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Lecture

Kalman Filters: Estimation and Localization

In course

ENG-366: Signals, instruments and systems

The goal of this course is to transmit knowledge in sensing, computing, communicating, and actuating for programmable field instruments and, more generally, embedded systems. The student will be able to put in practice the knowledge acquired using concrete ...

Description

This lecture covers the theory and application of Kalman Filters for estimation and localization in robotics. Topics include time-discrete motion and measurement models, multi-dimensional Kalman Filters, components of a Kalman Filter, and working around Kalman Filter limitations with Particle Filters.

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Instructor

Alcherio Martinoli

I received my Diploma in Electrical Engineering from the Swiss Federal Institute of Technology in Zurich (ETHZ), and a Ph.D. in Computer Science from the Swiss Federal Institute of Technology in Lausanne (EPFL). I am currently an Associate Professor at the School of Architecture, Civil, and Environmental Engineering and the head of the Distributed Intelligent Systems and Algorithms Laboratory. Before joining EPFL I carried out research activities at the Institute of Biomedical Engineering of the ETHZ, at the Institute of Industrial Automation of the Spanish Research Council in Madrid, Spain, and at the California Institute of Technology, Pasadena, U.S.A. Additional information can be found on my full CV.

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Related concepts (31)

Particle filter

Particle filters, or sequential Monte Carlo methods, are a set of Monte Carlo algorithms used to find approximate solutions for filtering problems for nonlinear state-space systems, such as signal processing and Bayesian statistical inference. The filtering problem consists of estimating the internal states in dynamical systems when partial observations are made and random perturbations are present in the sensors as well as in the dynamical system.

Kalman filter

For statistics and control theory, Kalman filtering, also known as linear quadratic estimation (LQE), is an algorithm that uses a series of measurements observed over time, including statistical noise and other inaccuracies, and produces estimates of unknown variables that tend to be more accurate than those based on a single measurement alone, by estimating a joint probability distribution over the variables for each timeframe. The filter is named after Rudolf E. Kálmán, who was one of the primary developers of its theory.

Ensemble Kalman filter

The ensemble Kalman filter (EnKF) is a recursive filter suitable for problems with a large number of variables, such as discretizations of partial differential equations in geophysical models. The EnKF originated as a version of the Kalman filter for large problems (essentially, the covariance matrix is replaced by the sample covariance), and it is now an important data assimilation component of ensemble forecasting.

Robot

A robot is a machine—especially one programmable by a computer—capable of carrying out a complex series of actions automatically. A robot can be guided by an external control device, or the control may be embedded within. Robots may be constructed to evoke human form, but most robots are task-performing machines, designed with an emphasis on stark functionality, rather than expressive aesthetics.

Motion estimation

Motion estimation is the process of determining motion vectors that describe the transformation from one 2D image to another; usually from adjacent frames in a video sequence. It is an ill-posed problem as the motion is in three dimensions but the images are a projection of the 3D scene onto a 2D plane. The motion vectors may relate to the whole image (global motion estimation) or specific parts, such as rectangular blocks, arbitrary shaped patches or even per pixel.

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