Kalman Filtering for Navigation and Target Tracking:
U.S. Navy Submarine applications related to Kalman filtering
We have prior experience for over 40+ years in a variety of defense areas including Submarine Inertial Navigation (compare the prior hyperlink to our clearer discussion below) [and an understanding and a facility with the underlying navigation error models constituting a psi-angle analysis of an Inertial Navigation System (INS) consisting of accelerometers and gyroscopes in an integrated whole]; Air Force Aircraft Navigation and Radio Multi-lateration Relative Navigation (JTIDS RelNav) and communication (JTIDS/MUFBARS/ICNIA); Sonobuoy DIFAR/LOFAR target tracking; Search and Screening; Antenna Radar Cross-Section Detectability; NavSat (a.k.a. Transit), LORAN-C (both hyperbolic and phase-shift rho-rho circular), Bathymetry (bottom sounding sonar map-matching) and GPS analysis and usage on Submarines; and GPS analysis and usage in test aircraft (along with test plans and procedures for many of the above); and Early Warning Radar Target tracking considerations relating to the target tracking filters and estimation concerns (and the underlying mathematical models of all of the above and more). Thanks to John Rommelfanger (MITRE, retired), we have a copy of Modern Navigation Systems, a short course by (the late) Walter R. Fried (Hughes Aircraft Company), 10-12 June 1992. Of course, we at TeK Associates already had both editions of Walter R. Fried’s book but having access to his slide-based concise summary is priceless. Thomas Kerr III knew Walter Fried personally and when Tom last saw him in 1994, based on Tom’s rather aggressive questions and comments from the audience, Walter Fried seemed pleased that Tom had evidently become a watchdog for navigation since they had first met back in 1980, when Tom made his first technical Navigation presentation at Position, Location, and Navigation Symposium (PLANS) in Atlantic City and Walter Fried was there as his session chairman. Tom received a written a accommodation certificate for his work and presentation there (not shown here), signed by Walter Fried himself.
Familiarity with historical application constraints and specs for many platforms (especially including C-3 Poseidon, C-4 Poseidon-back-fit [which, in those days, used multiple Univac CP-890/YUK computers in the Navigation Room], and similarly outfitted D-1 Trident SSBN\SSN submarine mission objectives, scenarios, and countermeasures). We have had first hand shipboard experience in San Diego in the 1980’s and earlier weapons system and fire control training in the 1970’s (regarding numbers and mixes of RV’s) at Dam Neck, VA. We have also been aboard the Compass Island (sister ship of Cobra Judy used for strategic radar target tracking) in the 1970’s, where components being planned for use within the SSBN Navigation Room are tested beforehand (in a Navigation Room that was identical to but “bass-ackwards” from how it is oriented within actual SSBN’s). The U.S.S. Compass Island was replaced in this role in the late 1970’s by the U.S.S. Vanguard (as obtained from NASA). We are aware of vintage 1970’s vibration tests for submarine INS components using “Big Bertha and the Little Chippers” on the deck above it. Present day barge tests with submerged C-4 plastic explosives emulating depth charges and use of 300 pound swinging hammers, capable of impacting at up to 100 g’s, now reveal weaknesses or non-compliance of electronics within the expected dangerous environments is just as important today (even if their names are no longer as colorful). We have also performed GPS testing, both dockside and at sea, onboard the SSN-701 LaJolla in the early 1980’s at the San Diego, CA submarine base (for NADC and for NOSC).
We have participated in several Independent Verification and Validation (IV&V) programs for sonar\sonobuoy target tracking (PTA and LOFAR/DIFAR and LAMPS), and in analysis and development programs for integrated augmented INS navigation for Submarines (SSBNs) and in Joint Tactical Information and Distribution System (JTIDS) Relative Navigation (RelNav), and in Development Testing and Evaluation for Operational Readiness [DT&E(OR)] for GPS navigation aboard submarines (SSNs). (To see a high level overview slide show on current status of GPS, please click here to obtain the main executable file “stpete.exe”. In order to view the slideshow, user must first download this associated .DLL file, then this .DLL file, then this VBX file, all to the same location in one folder on their local computer. Our Web Site host requires temporary conversion to exclusively lower case spellings. A constraint in running it is that a Windows host Operating System is required. Those typical OS’s that allow this are Windows 9X/2000/NT/Millenium/XP and Vista and likely on Windows 7/10. It also runs on older OS’s like Windows 3.1 and 3.11 For Workgroups.)
“Escape Velocity” from a Linkedin discussion: I agree with what everyone said except for:
Other interesting precedents (to set the stage):
Lest we forget, Emeritus Prof. Ronald L. Klein (UWV) published many articles on estimation Theory using Gaussian Quadrature formulas [in order to improve the accuracy of the Propagate Step integration of the system dynamics within an EKF]. Here and in what follows below, Thomas H. Kerr III’s comments and annotations are in a different color font to make it easier for readers to distinguish (and, perhaps, to ignore).
Emeritus Prof. Thomas Kailath (Stanford Univ.) alerted the estimation community to a precedent by some
Japanese researchers that posed linear estimation within a “Krein Space”
instead of within a Hilbert Space and
apparently obtained faster convergence as a consequence. While Matrix Positive definiteness plays a prominent role within all the analytic proofs supporting the
usual Hilbert Space-based derivation of Kalman filters, the Krein Space approach frequently involves
matrices that are indefinite (but, perhaps, the difference
of two positive definite matrices). The tool in common is still projections onto linear
-Sayed, A. H., and Kailath, T., “A State Space
Approach to Adaptive RLS Filtering,” IEEE Signal Processing Magazine, Vol. 11, No. 3, pp. 18-60, July 1994.
(Here they demonstrate that most of the myriad of RLS filters are merely variants of a Linear
For situations involving imaging and optics that have zero mean Poisson Process White noise (as the formal derivative of a Centered Poisson Process with independent increments just as Gaussian white noise is the formal derivative of a Brownian motion process [a.k.a., a Weiner process] with independent increments), please see: (1) Donald L. Snyder, Random Point Processes in Time and Space, Springer Texts in Electrical Engineering, 2nd Ed. 1991 (1st Ed. from John Wiley and Sons, NY, 1975). Prof. Donald L. Snyder (Washington University in St. Louis, MO); (2) Fishman, P., Snyder, D. L., “The statistical analysis of space-time point processes,” IEEE Trans. on Information Theory, Vol. 22, No. 3, pp. 257-274, May 1976; (3) Snyder, D. L., and Fishman, P., “How to Track a Swarm of Fireflies by Observing Their Flashes,” IEEE Trans. on Information Theory, Vol. 21, No. 6, pp. 692-695, Nov. 1975; (4) Salimpour, Y., Soltanian-Zadeh, H., Abolhassani, M. D., “Extended Kalman Filtering of Point Process Observations,” Conf. Proc. IEEE Eng. Med. Biol. Soc., Buenos Aires, Argentina, 6670-3, Conference Dates: 31 Aug.-4 Sept. 2010. My speculations: The above technologies could be of interest to SBIRS-high or SIBRS-low to detect and track Russia’s Avangard Hypersonic glide missiles, capable of traveling 20 times the speed of sound (i.e., 767 mph) and of performing maneuvers in taking an evasive zigzagged path as it speeds towards its designated target (and to, ostensibly, be deployed by Russia in 2019 and so far contained within a UR-100N UTTKh missile [designated in NATO terminology as the SS-19 Stiletto] first stage used to carry the glider up into the atmosphere but eventually to be replaced in this role by a new first stage missile that Russia is currently developing). It was test fired in 2018 from a silo in the Dombarovsky missile base in Orenburg Oblast, in the southern Ural Mountains and traveling more than 3,000 miles to Kura training ground in the Kamchatka region in Russia’s far northeast) and, perhaps, aim lasers toward them as potential targets of interest. [The U.S. and China are currently jointly working on a Hypersonic missile too, according to Jane’s Defense in late December 2018.] https://www.flightglobal.com/news/articles/dod-keeps-eye-on-hypersonic-missiles-and-manoeuvring-425086/ https://news.usni.org/2019/02/01/40831?_lrsc=a801f315-b3d7-4987-b0c7-78717bd0b9e9
Defeating Hypersonic Missile Threats:
Raytheon Hypersonic Contract:
U.S. X60A Hypersonic Test aircraft in 2019:
The Future of Laser Missile Defense:
Missile Defense Agency Advances Laser-Blasting UAVs:
Lasers: Beyond The Power Problem:
Air Force Releases Video of New Combat Drone, the XQ-58A Valkyie in 2019:
U.S. Army to Buy $39.6 Million Worth of Pocket-Sized Drones:
NASA Dream Chaser:
Invisibility Technology Takes Big Leaps That Can Be Seen:
Remembering a bit of history pertaining to the Cold War and the U.S.’s successful race to the moon:
NASA’s Original Apollo Moon Landing Guidance Computer Is Being Restored:
Also in the 1980’s from the Air Force Institute of Technology (AFIT) and elsewhere: (1) Maybeck, Peter S., and Rogers, Steven K., “Adaptive Tracking of Multiple Hot-Spot Target IR Images,” IEEE Trans. on Automatic Control, Vol. 28, No. 10, pp. 937-943, May 1983; (2) Maybeck, Peter S., and Hentz, Karl P., “Investigations of Moving-Bank Multiple Model Adaptive Algorithms,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 10, No. 1, pp. 90-96, Jan. -Feb. 1987; (3) Tobin, David M., and Maybeck, Peter S., “Enhancements to a Multiple Model Adaptive Estimator/Adpative Image-Tracker,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 24, No. 4, pp. 417-426, July 1988. A hot time in the old town tonight! Maybeck, P. S., Stochastic Models, Estimation and Control, Vol. 1, Academic Press, NY, 1979 (and Vols. 2 and 3 published in the 1980’s.)
