Now that a few years have passed since the LORAN-C budget was killed, it might be a good time to revisit that decision. Unlike other decisions, this one might conceivably be undone; there hasn’t been the widespread demolition of resources (e.g., towers, transmitters) followed by restoration of sites. Something else, though, did occur: recent success achieved by cooperative effort between the Coast Guard and UrsaNav Inc.

For brevity here it suffices to make a few surface-scratching notes. The vast majority of us in the navigation community recognized the potential benefit of LORAN (and an extended form eLORAN) as a crucial backup — at extremely low cost — to be used when GPS is unavailable.  Many of us, furthermore, anxiously pressed for sanity (e.g., my “2-cents worth” written, to no avail, in 2009).

What’s different now, conceivably, is a combined effect of multiple factors:
* The USCG/UrsaNav success surpassed goals that had been stated earlier.
* Awareness of GPS vulnerability (therefore need for backup) has increased.
* Delay in follow-through (site restoration) offers the chance for a remedy.

An utterance appearing in Coordinates Magazine’s March 2012 cover story was reached from a different context, but its importance prompted me to cite it in the April 2012 cover story — and to repeat it here: “Do we really need to wait for a catastrophe before taking action against GNSS vulnerabilities?”

Once again I’m adding my voice to the chorus of those speaking out before it’s too late.

I perform functional formulations and algorithm generation plus validation for both simulation and operational purposes in system integration. Specific areas include navigation, communication, data integrity, and tracking for aerospace, applying modern estimation to data from various sources (COMM, gyros, accelerometers, GPS/GNSS, radar, optical, etc.). 

