At ION GNSS 2011 in Portland OR, James L. Farrell, Javad Ashjaee and others will participate in a panel discussing the U.S. Dept. of Homeland Security’s concerns on the effects of GPS jamming and spoofing on our national critical infrastructure.

Subject: Panel discussion format and schedule

Dr. Todd Humphreys noted that our upcoming panel session is shaping up to be one of the highlights of ION GNSS 2011. The U.S. Dept. of Homeland Security recently completed a risk assessment of the effects of GPS jamming and spoofing on national critical infrastructure. Some of us participated as subject matter experts in this assessment.

The DHS report, which is the most thorough one to date on this topic, has left many people saying “Yes, it’s a problem. Now what?”

Our panel will help to address the “Now what?”

Topic:

How do we secure civil GNSS?

Schedule

• 8:30: Welcome and introduction: Moderator introduces topic, format, and ground rules
• 8:40: Moderator introduces panelists
• 8:45: Moderator frames the central question: “How do we secure civil GNSS?”
• 8:50: Logan Scott
• 9:00: Panel/audience response to Logan’s remarks
• 9:10: Javad Ashjaee
• 9:20: Panel/audience response to Javad’s remarks
• 9:30: Mark Psiaki
• 9:40: Panel/audience response to Mark’s remarks
• 9:50: Questions from audience, discussion among panelists

• 10:05 — 10:35: Morning break

• 10:35: Moderator welcomes audience and panel back, summarizes morning discussion
• 10:40: Oscar Pozzobon
• 10:50: Panel/audience response to Oscar’s remarks
• 11:00: James Farrell
• 11:10: Panel/audience response to James’s remarks
• 11:20: Felix Kneißl
• 11:30: Panel/audience response to Felix’s remarks
• 11:40: Questions from audience; discussion among panelists
• 12:10: Moderator and panelists offer concluding remarks
• 12:15: Panel concludes

ON GNSS 2011
September 19-23, 2011 (Tutorials: September 19-20)
Oregon Convention Center, Portland, Oregon

Click here for more information

http://www.ion.org/meetings/session.cfm?meetingID=34&t=P&s=5

“Attitude Determination by Kalman Filtering” is the title of three documents I had published.  In reverse sequence they are:
1) Automatica (IFAC Journal), v6 1970, pp. 419-430,
2) my Ph.D. dissertation (Univ. of Maryland, 1967),
3) NASA CR-598, Sept., 1966.
As indicated by the last reference, the work was the result of a contractual study sponsored by NASA (specifically Goddard Space Flight Center – GSFC – in Greenbelt Maryland).  I was working for Wetinghouse Defense and Space Center at the time.  The proposal I had written to win this contract cited my work prior to then, in both modern estimation (“Simulation of a Minimum Variance OrbitalNavigation System,” AIAA JSR v 3 Jan 1966 pp. 91-98) and attitude computation (“Performance of Strapdown Inertial Attitude Reference Systems,” AIAA JSR v 3 Sept 1966, pp. 1340-1347).  Let me hasten to explain the dates of those Journal publications: each followed its inclusion at an AIAA-sponsored conference, about a year earlier.

By the mid-1960s there was an appreciable amount of validation for Kalmen filtering applied to determination of orbits (that track record was convincing) but not yet for attitude.  A GSFC-sponsored investigation was then planned — the very first one for attitude using modern estimation methods.  GSFC management understandably wanted that contractual investigation to be performed by someone with demonstrable experience in both Kalman filtering and rotational dynamics.  In those days that combination was rare; the Westinghouse proposal was chosen as the winner.  At the time of that study, provisions realistically available for attitude updating consisted of mediocre-accuracy items such as magnetometers and horizon scanners– not bad but not spectacular either.
All that was of course before GPS weighed in, with its opportunity to reveal attitude from phase differences between antennas spaced at known distances apart.  That vastly superior capability effectively reduced earlier crude measurements to relative obscurity.  A directly parallel situation occurred in connection with navigation; the book that first tied together several facets of advancement in that field (integration, strapdown inertial, modern estimation with  acceptance of all data sources, multimode operation, extension to tracking, clear exposition of all commonly used representations of attitude, etc.) was”pre-GPS” (1976), and consequently regarded as less relevant. Timing can be decisive — that’s no one’s fault.

