Tutorials

Navigation-grade inertial systems are characterized by so-called “free inertial” position error drift rates on the order of one nautical mile-per-hour of operation.  Such performance implies a certain class of gyros and accelerometers and thus certain specifications on biases, scale factor errors and noise.  The first part of this tutorial will cover the basics of free-inertial processing (e.g., determination of position/velocity/attitude) and will consider the major error analyses that dominate system performance.  Attention will then be turned to the subject of aiding.  For more than five decades, the Kalman filter has been the primary tool used to reduce inertial drift through the integration of various sensors.  Specifically, the aiding sources (e.g., stellar, Doppler, GPS, etc) are used by the filter to estimate the errors in the free inertial processing.  Thus, the heart of any aided-inertial Kalman filter is the inertial error model including, specifically, sensor errors.  The tutorial will discuss these models and will proceed to explain how aiding source observations are then used by the filter, in conjunction with the models, to estimate the inertial errors.  For example, a given aiding source may provide an independent measurement of position, yet somehow the filter is able to use this in order to estimate gyro biases in the inertial system.  Join us as we unravel these mysteries.

The bumblebee paradox: engineers said that bumblebee flight was impossible, and yet they flew. That may be inspirational, teaching us to reach for goals despite the doubts and criticisms of other people, but it could not be more wrong.  Insects were the first organisms on Earth to develop flight and yet when humans successfully took to the skies, they used fixed wing aircraft more like birds and pterodactyls rather than flapping flight. The explanation of how insects are able to fly came not from applying fixed wing aerodynamics, which gave rise to the bumblebee paradox, but instead counted on completely new ideas published in the 1984 Ellington papers reporting on years of research into flapping wing flight aerodynamics.  This discovery was made possible by combining the tools of engineering and the measurements of biologists; neither discipline alone could have resolved the bumblebee paradox. More than 30 years before the mathematics of flapping flight had been worked out, the modified hind wings of dipteran flies had been established as gyroscopic sensors optimized to detect Coriolis forces, enabling stabilization of the unsteady fly in roll, pitch, and yaw. This leaves out the bumblebee, however, since it still retains all four of its wings. Attention has now turned into how other body parts could serve as inertial sensors for stabilizing unsteady insect bodies in flight. Beyond inertia, there are at least a dozen modes of sensing and half a dozen modes of transduction that all contribute to the guidance, navigation, and control of natural systems. Studying these integrated sensing and actuation systems may substantially aid the future development of cheap, fast, agile, autonomous flight.

In this tutorial, we will go beyond inertia. We will put inertial sensing in the context of how insects use all of their senses to navigate the world. Insects can detect acoustic waves, airflow, chemicals, gravity, magnetic fields, electromagnetic radiation, pressure, heat, ultrasonics, strain, and infrared. Precision in these noisy sensory signals is increased through range fractionation meaning the natural systems divide up the sensory space for representation rather than covering the entire spectrum like engineered sensors.  We will explore not just the sensory systems, but how these signals are actually perceived mechanically and organically and transformed into neural signals. Natural systems do not operate in a vacuum, but instead are tightly integrated and understanding their inertial sense requires that we study it in context.  Sensing and transduction and neural codes are a symbiosis that is the key to how noisy, low resolution low energy systems can still outperform engineered platforms.

From Atomic Clocks to Time Scales

Time and Frequency Division – NIST.

This tutorial will guide you through all the systems and tools involved in the generation and dissemination of time, including primary frequency standards, commercial atomic clocks, time scales, and the techniques and challenges associated with the distribution of accurate and assured time to its users.

We will cover the physics of traditional, commonly available, commercial atomic clocks, as well as a description of laboratory standards and nascent commercial laser-cooled atomic clocks, all based upon hyperfine splitting in Alkali systems.  We then will delve into the analytic tools used in the characterization of these clocks (Allan Variance and its many progeny), to allow discussing the relative quality of these different clocks, in terms of their Size, Weight and Performance (SWaP). 

Atomic clocks are used to generate time, the SI quantity that requires the highest degree of coordination and monitoring: time standards are not physical objects that require only occasional calibration, but fleeting pulses in time that occur once and then are gone.   An overview of the systems involved in the generation of time will be provided, briefly describing how Universal Coordinated Time (UTC) is created and maintained.

Finally, an ever more interconnected world where precision timing is both a powerful enabler and a great vulnerability is adding a new dimension to the topic of time dissemination.  The almost complete reliance on GNSS for the distribution of time to its large and very disparate number of users has brought to the fore the intrinsic vulnerabilities of a timing infrastructure based on a single technology.  As a conclusion to this tutorial, we will provide an overview of the efforts under way in the community to address the need of a diverse and robust timing infrastructure at the (inter)continental level.