Also see: Special Issue of IEEE Transactions of Automatic Control, Vol. 28, No. 3, 1983 devoted to nonstandard applications of Kalman Filters. For more standard applications of Kalman filters, please see 1982 NATO AGARDograph No. 256 and Feb. 1970, No. 139 (Noordhoff International Publishing, Lieden).
Also see or click on http://www.dtic.mil/cgi-bin/GetTRDoc?Location=U2&doc=GetTRDoc.pdf&AD=ADP011192 or please click on http://www.dtic.mil/dtic/tr/fulltext/u2/p011192.pdf
Click here to download a 1.56MByte pdf file that demonstrates our Navigation familiarity by our pioneering new developments in using Inertial Navigation Systems and GPS in support of airborne platforms performing terrain mapping, which is a slide presentation corresponding to: Kerr, T. H., “Use of GPS\INS in the Design of Airborne Multisensor Data Collection Missions (for Tuning NN-based ATR algorithms),” Institute of Navigation Proceedings of GPS-94, pp. 1173-1188, 20-23 Sept. 1994. Click here to download a 4.40MByte pdf file that conveys the entire report. (Thomas H. Kerr III became a senior member of AIAA via the required endorsements by running this specific report by Richard Battin [Draper Laboratory and MIT Aero. & Astro.] and by Wally Vander Velde [MIT Aero. & Astro.].)
Click here to see a 160 KByte quantitative analyses of the relative pointing accuracy associated with each of several alternative candidate INS platforms of varying gyro drift-rate quality (and cost) by using high quality GPS external position and velocity fix alternatives: (1) P(Y)-code, (2) differential mode, or (3) kinematic mode at higher rates to enhance the INS with frequent updates to compensate for gyro drift degradations that otherwise adversely increase in magnitude and severity to the system as time elapses. Click here to obtain the corresponding 1.40 MByte PowerPoint presentation.
TeK Associates Capabilities:
Knowledge of operational principles and behavior of INS gyros and accelerometers and likewise for GPS: Familiar with their underlying state variable error models and INS calibration procedures and typical failure modes and interactions.
Map of GPS Control Segment: https://www.gps.gov/multimedia/images/GPS-control-segment-map.pdf
Satellites being reported in view, as seen from the GPS Project Office, at a fixed location within CONUS (as the earth rotates and as the satellites move in their respective 6 orbital planes).
Realistically, the GPS receiver can move and the platform upon which it is based can move also (like a person with a GPS-equipped cell phone on a ferry boat sailing from Manhattan, NY to Statin Island).
GPS interference Solutions:
Sophisticated Spoofing of GPS:
Size of GPS Jammer markets: https://www.transparencymarketresearch.com/signal-jammer-market.html
Securing PNT Workshop Looks at GNSS Back-up Options - Inside GNSS:
Letter to Karen Van Dyke (DOT): http://rntfnd.org/wp-content/uploads/Alliance_for_Telecommunications_Industry_Solutions_ATIS_Copper_Optical_Access_Synchronization_and_Transport_Committee_COAST-2.pdf
Click here to see some other aspects of GPS evolution. Brad Parkinson’s 2017 wish list: https://rntfnd.org/wp-content/uploads/Three-Wishes-v11s.pdf
TeK Associates follows novel INS developments and relative INS accuracies: Familiar with Electro-statically supported Gyro (ESG) such as the airborne Micro, the SSBN ESG, as well as that in the Gravity-Probe satellite), Laser Gyros, Fiber Optics Gyros, Wine glass\tuning fork gyros, Microelectromechanical systems (MEMS) Gyroscopes. Prof. Christopher Jekeli’s (Ohio University, Columbus, OH) published mathematical model for Cold-Atom Gyros, as well as conventional mechanical spinning rotor gyros and their analysis.
We follow evolving procedures for moving platform shipborne and in-air alignment gyro-compassing and alternative mechanizations: Local Level, Space-Stable, Wander-Azimuth, Strapdown and associated transformations (and typical frequency of re-calculation sample rates). Surprisingly, new insights have recently been offered that much of the technology harkens back to analog gyro behavior more than is currently necessary in this digital age of extremely high processing speeds which can now support relatively high external GPS updates within strapdown gyroscope implementations. Previous notions of coning, sculling, the dynamics of Schuler loop oscillations being activated, or 24 hour diurnal oscillations are no longer necessary in Navigation systems mechanized with MEMS throughout and with GPS or differential GPS updates on the order of seconds or minutes because the gyros no longer need to go open loop without a compensating and ameliorating external “navaid” fix for anything that approaches a significant fraction of the ~hour and a half Schuler period .
We are familiar with typical operational constraints and weapon system accuracies of several military platforms as well: e.g., Ships Submersible Ballistic Nuclear (SSBN’s) submarines (a.k.a. “Boomers”), Ships Submersible Nuclear (SSN) submarines (a.k.a., “attack” subs), which allied country’s submarines use “degaussing” coils and which use “flash”, “deperm” procedures, etc. We are also familiar with the tenets, details, and history of “Search and Screening”: e.g., detection range, worse case detection threats, observables-in-the-military-sense, countermeasures and counter-countermeasures for various sensors, etc. See  to  for perspectives on our early experience in this area. We are also knowledgeable in the associated terminology such as that of U.S. submarine alertness levels: 1SQ, 2SQ,..., Operation Sanguine [before the name change in thr 1970’s to evade the scrutiny of protesters ], TACAMO, long trailing wire antenna (BCA), pig tail antenna, whip antenna, Blue-green laser, Counter Value vs. Counter Force, Mid-course star fix, firing keys (where located and who has access, and orderly sequence of events, and expected synchronizations and chain-of-command), etc.
Our SSBN submarines can launch while submerged; while those of many other countries must surface first before they can launch.