The item just noted — attitude representation — is worth further discussion here.  Unlike many other sources, the 1976 book offered an opportunity to use quaternion properties without any need to learn a specialized quaternion algebra.  A literature search, however, will point primarily to various sources (of necessity, later than 1976).that benefit from the superior performance offered through GPS usage. Again, in view of GPS as a game-changer, that is not necessarily improper.  Most publications on attitude determination don’t cite the first-ever investigation, sponsored by GSFC, for that innocent reason.

The word beginning that last sentence (“Most”) has an exception.  One author, widely quoted as an authority (especially on quaternions), did cite the original work — dismissing it as “ad-hoc” — while using an exact copy of the sensitivity matrix elements pubished in my original investigation (the three references cited at the start of this blog).
While I obviously didn’t invent either quaternions or the Kalman filter, there was another thing I didn’t do: fail to credit, in my publications, pre-existing sources that contributed to my findings. Publication of the material cited here, I’ve been told, paved the way for understanding and insight to many who followed. No one owes me anything for that; an analyst’s work, truthfully and realistically presented, is what the analyst has to offer.

It is worth pointing out that both the attitude determination study and the 1976 book cover another facet of rotational analysis absent from many other related publications: dynamics — in the sense of physics.  Whereas modern estimation lumps time-variations of the state together into one all-encompassing “dynamic” model, classical physics makes a separation: Kinematics defines the relation between position, rates, and accelerations.  Dynamics determines translational accelerations resulting from forces or rotational accelerations resulting from torques.

Despite absence of GPS from my early (1960s/70s) investigations, one feature that can still make them useful for today’s analysts is the detailed characterization of torques acting — in very different ways — on spinning and gravity-gradient satellites, plus their effects on rotational motion. Many of the later studies focused on the rotational kinematics, irrespective of those torques and their consequences. Similarly, the “minimal-math”approach to explaining integrated navigation has enabled many to grasp the concepts.  Printed testimony to that effect, from courses I taught decades ago, is augmented by more recent source noted near the end of another page shown on this site.

It would be worth investigating Mode-S transmission once per second, at a very low-level (undetectable at distances beyond an airport). Message content could take the form discussed in an accompanying blog.

I feel compelled to voice support of these authors — not just because points they raise are consistent with many of my own writings (a bit more on that later) — but because, unlike a “one-man-band” (myself), they could be in a position to catalyze remedial action.

The briefs just cited point, correctly, to shortcomings in stewardship of a vital resource.  Those shortcomings are so severe that, after a lifetime of acknowledging how management is far beyond my range of capability, I’m now jumping in over my head.  Maybe my only way to help coax decision-makers gently toward action is to assert that paralysis-of-the-will is easily recognized, even to someone with no administrative capability at all.

In regard to concurrence from my own writings — rather than a long list of sources, I’ll name just one: a short GPS World TechTalk blog, with links to other papers, blogs, etc. that can be accessed at the readers’ option.  Those who exercise that option will find a wealth of evidence for, and advocacy of, available means to enhance satellite navigation performance under adverse conditions.  By that I’m not implying that I had already covered all the points raised this Spring — i.e., the briefs cited at the beginning of this post include items not covered in my earlier writings.

The point is that Sally Basker and the Overlook authors (Doug Taggart et.al.) are right.  So was GPS World’s “Masked Engineer” of 2010.  So are many more, too numerous to list here, who speak out on these issues — repeatedly.  We repeat our concerns, not to be burdensome and annoying like some broken record; we persist because the problems being identified persist.  Action is essential — or, as long as I’m jumping in over my head — continued inaction is inexcusable.

