindful abstraction from these examples