We are cognizant of the Society of Old Crows, of the Countermeasures Handbook (we possess several back issues), and Paladin Press publications over the years (that should never have been allowed to appear). CV motion models, Lamps helicopters and ships, use of ship-borne winch and cables dropped from helicopters seeking to land onboard in rough seas (where cable is secured to winch and helicopter pulls cable taught and is reeled in slowly so that Helicopter motion automatically matches that of the deck of the ship as both pitch, roll, and yaw together (to avoid damaging the helicopter with a nasty unexpected impact with the deck of the much more massive ship capable of preserving inertia by inflicting a severe impulse force as a big crushing blow over the short period of time-BANG!) We know about historical “pipe dreams” that failed miserably as well as alternative more robust approaches (using older technology) that was good enough without being vulnerable to a myriad of difficulties associated with other things going wrong (one example being trying to use a laser-based reflection system to guide the helicopter to land on the deck in rough seas-obvious vulnerabilities being: fog, battle smoke, electronic failures at an extremely critical time a’la Murphy’s law, laser orientation capability for interacting with surface ship’s deck-in-motion possibly falling out of sufficient calibration [as needed to retrieve the necessary reflection close to perpendicular to the moving deck for instantaneous round trip timing-so you can’t solve the problem until you have already solved the problem] and needing additional INS components with their additional costs and vulnerabilities and operational procedures). Thank Michael Athans and AlphaTech for the less practical approach, described above. Example 2: What about the attempt to align several (two or more) surface ships at sea in tandem to create an effective landing strip for those super-sized carrier air craft to take-off and land for re-supply at sea. Although some of their numerous computer studies demonstrated feasibility, please just think about being in the North Atlantic with typical winter weather conditions involving very high sea states and then try to pull off this stunt. We have Raman Mehra and Scientific Systems to thank for this second one. Both examples were funded by the U.S. Navy and further reported in an open unclassified forum but my critical ear hears all and I don’t soon forget these apparent technical boondoggles but do continue to wonder how they ever got pass other watchdogs. I guess it pays to be well connected. It’s not my cup of tea though. I have to “say what I see and what I smell”. We Kerr’s (curs) are well known watchdogs too. We try to avoid stepping in “it” as our predecessors did! Sometimes we mark our territory as a good alpha dog. Arrrooooo! Better to lead than to follow since the scenery is much better and more interesting (as every sled dog knows).
Discussing Gyroscopes (the heart of an INS)
The classical mechanical gyroscope has a relatively massive rotor suspended within a framework of light supporting rings called gimbals which have nearly frictionless bearings (as the ideal that is sought) that are used to help isolate the central spinning rotor from all outside influences (i.e., torques). At high rotation speeds of the rotor, the gyroscope exhibits extraordinary stability of its balance and maintains the orientation of the direction of the high speed rotation axis of its central rotor in where it points in 3-dimensional space. The implication or consequence of the physical law known as the “conservation of angular momentum” is that the angular momentum of the rotor is constant and it maintains not only its magnitude or speed of spin, but also its direction in space of the spin axis in the absence of any external torques. The classical gyroscope finds application in gyro-compasses (as an alternative to using a magnetic compass) and in more sophisticated Inertial Navigation Systems (that reveal location and orientation of vehicles on the earth; and under and over the sea, respectively, in submarines and ships; and in space in aircraft, in rockets, and in missiles). However, there are many more common examples of gyroscopic motion and its associated stability: spinning tops and their associated almost mysterious precession behavior, the spinning wheels of bicycles and motorcycles keeping them from falling over even in a severe leaning angle, the spin of the Earth in space as it orbits the sun, even the behavior of a boomerang as it is being hurled are all examples of gyroscopic motion.
We are cognizant of the necessary interaction between the architectures associated with various alternative approaches to multi-target tracking and Kalman filter-based target tracking algorithms in use (alternative tracking algorithms hypothesized as possible modern replacements).
Our primary strength is having an in depth awareness of all the Kalman filter estimation-based approaches used to date for handling failure\fault detection in an INS or in GPS RAIM, or in a GPS/INS hybrid. We are analytic algorithm specialists. This is our area of greatest familiarity.
Historical Account of our experience therein:
 Kerr, T. H., “Modeling and Evaluating an Empirical INS Difference Monitoring Procedure Used to Sequence SSBN Navaid Fixes,” Proceedings of the Annual Meeting of the Institute of Navigation, U.S. Naval Academy, Annapolis, Md., 9-11 June 1981. (Selected for reprinting in Navigation: Journal of the Institute of Navigation, Vol. 28, No. 4, pp. 263-285, Winter 1981-82).
 Kerr, T. H., “Impact of Navigation Accuracy in Optimized Straight-Line Surveillance\Detection of Undersea Buried Pipe Valves,” Proceedings of National Marine Meeting of the Institute of Navigation (ION), Cambridge, MA, 27-29 October 1982.
Kerr, T. H., “Stability Conditions for the RelNav Community as a
Decentralized Estimator-Final Report,” Intermetrics, Inc. Report No.
IR-480, Cambridge, MA, 10 August 1980, for NADC (Warminster, PA).
T. H., and Chin, L., “A Stable Decentralized Filtering Implementation
for JTIDS RelNav,” Proceedings of
IEEE Position, Location, and Navigation Symposium (PLANS), Atlantic
City, NJ, 8-11 December 1980.
 Kerr, T. H., and Rogers, R., “Report on PINS Filter Design Review (of Magnavox),” Intermetrics Memo, Cambridge, MA, 11 August 1983, for NOSC (San Diego, CA). (Minesweeper Navigation)
Kerr, T. H., “GPS\SSN Antenna Detectability,” Intermetrics Report No.
IR-MA-199, Cambridge, MA, 15 March 1983, for NADC (George Lowenstein).
 Kerr, T. H., “Functional and Mathematical Structural Analysis of the Passive Tracking Algorithm (PTA),” Intermetrics Report No. IR-MA-208, Cambridge, MA, 25 May 1983, for NADC. (LAMPS Sonobuoy algorithms.)
 Kerr, T. H., “Navy GPS\SSN Phase II User Equipment DT&E Magnavox Modification Center (Mod Center) Test Report,” 1 June 1985, for NADC Code 4022 (George Lowenstein).
 Kerr, T. H., “Navy GPS\SSN Phase II User Equipment DT&E Rockwell-Collins Modification Center (Mod Center) Test Report,” 1 June 1985, for NADC Code 4022 (George Lowenstein).
 Kerr, T. H., “Navy GPS\SSN Phase II User Equipment DT&E Rockwell-Collins Developmental Test and Evaluation (Operational Readiness) [DT&E (OR)] Test Report,” 10 June 1985, for NADC Code 4022 (George Lowenstein).
 Kerr, T. H., “Magnavox Military Utility Test Report,” 10 June 1985, for NADC Code 4022 (for George Lowenstein).
 Kerr, T. H., “Phase III GPS Integration; Volume 1: GPS U.E. Characteristics,” Intermetrics Report IR-MA-177, Cambridge, MA, January 1983, for Navair and for NOSC (Richard Akita).
 Kerr, T. H., “Decentralized Filtering and Redundancy Management Failure Detection for Multi-Sensor Integrated Navigation Systems,” Proceedings of the National Technical Meeting of the Institute of Navigation (ION), San Diego, CA, 15-17 January 1985.
 Kerr, T. H., “Use of GPS\INS in the Design of Airborne Multisensor Data Collection Missions (for Tuning NN-based ATR algorithms),” the Institute of Navigation Proceedings of GPS-94, Salt Lake City, UT, pp. 1173-1188, 20-23 Sept. 1994.
 Kerr, T. H., “Further Comments
on ‘Optimal Sensor Selection Strategy for Discrete-Time Estimators’,” IEEE
Trans. on Aerospace and Electronic Systems, Vol. 31, No. 3, pp. 1159-1166,
T. H., “Sensor Scheduling in Kalman Filters: Evaluating a Procedure for
Varying Submarine Navaids,” Proceedings
of 57th Annual Meeting of the Institute of Navigation, pp.
310-324, Albuquerque, NM, 9-13 June 2001.
 Kerr, T. H., “Sensor Scheduling in Kalman Filters: varying navaid fixes for trading-off submarine NAV accuracy vs. ASW exposure,” Proceedings of The Workshop on Estimation, Tracking, and Fusion: A Tribute to Yaakov Bar-Shalom (on the occasion of his 60th Birthday) following the Fourth ONR/GTRI Workshop on Target Tracking and Sensor Fusion, Naval Postgraduate School, Monterey, CA, pp. 104-122, 17 May 2001.