My 2007 book on GPS and GNSS (GNSS Aided Navigation & Tracking), as its title implies, involves both navigation and tracking. This discussion describes the latter, covered in the longest chapter of the book (Chapter 9).  In addition to the flight-validated algorithms for navigation (processing of inertial sensor data, integration with GPS/GNSS, integrity, etc.), this text offers extensive coverage of tracking. Formulations are given for a variety of modes, in 2-D (e.g., for runway incursion prevention or ships) and 3-D (in-air), using GPS/GNSS and/or other sensors (e.g., radar, optical).  Position and velocity vectors are formed, in some operations joined by some or all components of acceleration.

applies to tracking as well as to navigation.  The book identifies subtleties that arise in specific applications (aircraft, ships, land vehicles, satellites, long-range or short-range projectiles, reentry vehicles, missiles, … ). In combination with a variety of possible conditions affecting sensor suite and location (air-to-air; air-to-ground; air-to-sea surface; surface-to-air, etc. – with measurements associated with distance or direction or both; shared or not shared among participants who may communicate from different positions), it is not surprising that striking contrasts can arise, influencing the characterization and approaches used.  The array of formulations offered, while fully accounting for marked differences among operations, nevertheless exploits an underlying commonality to the maximum possible extent.

Tracking dynamics of aircraft, missiles, ships, satellites, projectiles, …

Check out a preview of “GNSS Aided Navigation & Tracking” (click here)

GNSS Aided Navigation & Tracking

– Inertially Augmented or Autonomous
By James L. Farrell
American Literary Press. 2007. Hardcover. 280 pages
ISBN-13: 978-1-56167-979-9

This text offers concise guidance on integrating inertial sensors with GPS and also its international version (global navigation satellite system; GNSS) receivers plus other aiding sources. Primary focus is on low-cost inertial measurement units (IMUs) with  frequent updates, but  other functions (e.g., tracking in numerous modes) and sensors (e.g., radar) are also addressed.

Price is: $100.00 Plus Shipping
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Dr. Farrell has many decades of experience in this subject area; in the words of one reviewer, the book is “teeming with insights that are hard to find or unavailable elsewhere.”

An engineer and former university instructor, Farrell has made a number of contributions to multiple facets of  navigation.  He is also the author of Integrated Aircraft Navigation (1976; five hard cover printings; now in paperback) plus over eighty journal or conference manuscripts and various columns.

Frequent aiding-source updates, in applications that require precise velocity rather than extreme precision in position, enables integration to be simplified. All aspects of integration are covered, all the way from  raw measurement pre-processing to final 3-D position/velocity/attitude, with far more thorough backup and integrity provisions.  Extensive experimental results  illustrate the attainable accuracies (cm/s RMS  velocities in three-dimensions) during flight under extreme vibration.

The book on GPS and GNSS provides several flight-validated formulations and algorithms not currently in use because of their originality. Considerable opportunity is therefore offered in multiple areas including
* full use of highly intermittent ambiguous carrier phase
* rigorous integrity for separate SVs
* unprecedented robustness and situation awareness
* high performance from low cost IMUs
* “cookbook” steps
* new interoperability features
* new insights for easier implementation.

Discussion of these traits can be seen in the excerpt (over 100 pages) from the  link at the top of this page.

A 1999 publication I coauthored took dead aim at a characteristic that received far too little attention — and still continues to be widely overlooked: mechanical mounting misalignment of inertial instruments.  To make the point as clearly as possible I focused exclusively on gyro misalignment — e.g., the sensitive axes of roll, pitch, and yaw gyros aren’t quite perpendicular to one another.  It was easily shown that the effect in free-inertial coast (i.e., with no updates from GPS or other navaids) was serious, even if no other errors existed.