Complete Viewable & printable Resume Click Here
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Questions submitted by members of various forums, understandably, frequently involve one or more of the following topics:
 * some or all facets of inertial navigation
 * means of updating and reinitializing the drifting inertial solution
 * satellite navigation (GPS/GNSS) for providilng the updates
 * other means of updating (radar, laser, optics, VOR, DME, hyperbolic, … )
 * best ways to use what’s available for various applications.
The pool of literature that might be offered can be vast, partly due to a vast array of operations – each with application-dependent requirements.  Finding just the relevant information from a mountain of available references can be a daunting task, especially for young designers.  I’ll try to make their search easier, by offering a list they can ask themselves early in the design process:
 * do you need a lat/lon/altitude Earth reference or just a designated point?
 * is the path determined from provisions onboard (nav) or remote (track)?
 * what’s your required accuracy for “absolute” (geolocation) position?
 * what’s your required accuracy for relative position (e.g., from a runway)?
 * do you need precise incremental position history (SAR motion compensation)?
 * do you need precise angular orientation (e.g., laser pointing)?
 * do you need precise angular rates (for image or antenna stabilization)?
 * for direction do you use a North reference or just along-track/cross-track?
 * will you have dependable access to updating information (GPS, radar, …)?
 * if not, how irregular will dynamics be over active parts of your mission?
 * if so, how irregular will the dynamics be during inter-update periods?
 * also if so, what data rate? Longest expected “blind period” between updates?
 * also if so, will measurements need averaging to meet your required accuracy?
 * also if so, how accurate are your measurements AND their time stamps?
 * also if so, can you use postprocessing or do you need everything real-time?
 * are you willing to accept partial updates (some but not all directions)?
 * do you need just position or derivatives too (velocity, acceleration)?
 * if so, how long can your dynamics be trusted to conform to model fidelity?
 * are you doing INS update (e.g., replacing acceleration with tilt states)?
 * if so, will you need to deduce drift rates – and how long will those hold?
 * do your sensors measure distances, angles, doppler, differences of those?
 * for how long does your sensor information content provide observability?
 * how’s your sensor integrity (bad readings at least detectable if present)?
 * for safety-critical operations — what are your backup provisions?
 * are you accommodating multiple modes with time-shared sensing resources?
 * do you need to perform image registration with different imaging sensors?
etc.etc. — the list goes on.  I won’t even try to claim thoroughness; you get the idea.  Designers with new tasks dumped in their lap can understandably feel overwhelmed.  Searching for references can become a trip through a maze of half-relevant sources.
A first step, then, is to separate the relevant (what you need) from the irrelevant (what you don’t need), instantly dismiss any thought of the latter, and do the opposite with the former (nail it).
Brief examples — the first two items from the above list —
 * If you just need to know your location relative to a designated point, irrespective of its latitude and lingitude — this might help.
 * If you’re tracking instead of navigating — check these out —
and one from the last item from that list —
Again, you get the idea — volumes have been written on all facets.  Many won’t apply to your immediate task; disregard those.
The good news is — paths to logical solutions are known and documented.  To avoid abandoning you to an enormous maze of references I’ll point out some fundamental and advanced (state-of-the-art) tracts that address all issues just cited and more.  Several blogs and short “1-pagers” will help individual designers to choose, based on their specific tasks, passages from available references.
Before GPS we struggled hard for accurate measurements in enough places.  That actually produced a benefit — we had to be resourceful.  My biggest challenge was to understand subjects (Kalman filtering, strapdown inertial navigation) then considered exotic.  Again a benefit; pulling information from 1950s books and papers forced me to understand, focus, and reduce concepts to whatever level became necessary.  The experience prompted me to write the first of my two books on navigation.
That first book has been used in myriad courses, including one currently taught by Prof. Hablani who wrote the most recent testimonial shown on that URL .
Some topics that earlier book explained in detail recently came up in another discussion — http://www.linkedin.com/groupAnswers?viewQuestionAndAnswers=&discussionID=44646633&gid=160643&commentID=68798460&trk=view_disc
For example, slow (“W” radian/sec) oscillations with “W” corresponding to the Schuler period (between 83 and 84 minutes). In that case position error from accelerometer bias, propagating as (1 – cos Wt), rises much sooner than gyro drift, propagating as (t – sin Wt/W). Page 80 of that book sketches an example of behavior over a cycle.  Development offered beyond there expands as far as many analysts wish to go (other natural frequencies of error propagation, rectification of vibration-sensitive errors, etc.).
Not long after that first book appeared, GPS became operational — and I was a newcomer to that.  By the time I understood it there were many experts.  Once again I had to catch up, and the process was gradual.  With an exceptionally strong client interested in my inertial background, a synergism was formed. That led to a flight test producing state-of-the-art accuracy in dynamics; see the table describing several innovations also resulting from the work just described.
That second book, after a review chapter, begins where the first (pre-GPS) one left off.  It also (1)is used in tutorials and (2)has received testimonials from other instructors, as the URL shows.  Sources cited here, plus an online 1.5-hr tutorial, free to Inst-of-Navigation members, plus a “try-before-you-buy” 100-page excerpt available from this site, should be helpful to many.


At ION GNSS 2011 in Portland OR, Javad Ashjaee, James L. Farrell and others participated 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.


 As Dr. Todd Humphreys noted, 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?”

This panel addressed the question “Now what?”


Topic: How do we secure civil GNSS?



    • 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


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





A subsequent experiment conducted in Texas, attracting national attention at that time, became the topic of eMail communications among several professionals in the satnav community.  That sequence of communications resulted in a summary published in GPSWorld.

Life before GPS

Before GPS took over so many operations by storm (e.g., navigation,tracking, timing, surveying, etc.), designers had access to other — far less capable — provisions.  That condition forced our hands; to derive maximum benefit from what was available, we had to extract full information content from those provisions.  Now that GPS is subjected to challenges (aging, jamming, spoofing, etc.), some of those older methods are receiving increased scrutiny.  Recently I’ve received renewed interest in areas I analyzed decades ago.  Old publications from two of those areas are discussed here: 1) attitude determination and 2) nav integration.

“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.


The number of runway incursions, as shown on an FAA URL  was nearly a thousand in FY 2011 and 1150 for FY 2012.  A subsequent article shows renewed interest in their prevention.