(To see a high level overview slide show associated with the topics of the preceding paper, please click here to obtain the main executable file “stpete.exe”. In order to view the slideshow, user must first also download these auxiliary files: this associated .DLL file, then this .DLL file, then this VBX file, all to the same folder location on their local computer, where “stpete.exe” resides. Our Web Site host required temporary conversion to exclusively lower case spellings. Once this is done, merely click on “stpete”.exe to start the show and click on screen to move to the next screen in the sequence until the end [when it closes and stops].)
 Biezad, D. J., Integrated Navigation and Guidance Systems, AIAA Education Series, Reston, VA, 1999.
 Sofir, I., “Improved Method for Calculating Exact Geodetic Latitude and Attitude-Revisited,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 23, No. 2, ff. 369, 2000.
 Siouris, G. M., “Navigation: Inertial,” Encyclopedia of Physical Science and Technology, 2nd Edition, V. 10, pp. 595-647, Academic Press, NY, 1992.
 Jordan, J. F., Wood, L. J., “Navigation: Space Missions,” Encyclopedia of Physical Science and Technology, 2nd Edition, Vol. 10, pp. 649-673, Academic Press, NY, 1992.
 Ward, P., “Navigation: Satellites,” Encyclopedia of Physical Science and Technology, 2nd Edition, Vol. 10, pp. 675-702, Academic Press, NY, 1992.
 Farrell, J. L., “Strapdown at the Crossroads,” Navigation, Journal of the Institute of Navigation, Vol. 51, No. 4, pp. 249-257, Winter 2004. (A good modern perspective! Correction in Vol. 52, No. 1, page iii, Spring 2005. Strong conclusions in this paper should be viewed as being somewhat controversial.)
 Kerr, T. H., “Comment on `Precision Free-Inertial Navigation with Gravity Compensation by an Onboard Gradiometer’,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 30, No. 4, July-Aug. 2007.
 Felter, S. C., Wu, N. E., “A Relative Navigation System for Formation Flight,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 33, No. 7, pp. 958-967, July 1997.
 Juang, J.-C., Huang, G.-S., “Development of GPS-Based Altitude Determination Algorithms,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 33, No. 7, pp. 968-976, July 1997.
 Chatterji, G. B., Menon, P. K., Sridhar, B., “GPS/Machine Vision Navigation System for Aircraft,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 33, No. 7, pp. 1012-1095, July 1997.
 Xiong, P., “Spacial and Temporal Processing for Global Navigation Satellite Systems: GPS receiver paradigm,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 39, No. 7, pp. 936-948, July 2003.
 Madhani, P. H., “Application of Successive Interference Cancellation to GPS Pseudolite Near-Far Problem,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 39, No. 4, pp. 481-488, April 2003.
 Luo, N., “Multiple Moving Platform, GPS, Relative Positioning,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 39, No. 7, pp. 936-948, July 2003.
 Fante, R. L., “Multipath-induced bias, GPS time-of-arrival, Evaluation and Reduction,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 39, No. 7, pp. 911-920, July 2003.
 Qi, H., “GPS/INS Integration: Direct Kalman Filtering Approach,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 38, No. 1, pp. 687-693, Jan. 2002.
 Shin, D.-H., “TOA and TDOA Positioning Error,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 38, No. 1, pp. 307-308, Jan. 2002.
 Pervan, B., “Sigma Inflation for Local Area Augmentation of GPS,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 37, No. 10, pp. 1301-1311, Out. 2001.
 Praasch, M. S., “SS-Ranging Multipath Model Validation for DGPS,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 37, No. 1, pp. 298-304, Jan. 2001.
 Ray, J. K., “Carrier Multipath Mitigation, Multiantenna System,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 37, No. 1, pp. 183-195, Jan. 2001.
 Kim, K. H., Lee, J. G., Park, C. G., “Adaptive Two Stage Extended Kalman Filter for a Fault-Tolerant INS-GPS Loosely Coupled System,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 45, No. 1, pp. 125-137, Jan. 2009.
 Jardak, N., Samama, N., “Indoor Positioning Based on GPS-Repeators: Performance Enhancement using an Open Code Loop Architecture,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 45, No. 1, pp. 347-359, Jan. 2009.
 “Noncoherrent Integrations for GNSS Detection: Analysis and Comparisons,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 45, No. 1, pp. 360-375, Jan. 2009.
 Chiang, K.-W., Noureldin, A., El-Sheimy, N., “Constructive Neural-Networks-Based MEMS/GPS Integration Scheme,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 44, No. 2, pp. 582-594, April 2008.
 Farrell, W. J., “Interacting Multiple Model Filter for Tactical Ballistic Missile Tracking,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 44, No. 2, pp. 418-426, April 2008.
 Borio, D., Camoriano, L., Lo Presti, L., Fantino, M., “DTFT-Based Frequency Lock Loop for GNSS Applications,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 44, No. 2, pp. 595-612, April 2008.
 Kaplan, L. M., “Assignment Costs for Multiple Sensor Track-to-Track Association,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 44, No. 2, pp. 655-675, April 2008.
 Bon, N., Khenchaf, A., Garello, R., “GLRT Subspace Detection for Range and Doppler Distributed Targets,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 44, No. 2, pp. 678-695, April 2008.
 Juang, J.-C., “Multi-Objective Approach to GNSS Code Discrimination Design,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 44, No. 2, pp. 481-492, April 2008.
 Geren, W. P., Murphy, T., Pankaskif, T. A., “Analysis of Airborne GPS Multipath Effects using High-Fidelity EM Models,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 44, No. 2, pp. 711-723, April 2008.
 Jan, S.-S., Gebre-Egziabher, D., Walter, T., Enge, P., “Improving GPS-Based Landing System Performance using an Empirical Barometric Altimeter Confidence Bound,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 44, No. 1, pp. 127-146, Jan. 2008.
 Lambert, H. C., “Tracking Filter for the Mitigation of the Ionospheric Range Bias,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 44, No. 1, pp. 339-348, Jan. 2008.
 Tudoroiu, N., Khorasani, K., “Satellite Fault Diagnosis using a Bank of Interacting Kalman Filters,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 43, No. 4, pp. 1334-1350, Oct. 2007.
 Musicki, D., La Scala, B., “Multi-Target Tracking in Clutter Without Measurement Assignment,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 44, No. 3, pp. 877-896, July 2008.
 Blanch, J., Walter, T., Enge, P., “Position Error Bound Calculation for GNSS Using Measurement Residuals,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 44, No. 3, pp. 977-984, July 2008.
 Musicki, D., “Multi-Target Tracking using Multiple Passive Bearings-Only Asynchronous Sensors,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 44, No. 3, pp. 1151-1160, July 2008. Also see: http://www.gallup.unm.edu/~smarandache/NATOASI_ATJDTSPK.pdf
 Foster, C. C., Elkaim, G. H., “Extension of a Two-Step Calibration Methodology to Include Nonorthogonal Sensor Axes,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 44, No. 3, pp. 1070-1078, July 2008.
 Borio, D., Camoriano, L., Lo Presti, L., “Impact of GPS Acquisition Strategy on Decision Probabilities,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 44, No. 3, pp. 996-1011, July 2008.
 Lee, J., Pullen, S., Enge, P., “Sigma-Mean Monitoring for the Local Area Augmentation of GPS,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 42, No. 2, pp. 625-635, Apr. 2006.
 Bednarz, S., Misra, P., “Receiver Clock-Based Integrity Monitoring for GPS Precision Approaches,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 42, No. 2, pp. 636-643, Apr. 2006.
 Heo, M.-B., Pervan, B., “Carrier Phase Navigation Architecture for Shipboard Relative GPS,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 42, No. 2, pp. 670-679, Apr. 2006.
 Pacher, M., Porter, A., Polat, M., “INS-Aiding Using Bearings-Only Measurements of an Unknown Ground Object,” Navigation: Journal of the Institute of Navigation, Vol. 53, No. 1, pp. 1-20, Spring 2006.
 Wendel, J., Metzger, J., Moenikes, R., Maier, A., Trommer, G. F., “A Performance Comparison of Tightly Coupled GPS/INS Navigation Systems Based on Extended and Sigma Point Kalman Filters,” Navigation: Journal of the Institute of Navigation, Vol. 53, No. 1, pp. 21-31, Spring 2006.