Misalignment: mechanical mounting imprecision

Whenever this topic is discussed, certain points must be put to rest.  The first concerns terminology; much of the petinent literature uses the word misalignments to describe small-angle directional uncertainty components (e.g., error in perception of downward and North, which drive errors in velocity).  To avoid misinterpretation I refer to nav-axis direction uncertainty as misorientation.  In the presence of rotations, mounting misalignment contributes to misorientation.  Those effects, taking place promptly upon rotation of the strapdown inertial instrument assembly, stand in marked contrast to leisurely (nominal 84-minute) classical Schuler dynamics.

A third point involves error propagation and a different kind of calibration (in-flight).  With the old (gimbal) mechanization, in-flight calibration could counteract much overall gyro drift effect.  Glib assessments in the 1990s promoted widespread belief that the same would likewise be true for  strapdown.  Changing that perspective motivated the investigation and publication mentioned at the top of this blog.

The final point concerns the statistical distribution of errors.  Especially with safety involved (e.g., trusting free-inertial coast error propagation), it is clearly not enough to specify RMS errors.  For example, 2 arc-sec is better than 20 but what are the statistics?  Furthermore there is nothing to preclude unexpected extension of duration for free-inertial coast after a missed approach followed by a large change in direction.  A recent coauthored investigation (Farrell and vanGraas, ION-GNSS-2010 Proceedings) applies Extreme Value Theory (EVT) to outliers, showing unacceptably high incidences of large multiples (e.g., ten-sigma and beyond).  To substantiate that, there’s room here for an abbreviated explanation –  even in linear systems, gaussian inputs produce gaussian outputs only under very restrictive conditions.

The practice of dead reckoning (a figurative phrase of uncertain origin) is five centuries old.   In its original form, incremental excursions were plotted on a mariner’s chart using dividers for distances, with directions obtained via compass (with corrections for magnetic variation and deviation). Those steps, based on perceived velocity over known time intervals, were accumulated until a correction became available (e.g., from a landmark or a star sighting).

Modern technology has produced more accurate means of dead reckoning, such as Doppler radar or inertial navigation systems.   Addressed here is an alternative means of dead reckoning, by exploiting sequential changes in highly accurate carrier phase. The method, successfully validated in flight with GPS, easily lends itself to operation with satellites from other GNSS constellations (GALILEO, GLONASS, etc.).  That interoperability is now one of the features attracting increased attention; sequential changes in carrier phase are far easier to mix than the phases themselves, and measurements formed that way are insensitive to ephemeris errors (even with satellite mislocation,  changes in satellite position are precise).

Even with usage of only one constellation (i.e., GPS for the flight test results reported here), changes in carrier phase over 1-second intervals provided important benefits. Advantages to be described now will be explained in terms of limitations in the way carrier phase information is used conventionally.   Phase measurements are normally expressed as a product of the L-band wavelength multiplied by a sum in the form (integer + fraction) wherein the fraction is precisely measured while the large integer must be determined. When that integer is known exactly the result is of course extremely accurate.  Even the most ingenious methods of integer extraction, however, occasionally produce a highly inaccurate result.   The outcome can be catastrophic and there can be an unacceptably long delay before correction is possible.   Elimination of that possibility provided strong motivation for the scheme described here.

Linear phase facilitates streaming velocity with GNSS interoperability

With formation of 1-sec changes, all carrier phases can be forever ambiguous, i.e., the integers can remain unknown; they cancel in forming the sequential differences. Furthermore, discontinuities can be tolerated; a reappearing signal is instantly acceptable as soon as two successive carrier phases differ by an amount satisfying the single-measurement RAIM test.   The technique is especially effective with receivers using FFT-based processing, which provides unconditional access, with no phase distortion, to all correlation cells (rather than a limited subset offered by a track loop).

Another benefit is subtle but highly significant: acceptability of sub-mask carrier phase changes. Ionospheric and tropospheric timing offsets change very little over a second. Conventional systems are designed to reject measurements from low elevation satellites. Especially in view of improved geometric spread, retention here prevents unnecessary loss of important information.   Demonstration of that occurred in flight when a satelllite dropped to horizon; submask pseudoranges of course had to be rejected, but all of the 1-sec carrier phase changes were perfectly acceptable until the satellite was no longer detectable.