A hundredfold reduction in velocity error (from meters/sec to cm/sec) was shown in flight for squitter message transmission — but with measurement-based message content, as discussed in an accompanying blog.  A publication describing highly favorable results in air (3-D) could readily extend to 2-D (surface).

A 1996 crash that killed U.S. Commerce Secretary Ron Brown drew attention to a problem that has caused thousands of airline fatalities.  Controlled flight into terrain (CFIT) results from an autopilot driven by erroneous information regarding aircraft‘s flight path relative to its surroundings.  This writer narrowly escaped death in early January 1981 when an errant foreign airliner very nearly collided with the World Trade Center (that time it would have been accidental); an alert air traffic controller issued a turn directive just in time.  A highly informative IEEE-AES Systems Journal article by Swihart et.al. —
…. “Automatic Ground Collision Avoidance System Design, Integration, and Test” (May 2011, pp.-4-11)
addresses CFIT while envisioning, near the end, future extension to unmanned aircraft.  The authors correctly describe the effort as the beginning of a long-awaited development with a huge payoff in lives to be saved and, secondarily, in vehicles not destroyed.  As proof of my full concurrence — both with the intent and with the “long-awaited” characterization — I cite the following:

* a “GPS for Collision Avoidance” seminar I prepared in 2000 (hardly anyone attended — no funding, no interest — but safety shouldn’t take a back seat to economics).
* two coauthored papers (ICNS 2009 and ION-GNSS-2011) resulting from recent low-level support to Ohio Univ. by NASA.


It remains true to this day: much more needs to be done.  Without significant increase in development, life will be increasingly hazardous.  Both heavier traffic and unmanned aircraft will contribute to the increased danger.


Tracking acceleration dynamics by GNSS, radar, imaging

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.

This author was fortunate to be “at-the-right-places at-the-right-times” when a need arose to address each of the topics covered.  As a result, the words of one reviewer — that the book is

…………….. “teeming with insights that are hard to find or unavailable elsewhere.”

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, …

Formulations described in Chapter 9 were used for tracking of both aircraft and missiles, concurrently, through usage of an agile beam radar.  For another example, air-to-surface operations subdivide into air-to-ground and vessel tracking from the air.  That latter case constrains tracked objects’ altitudes to mean sea level — a substantial benefit since it obviates the need for elevation measurements, which are subject to large errors from refraction (bearing and range measurements, much less severely degraded, suffice). Air-to-ground tracking, by contrast, further subdivides into stationary and moving targets; the former potentially involves imaging possibilities (by real or synthetic aperture) while the latter — if not being imaged by inverse SAR — separates its signature from clutter via doppler.

Reentry vehicles, quite different from other track operations, present a unique set of “do’s” and “don’ts” owing to high-precision range measurements combined with much larger cross-range errors (because of proportionality to extreme distances involved).  Pitfalls from uncertain axial direction of “pancake” shaped one-sigma error ellipsoids must be avoided.  A counterexample, having angle observations only (without distance measurements), is also addressed.  Orbit determination is unique in still another way, often permitting “patched-conic” modeling for its dynamics.  A program based on Lambert’s theorem provides initial trajectories from two position vectors with the time interval separating them.

Those operations and more are addressed with most observations from radar or other (e.g., infrared imaging) sensors rather than satellite measurements.  That of course applies to tracked objects carrying no squitters. Friendlies tracking one another, however, open the door for using GNSS data.  Those subjects plus numerous supporting functions are discussed at some length in Chapter 9.  Despite very different dynamics applicable to various operations, the underlying commonality (Chapter 2) connects the error propagation traits in their estimation algorithms and also — though widely unrecognized — short-term INS error propagation under cruise conditions (Chapters 2 and 5).  Support operations such as synthetic aperture radar (SAR) and transfer alignment are described in the chapter Addendum.

The book on GPS and GNSS


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.

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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.