 Farrell, J. L., “Full Integrity Testing for GPS/INS,” Navigation: Journal of the Institute of Navigation, Vol. 53, No. 1, pp. 33-40, Spring 2006.
 Hwang, P. Y., Brown, R. G., “RAIM-FDE Revisited: A New Breakthrough in Availability Performance with nioRAIM (Novel Integrity-Optimized RAIM),” Navigation: Journal of the Institute of Navigation, Vol. 53, No. 1, pp. 41-51, Spring 2006.
 Alves, D. B. M., Monico, J. F. G., “Mitigating Systematic Errors for Single Frequency GPS Receivers Employing A Penalized Least Squares Methodology,” Navigation: Journal of the Institute of Navigation, Vol. 53, No. 1, pp. 53-60, Spring 2006.
Fante, R. L., Vaccaro, J. J., “Cancellation of Jammers and
Jammer Multipath in a GPS Receiver,” IEEE
AES Systems Magazine, Vol. 13, No. 11, pp. 25-28, Nov. 1998.
Rabideau, D. J., “Clutter and Jammer Multipath Cancellation in
Airborne Adaptive Radar,” IEEE
Trans. on Aerospace and Electronic Systems, Vol. 36, No. 2, pp. 565-583,
White, N. A., Maybeck, P. S., DeVilbiss, S. L., “Detection of
Interference/Jamming and Spoofing in a DGPS-Aided Inertial System,”
IEEE Trans. on Aerospace and Electronic Systems, Vol. 34, No. 4
pp. 1208-1217, Oct. 1998.
 Saha, R. K., “Effect of Common Process Noise on Two-Sensor Track Fusion,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 19, No. 4, pp. 829-835, July-August 1996.
 Fitzgerald, R. J., “Effects of Range-Doppler Coupling on Chirp Radar Tracking Accuracy,” IEEE Transactions on Aerospace and Electronic Systems, Vol. AES-10, No. 4, pp. 528-532, July 1974.
Brennan, L. E., Reed, I. S., “Theory of Adaptive Radar,”
IEEE Trans. on Aerospace and Electronic Systems, Vol. 9, No., pp.
237-252, March 1973.
 Arregui, F. J. (ed.), Sensors Based on Nanostructured Materials, Springer Science & Business Media LLC, 2009.
 Righini, G. C., Tajani, A., Cutolo, A., An Introduction to Optoelectronic Sensors, World Scientific, NY, 2009.
 Vladimir Cherkassky and Filip Mulier, Learning from Data: Concepts, Theory, and Methods, John Wiley & Sons, Inc., NY, 1998.
 Gupta, S. N., “An Extension of Closed-Form Solutions of Target-Tracking Filters with Discrete Measurements,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 20, No. 6, pp. 839-840, Nov. 1984.
 Junichiro Toriwaki, Hiroyuki Yoshida, Fundamentals of Three-Dimensional Digital Processing, Springer-Verlag, London, 2009.
 Julien Bourgeois, Wolfgang Minker, Time-Domain Beamforming and Blind Source Separation: Speech Input in the Car Environment, Springer Science + Business Media, NY, 2009.
 Jekeli, C., “Navigation Error Analysis of Atom Interferometer Inertial Sensing,” Navigation: Journal of the Institute of Navigation, Vol. 52, No. 1, pp. 1-14, Spring 2005.
 Another intriguing wrinkle is conveyed in Fernandez-Alcada, R., Navarro-Moreno, Ruiz-Molina, J. C., Oya, A., “Recursive Linear Estimation for Doubly Stochastic Poisson Processes,” Proceedings of the World Congress on Engineering (WCE), Vol. II, London, UK, pp. 2-6, 2-4 July 2007.
 Huddle, J.R., “Inertial Navigation System Error Model Considerations in Kalman Filter Applications,” Control and Dynamic Systems: Advances in Theory and Applications - Nonlinear and Kalman Filtering Techniques, Vol. 20, Academic Press, NY, pp. 294-340, Part 2 of 3, 1983.
 Lechner, W., “Application of Model Switching and Adaptive Kalman Filtering for Aided Strapdown Navigation Systems,” Control and Dynamic Systems: Advances in Theory and Applications - Nonlinear and Kalman Filtering Techniques, Vol. 20, Academic Press, NY, pp. 155-185, Part 2 of 3, 1983.
 Chien, T. T., “An Adaptive Technique for a Redundant-Sensor Navigation System,” Report No. T-560, C. S. Draper Laboratory, Cambridge, MA, 1972.
 Salazar, M. R., “State Estimation of Ballistic Trajectories with Angle-Only Measurements,” Control and Dynamic Systems: Advances in Theory and Applications - Nonlinear and Kalman Filtering Techniques, Vol. 21, Academic Press, NY, pp. 117-175, Part 3 of 3, 1984.
 Hsiao, C.- Y., “Computational Techniques in Angle-Only Tracking Filtering,” Control and Dynamic Systems: Advances in Theory and Applications - Nonlinear and Kalman Filtering Techniques, Vol. 29, Academic Press, NY, pp. 101-134, Part 2 of 3, 1988.
 Liang, D. F., “Comparisons of Nonlinear Recursive Filters for Systems with Non-negligible Nonlinearities,” Control and Dynamic Systems: Advances in Theory and Applications - Nonlinear and Kalman Filtering Techniques, Vol. 20, Academic Press, NY, pp. 341-402, Part 2 of 3, 1983.
 Yannis A. Phillis, “Algorithms for Systems with Multiplicative Noise,” Control and Dynamic Systems: Advances in Theory and Applications - Nonlinear and Kalman Filtering Techniques, Vol. 30, Academic Press, NY, pp. 65-83, Part 3 of 3, 1989.
 Yannis A. Phillis and Vassilis S. Kouikoglou, “Minimax Estimation and Control of Multiplicative Systems,” Control and Dynamic Systems: Advances in Theory and Applications - Nonlinear and Kalman Filtering Techniques, Vol. 31, Academic Press, NY, pp. 93-124, Part 1 of 3, 1989.
 Ahn, B.-H., Regan, R., et al, “Inertial Technology for the Future,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 20, No. 4, pp. 414-444, Jul. 1984.
 Jayawardhana, B., Logemann, H., and Ryan, E. P., “The Circle Criterion and Input-to-State Stability: new perspectives on a classical result,” IEEE Control System Magazine, pp. 32-67, Vol. 31, No. 4, August 2011.
 Yan, J., Hoagg, J. B., Hindman, R. E., Bernstein, D. S., “Longitudinal Aircraft Dynamics and the Instantaneous Acceleration Center of Rotation: the case of the vanishing zeros,” IEEE Control System Magazine, pp. 68-92, Vol. 31, No. 4, August 2011.
 Bergin, J., Guerci, J. R., MIMO Radar: Theory and Practice, Artech House, Boston, 2018.
 Son, J. S., Thomas, G., Flores, B. C., Range-Doppler Radar Imaging and Motion Compensation, Artech House, Boston, 2001.
 Guerci, J. R., Space-Time Adaptive Processing for Radar, Artech House, Boston, 2003.
 Hudson, J. E., Adaptive Array Principles, Peter Peregrinus, Ltd., London, U. K., 1981, reprinted 1989, 1991.
 Copps, E. M., “An aspect of the role of the clock in a GPS
receiver,” Navigation, Journal of The (U.S.) Institute of Navigation, Vol. 31, No. 3, pp.
233-242, 1986. Also in Global Positioning System, papers published in Navigation, reprinted by
The (U.S.) Institute of Navigation, Vol. III, pp. 44-53,
 Kashyap, S. K., Naidu, V. P. S., Singh, J., Girija, G., Rao, J. R., “Tracking of Multiple Targets Using Interactive Multiple Model and Data Association Filter,” Journal of Aerospace Science and Technologies, Vol. 58, No. 1, pp. 66-74, 2006.