One additional (deeper) topic, requiring much more rigorous analysis, arises from sequential correlations among 1-sec phase change observables. The issue is thoroughly addressed and put to rest in the later sections of the 5th chapter of GNSS Aided Navigation and Tracking.

Dead reckoning capability without-IMU was verified in flight, producing decimeter/sec RMS velocity errors outside of turn transients (Section 8.1.2, pages 154-162 of the book just cited). With a low-cost IMU, accuracy is illustrated in the table near the bottom of a 1-page description on this site (also appearing on page 104 of that book). All 1-sec phase increment residual magnitudes were zero or 1 cm for the seven satellites (six across-SV differences) observed at the time shown. Over almost an hour of flight at altitude (i.e., excluding takeoff, when heading uncertainty caused larger lever-arm vector errors), cm/sec RMS velocity accuracy was obtained.

Methods I use for processing GPS data include many sharp departures from custom.  Motivation for those departures arose primarily from the need for robustness.  In addition to the common degradations we’ve come to expect (due to various propagation effects, planned and unplanned outages, masking or other forms of obscuration and attenuation), some looming vulnerabilities have become more threatening.  Satellite aging and jamming, for example, have recently attracted increased attention.  One of the means I use to achieve enhanced robustness is acceptance-testing of every GNSS observable, regardless of what other measurements may or may not be available.

Classical (Parkinson-Axelrad) RAIM testing (see, for example, my ERAIM blog‘s background discussion) imposes requirements for supporting geometry; measurements from each satellite were validated only if more satellites with enough geometric spread enabled a sufficiently conclusive test.  For many years that requirement was supported by a wealth of satellites in view, and availability was judged largely by GDOP with its various ramifications (protection limits).  Even with future prospects for a multitude of GNSS satellites, however, it is now widely acknowledged that acceptable geometries cannot be guaranteed.  Recent illustrations of that realization include
* use of subfilters to exploit incomplete data (Young & McGraw, ION Journal, 2003)
* Prof. Brad Parkinson’s observation at the ION-GNSS10 plenary — GNSS should have interoperability to the extent of interchangeability, enabling a fix composed of one satellite from each of four different constellations.

Among my previously noted departures from custom, two steps I’ve introduced  are particularly aimed toward usage of all available measurement data.  One step, dead reckoning via sequential differences in carrier phase, is addressed in another blog on this site.  Described here is a summary of validation for each individual data point — whether a sequential change in carrier phase or a pseudorange — irrespective of presence or absence of any other measurement.

While matrix decompositions were used in its derivation, only simple (in fact, intuitive) computations are needed  in operation.  To exphasize that here, I’ll put “the cart before the horse” — readers can see the answer now and optionally omit the subsequent description of how I formed it.  Here’s all you need to do: From basic Kalman filter expressions it is recalled that each scalar residual has a sensitivity vector H and a scalar variance of the form

The ratio of each independent scalar residual to the square root of that variance is used as a normalized dimensionless test statistic.  Every measurement can now be used, each with its individual variance.  This almost looks too good to be true and too simple to be useful, but conformance to rigor is established on pages 121-126 and 133 of GNSS Aided Navigation and Tracking.  What follows is an optional explanation, not needed for operational usage.

The key to my single-measurement RAIM approach begins with a fundamental departure from the classical matrix factorization ( QR=H ) originally proposed for parity.  I’ll note here that, unless all data vector components are independent with equal variance, that original ( QR=H ) factorization will produce state estimates that won’t agree with Kalman.  Immediately we have all the motivation we need for a better approach.  I use the condition

where U is the inverse square root of the measurement covariance matrix.  At this point we exploit the definition of a priori state estimates as perceived characterizations of actual state immediately before a measurement — thus the perceived error state is by definition a null vector.  That provides a set of N equations in N unknowns to combine with each individual scalar measurement, where N is 4 (for the usual three unknowns in space and one in time) or 3 (when across-satellite differences produce three unknowns in space only).