NAVIGATION via Visual Cues Using Only Imaging Sensors:
In anticipation of later success, I have explored some possibilities offered by
the following novel Kalman filter variants that use matrix sensor (allowing simultaneous angle) measurements in lieu of
the more familiar version of a Kalman filter involving only vector sensor (one-direction-at-a-time) measurements.
In the above, DCM = Direction Cosine Matrix; and for the Quaterion Matrices, the quaterions are to be normalized. One can convert from quaternions to DCM and vice versa. For the Matrix KF material, above, a major contributor was Daniel Choukroun, B. S. (Summa cum Laude), M.S., Ph.D. (1997, 2000, 2003), post-doc (UCLA), currently an Assistant Professor at Delft University of Technology, Netherlands.
In Thomas H. Kerr III's humble opinion,
Tracking (AOT) can
also be accommodated within the above structure by updating from two (or more) different
time-synchronized (via sorted time-tags) noncolocated sensors (with lever arms
appropriately accounted for) simultaneously (thus used as a matrix measurement). The optimal estimator retains a linear syructure and is finite dimensional. This is the benefit of this novel approach.
While linear systems are very tractable, general nonlinear systems are less so. Bilinear systems are close to being linear systems and so are
somewhat more tractable, and likewise for their associated Optimal estimators.
We can provide 17 more examples of practical estimators for bilinear systems, as have been reported in the technical literature by others over the last 40+ years, (some involving Lie Algebras and Lie Brackets such as those provided by A. S. Willsky and J. T.-H. Lo for SO(2) and by many others later).
 H. C. Lambert, “Tracking filter for the mitigation of the ionospheric range bias,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 44, No. 1, pp. 339–348, Jan. 2008.
 S. Blackman and R. Popoli, Design and Analysis of Modern Tracking
Systems, Artech House, Boston, MA, 1999.
 N. Bergman, “Recursive Bayesian estimation: Navigation and tracking applications,” Ph.D. dissertation, Linkoping University, SE-581 83 Linkoping, Sweden, April 1999.
 N. Bergman, Sequential Monte Carlo Methods in Practice, New York: Springer, New York, 2001 (Chapter: Posterior Cramér-Rao Bounds for Sequential Estimation, pp. 321–338).
 Vytas B. Gylys, Kalman Filters and Nonlinear Filters, Texas Instruments Inc.
 Wasim Huleihel, Joseph Tabrikian, and Reuven Shavit, “Optimal Adaptive Waveform Design for Cognitive MIMO
 M. Morf, J.R. Dobbins, B. Friedlander, T. Kailath, “Square-root algorithms for
parallel processing in optimal estimation,” Automatica,
Vol. 15, No. 3, pp. 299-306, 1979.
 F. Landis Markley, John L. Crassidis, Yang Cheng, “Nonlinear Attitude Filtering
Methods,” American Institute of Aeronautics and Astronautics, pp. 1-32,
Landis.Markley@nasa.gov AIAA Fellow
Other topics that I routinely follow:
 Niu, X., Nassar, S., El-Sheimy, N., “An Accurate Land-Vehicle MEMS IMU/GPS Navigation System Using 2D Auxiliary Velocity
Updates,” Navigation: Journal of the Institute of Navigation, Vol. 54, No. 3, pp. 177-188, Fall 2007.
 Lo, J. T.-H. and Willsky, A. S., “Stochastic Control of Rotational Processes with One Degree of Freedom,” SIAM Journal on Control, Vol. 13, No. 4, 886ff, July 1975.
 Patrick K. Simpson (Ed.), Neural Networks Theory, Technology, and Applications, Selected Conference Papers, IEEE Technology Update Series, NY, 1996.
 Jekeli, C., Inertial Navigation Systems with Geodetic Applications, Walter deGruyter GmbH \& Co. KG, Berlin, Ger., 2001.
For the following navigation textbooks:
 Chatfield, A. B. (Ed.), Fundamentals of High Accuracy Inertial Navigation, Paul Zarchan, Editor-in-Chief, AIAA Progress in Astronautics and Aeronautics Series, AIAA, 1997.
 Savage, P. G., “Strapdown Sculling Algorithm Design for Sensor Dynamic Amplitude and Phase-Shift Error,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 35, No. 6, pp. 1718-1729, Nov.-Dec. 2012.
 Viterbi algorithm being equivalent to Dynamic Programming: https://scholar.google.com/scholar?q=viterbi+algorithm+dynamic+programming&hl=en&as_sdt=0&as_vis=1&oi=scholart&sa=X&ved=0ahUKEwiwhOicsejaAhVGc98KHScLD1UQgQMIJTAA
 Uwe D.
Hanbeck, “Recursive Nonlinear Set-Theoretic Estimation Based on
Pseudo-Ellipsoids,” Proceedings of the IEEE Conference on Multisensor Fusion and Integration for Intelligent
Systems, pp. 159–164 (MFI’
Fuqiang You, Hualu Zhang, Fuli Wang, “A new set-membership estimation method based on zonotopes and
Transactions of the Institute of Measurement and Control, Vol. 40, issue 7, pp. 2091-2099, Article first published online:
27 July 2016; Issue published: 1 April 2018
 Donald Cooke, Fun with GPS, ESRI Press, 380 New York St., Redlands, CA, 2005.
Quantum Navigation using magnetic sensing of gravity
anomalies to match known maps of such: https://www.wired.com/story/quantum-physicists-found-a-new-safer-way-to-navigate/
USS Cobra Judy Radar Ship is the sister ship of the U.S.S. Compass Island. The Compass Island had been used in the early and mid 1970’s as a test suite for demonstration and shake down of SSBN Navigation changes and upgrades before deploying within the submarine fleet. Both sister ships had little lateral “fins” on the bottom of the hull below the water line that could be extended out horizontally from the hull to stabilize the platform in rough seas (of a high sea state). A complete SSBN Navigation Room was present on the Compass Island, but intentionally installed backwards from its orientation aboard SSBN’s. A prior NASA observation ship, the U.S.S. Vangard, replaced the Compass Island in this role in the late 1970’s.
Pre- (and post-)GPS Relative Navigation (RelNav) enabled networks of different platforms to reference both “friendlies” and enemy targets with respect to a single common (virtual) grid using the L-band JTIDS (time-slotted and frequency hopped from 960 MHz to 1215 MHz, with gaps imposed for TACAN and IFFN). This capability was especially useful when all participants were at sea and far from any geographic landmarks of absolute location. The grid tended to move and rotate slightly. It’s location was dictated by the Navigation Controller (NC), the platform having the best navigation accuracy (as a self-assessment), but in lieu of the demise of the original NC, the NC was replaced by the next best platform in this role to avoid possessing a single point vulnerability. JTRS (pronounced Jitters) is slated to replace JTIDS as an entirely software radio system (with its own unique set of problems yet to be solved). JTIDS included NTDS/ATDS. Air Force JTIDS used DTDMA protocol without RelNav. Navy version was TDMA with RelNav. Marine version of JTIDS was PLRS. Reed Solomon Code throughout. GPS uses Gold Code in two flavors or cycle lengths (to be upgraded).
Hybrid High-Rate Output Candidate Design for JTIDS/GPS/INS Integration and INS Navaid Selection.
Sam Blackman (Raytheon/Hughes), the (late) Oliver Drummond, Yaakov Bar-Shalom (UCONN), and Rabinder Madan.
Blazers of the exciting area of multi-sensor\multi-target tracking (sometimes pursued even in clutter) [related to optimal resource allocation and solved by invoking Munkres or the Hungarian or Jonker- Volgenent- Castanon’s (J-V-C) or Murty’s (1968) or Sam Blackman's Multi- Hypothesis Testing (MHT) algorithms. The first 3 techniques are all from the Operations Research area; the last is based on Bayesian Statistical analysis.
Not shown here: Prof. David Castanon (Boston University) and Charles Morefield (originally of Aerospace Corporation in the 1970’s when he posed multi-target tracking as a 0-1 Integer Programming Problem, more recently Chairman of the Board at Alphatech (after Michael Athans stepped down and went to Portugal) before Alphatech became part of BAE in Burlington, MA), and Thomas Kurien (Raytheon). Also see Particle Filter variations in: Vermaak, J., Godsill, S. J., Perez, P., “Monte-Carlo Filtering for Multi-Target Tracking and Data Association,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 41, No. 1, pp. 309-331, Jan. 2005. Also see Miller, M. L., Stone, H, S., Cox, I. J., “Optimizing Murty’s Ranked Assignment Method,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 33, No. 7, pp. 851-862, July 1997. Another: Frankel, L., and Feder, M., “Recursive Expectation-Maximizing (EM) Algorithms for Time-Varying Parameters with Applications to Multi-target Tracking,” IEEE Trans. on Signal Processing, Vol. 47, No. 2, pp. 306-320, February 1999. Yet another: Buzzi, S., Lops, M., Venturino, L., Ferri, M., “Track-before-Detect Procedures in a Multi-Target Environment,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 44, No. 3, pp. 1135-1150, July 2008.
Fourth ONR/GTRI Workshop on Target Tracking and Sensor Fusion, Naval Postgraduate School, Monterey, CA, 17 May 2001.Notice the guy (i.e., THK III) apparently in sun glasses (actually transitions) in the back row there (left of center, as always).
Lockheed Martin’s Paveway II Dual Mode Laser-Guided Bomb (DMLGB), which uses both laser-guided and inertial/GPS guidance, has achieved the U.S. Navy's initial operational capability and is now preparing for operational employment.
The DMLGB is designed to execute precision strike missions against stationary and mobile targets in all stationary and mobile targets in all weather conditions, according to Lockheed. The kits can operate in laser only, inertial/GPS, or dual-mode to provide pilots with flexibility to engage various types of targets in a single mission, says Lockheed Martin.
Extra! Extra! Read all about it!
GNSS has announced that its customers with JAVAD GNSS “triple-frequency”
type OEM boards (TR-G2T, TR-G3T, TRE-G2T, TRE-G3T, TRE-G3TAJ) and receivers
(TRIUMPH-1, Alpha TR-G2T/TR-G3T, DeltaS TRE-G2T/TRE-G3T/TRE-G3TAJ, SigmaS
TRE-G2T/TRE-G3T/TRE-G3TAJ) can now track the
L5 demonstration signal.
first GPS satellite with the L5 signal [Block IIR-20(M)] was successfully
launched on 24 March 2009 and its L5 = 1176.45
payload activated on 10 April 2009.
signal characteristics clearly indicate that JAVAD GNSS receivers allow
high-quality code and carrier-phase measurements of the L5 signal. The
signal-to-noise ratio typically varies from about 30 dB*Hz at low elevations up
to 57 dB*Hz at zenith (see figures below: top is SNR for L5; bottom is SNR for
GPS PRN 1).
white-noise and multipath tracking errors are comparable to what is normally
seen for the L1 and L2 signals.
interested in sample raw data with the “triple-frequency”
code and carrier phase measurements from IIR-20(M), can download sample data
(see the ADVANCED section on www.javad.com).
Note that these sample raw data are available in the JAVAD GNSS proprietary
binary format as well as Rinex 3.0.
Air Force Successfully Transmits an L5 Signal From GPS IIR-20(M) Satellite
4/13/2009 - LOS ANGELES AIR FORCE BASE, Calif. -- The U.S. Air Force GPS IIR-20(M) satellite successfully transmitted for the first time a GPS signal in the L5 frequency band today. L5, the third civil GPS signal, will eventually support safety-of-life applications for aviation and provide improved availability and accuracy.
This broadcast brings into use the GPS International Telecommunication Union filing at 1176.45 MHz in the highly protected and co-allocated Radio Navigation Satellite Service and Aeronautical Radio Navigation Service band. A joint team consisting of the GPS Wing, Lockheed Martin, ITT and The Aerospace Corporation developed the “L5 Demonstration” signal payload and integrated it onto the GPS IIR-20(M) spacecraft, which launched March 24, 2009.
to the men and women of the Air Force, our industry partners and national
research institute, this morning’s
successful L5 transmission marks an important milestone in GPS civilian
applications. This new third civil signal will make possible the research and
development of safety-of-life applications for the commercial transportation
sector, and in the future, will play a vital role in improving safety, fuel
efficiency, and capacity in our airspace, waterways, highways, and railroads.
event marks another important step in the ongoing effort to maintain and
modernize GPS as the global standard for space-based positioning, navigation,
said Joel Szabat, Deputy Assistant Secretary for Transportation Policy, U.S.
Department of Transportation.
New GPS Satellite’s Problems Indicated on 4 May 2009
Lt Col David Goldstein, chief engineer for the GPS Wing, told the plenary session at the European Navigation Conference in Naples, Italy, that the Wing is experiencing some “out of family” measurements from the recently launched IIRM (20) satellite. This appears to corroborate some unofficial rumors that have circulated recently about problems with “legacy signals” from the satellite, that is, L1 and L2. The April 10 broadcast of the first L5 signal secured that frequency for the U.S. GPS program; since that signal contains no navigation message at present, it is presumably not affected by these problems.
Goldstein told the ENC opening session, Monday 4 May 2009, that the Air Force will not launch any further satellites until this issue is resolved. IIR(M) 21, the last of the IIR(M) series, is currently scheduled to rise sometime in August, with the first of the IIF generation to follow in late 2009 or early 2010.
Normally, a satellite is set healthy within 28 days of launch, after extensive testing, but this has not occurred with the satellite launched on 24 March 2009. The U.S. Air Force has formed a response team and is working “nearly round the clock” to resolve the problem, but according to Goldstein is not rushing the issue, seeking a thorough solution since the overall constellation is robust at 30 satellites.
“We are currently examining data from the satellite that is not consistent with data from the other IIR(M)s,” he stated, characterizing the variances as “measurements with larger than expected pseudorange errors that are elevation-dependent, and that we have not seen before. We have experimented with a few fixes and it looks very promising.”
He described the response team’s approach as making a “fishbone diagram” of all potential failure mechanisms, and working through them methodically. “We think we have identified the failure but it may be several more months before the analysis is complete, and the situation is fully resolved.”
The big delay in preventing GPS from being completed by the planned date of 1984 was the Space Shuttle Challenger disaster. Most GPS satellites were planned to be inserted from a Space Shuttle but instead had to be inserted from Delta rockets as a fall back that delayed a full GPS satellite constellation from existing until 1994.
The open literature discussion of L3 in the early 1980’s for GPS was that like L2 (=1227.5 MegaHertz) and L1 (=1575.42 MegaHertz), it was also an integer multiple of a single onboard clock frequency being L3 (= 1381 MegaHertz). It was speculated that L3 was used to cross-communicate between GPS satellites like a JTIDS RelNav “network in the sky”. Some have speculated that it had related to autonomously maintaining proper satellite ephemeris of the network since in the “bad old days of Mutually Assured Destruction (MAD)” as a policy strategy, he who had the last accurate weapon fired “won”. Land-based Minuteman ICBM’s (with AIRS navigation systems) utilized GPS for a midcourse nav fix. Ship launched SLBM’s did not (at least not in the 1970’s). GPS supposedly had sufficient untended (by human intervention) ephemeris to last for 6 months unaided, according to NADC in the early 1980’s.
L3 is now both known by the private sector and is controversial in the civilian Radio Astronomy community, as seen below.
The Global Positioning Satellite system has a mode, “L3” at 1381 MHz, which is used for global alarm. If it is within your observing band, then all astronomical signal gets swamped. With advanced notice, the observatory is in a position to alert the responsible authorities and request rescheduling GPS L3 transmission.
As circulated in unclassified literature in the 1980’s, L3 is a part of NUGET, GPS satellites monitor and report on whether they have detected a nuclear blast anywhere in the world.
GPS L3 Interference and Radio Astronomy
European radio astronomy stations operating in the frequency band 1330 - 1400 MHz are experiencing harmful interference at a frequency of about 1381 MHz, which is so strong that it ruins the observations in this frequency range when it occurs. This interference is generated by transmissions from the GPS L3 channel.
An example of this type of interference observed with the Westerbork Synthesis Radio Telescope, WSRT, in the Netherlands is shown in Figure 1 for the amplitude and Figure 2 for the phase of the observed signal. The radio astronomical observation concerns a radio source at 23h36m35.20s right ascension and 26o40’36.00” declination (epoch J2000). The absolute scale for the amplitude of the interference signal is not calibrated since the antenna gain into the direction of the satellite, which was emitting in the far sidelobes of the antennas, is not known.
The indicated level of detrimental interference for the observations presented in the figures below is -239 dB(W/m2/Hz), which was determined using the methodology of Recommendation ITU-R RA.769. This methodology includes the assumption that the interference is received through the far antenna sidelobes, where an antenna gain of 0 dBi applies.
The L3 spread spectrum transmissions centered at 1381 MHz also transgresses into the frequency range 1400 - 1427 MHz, a spectral band where the radio astronomy has a primary allocation to which RR footnote 5.340 applies, which states that “all emissions are prohibited”. Using a band-stop filter the signal could be suppressed to a level of -252 dB(W/m2/Hz), i.e. still 3 dB above the level of interference detrimental to radio astronomy continuum observations as given in Recommendation ITU-R RA.769.
The fundamental problem remains that the GPS L3 emission is intentionally produced in the band 1400 - 1427 MHz and is therefore in conflict with footnote 5.340 of the ITU-R Radio Regulations.
It should be noted that in the ITU Radio Regulations for Region 1 the band 1300 - 1350 MHz includes a primary allocation to RADIONAVIGATION-SATELLITE (Earth-to-space) and no allocation to a space service in the band 1350-1400 MHz. Thus no space-to-Earth transmissions are allowed according to these Regulations. For the frequency band 1330-1400 MHz footnote 5.149 applies, which states that “administrations are urged to take all practicable steps to protect the radio astronomy service from harmful interference. Emissions from spaceborne or airborne stations can be particularly serious sources of interference to the radio astronomy service (...)”.
CRAF considers that a regulatory solution for this issue is required, in order to avoid the creation of an undesirable regulatory precedent, where the operation of an application is allowed in conflict with the ITU Radio Regulations.
On this matter CRAF is currently in the process of negotiation with concerned Administrations and expects that it can be solved in due course.
Recent solutions to GNSS incursions into frequencies reserved for Radio Astronomy have been advertised (but the band of concern apparently differs from what is complained about above): Julien, O., Issler, J.-L., "Mitigating the Impact of GNSS Signals in the Radio Astronomy Band 1610.6-1613.8 MHz," Navigation: Journal of the Institute of Navigation, pp. 229-240, Vol. 56, No. 4, Winter 2009.
In 1957, Walter Marrow (Lincoln Laboratory of MIT), who later became its head but retired from that position early in the new millennium, launched a missile full of thousands of small metal space needles into LEO, which took about six months to decay out of orbit and burn up in the atmosphere. The entire event was viewed by Lincoln’s Haystack radar. Radio Astronomers were livid since reception was impossible during that time period.
“The activation of the L2C signal in January 2006 will be of great benefit to the civil
said Colonel Jester, Chief, Space Operations Branch, Air Force Space Command. “But they will be using this signal at their own risk until the command and control of
L2C is realized in the Fiscal Year 2013 timeframe. Receivers able to fully utilize the
L2C signal will be the responsibility of the civil community. The military will build receivers focused on the new M-code
The United States Government Accountability Office (GAO) issued on 7 May 2009 an alarming report on the future of GPS, characterizing ongoing modernization efforts as shaky. The agency appears to single out the IIF program as the weak link between current stability and ensured future capability, calling into doubt “whether the Air Force will be able to acquire new satellites in time to maintain current GPS service without interruption.” It asserts the very real possibility that “in 2010, as old satellites begin to fail, the overall GPS constellation will fall below the number of satellites required to provide the level of GPS service that the U.S. government commits to.” read more»
“There is a very minor problem with the L1, L2, and M-code navigation signals. Any causes would be pure speculation at this point, but the issue is the satellite will not be set healthy until these problems are fixed…. The ITT, LMCO and GPS Wing teams are working the problem hard. It may be a few weeks before the satellite is set healthy, but when that time comes I am sanguine that all the signal issues will be mitigated and the navigation message will be on par with the other IIR(M) payloads.” — Colonel Mark Crews
BY DON JEWELL | email@example.com
I am sure that many of you remember Colonel Mark Crews when he served with distinction as the chief engineer for the GPS Wing at SMC. Mark made some legendary and landmark contributions to the future of the GPS constellation as we know it, nationally and internationally. After you read what Dr. Crews has to say about the L5 payload, I will launch into an issue concerning user equipment that has been on mind for sometime — with a trip to the shrink’s couch. read more»
Brad Parkinson, the first GPS Program Office director, chief architect and advocate for GPS, submitted written testimony to Congress on mitigation options for possible GPS brownouts. His presentation comes in reference to the recent GAO report highlighting the risk that the GPS constellation may fall below the minimum level of 24 satellites required for full operational capability. In his opening, Parkinson states that ”GAO correctly points out the possibility that the GPS constellation will be reduced to less than the current number of 30 to 32 satellites. In fact, it is possible that the constellation will be at a level of less than 24 satellites. I would like to focus on the options that would help reduce this risk." read more» Click here to download a 91KByte pdf file conveying Sir Brad Parkinson’s excellent 10 side PowerPoint presentation to Congress. Prof. Parkingson’s original 228KByte PowerPoint is here, including his speaker's notes as prompters.
Andrew Sage, a director of UK-based transport consultancy Helios, delivered a presentation at the European Navigation Conference entitled: The race to be the partner of choice for GPS. read more»
Analyses of a Drop in GPS Satellite Numbers
Professor Richard Langley of the University of New Brunswick (also GPS World Innovation editor) has done several analyses to see how the use of GLONASS satellites could help compensate for a potential reduction in the number of available GPS satellites. These studies came in response to a warning from the U.S. Government Accountability Office about the potential drop in the number of healthy satellites in the GPS constellation as a result of delays in both the Block IIF and Block III modernization programs.read more>>
The SVN-49 Story: What Went Wrong, How It Got Found, and FixedDuring a very reassuring teleconference today with Colonel David Madden (GPSW/CC) and Colonel David Buckman (AFSPC - GPS Command Lead), we learned the true story of exactly what happened to SVN-49 , aka IIR-20(M), launched March 24, and why it has not been set to a healthy status. This teleconference should put an end to all the speculation concerning SVN-49 and its future status. In sum, there is nothing wrong with the L1, L2, or L5 signal transmitters, and they will not have to undergo expensive re-testing.
Latest GPS Satellite Early Orbit Checkout Extended read more>>The U.S. Air Force is investigating the cause and effects of signal distortions observed from the GPS IIR-20(M) spacecraft launched on March 24, 2009. Routine early orbit checkout procedures determined that GPS IIR-20(M) signals were inconsistent with the performance of other GPS IIR-M satellites. The signal distortion was initially observed as an elevation-dependent bias in ranging measurements from GPS monitor stations.
Coast Guard Directed to Maintain and Upgrade LoranThe U.S. Senate, in a Coast Guard Authorization Act for Fiscal Years 2010 and 2011 currently before the Committee on Commerce, Science, and Transportation, directs the Secretary of Transportation to maintain the current Loran-C navigation system and prepare for modernization to eLoran, and authorizes $37 million per year for 2010 and 2011 towards that purpose. Similar action is also currently pending in the House.
Resource for Comparing Precise Point Positioning (PPP) SolutionsGNSS researchers at the University of New Brunswick, Canada, have created a Precise Point Positioning (PPP) Software Centre website to offer an easy means of comparing solutions from online PPP applications. Users are invited to send a RINEX observation file that will be simultaneously processed by three online PPP applications.
Final Modernized GPS IIR Satellite to Lift off from Cape Canaveral The last in a series of eight modernized Global Positioning System Block IIR (GPS IIR-M) satellites built by Lockheed Martin for the U.S. Air Force is set to launch aboard a Delta II rocket on Aug. 17 from Cape Canaveral Air Force Station, Florida. More....
GPS IIR-21(M) Satellite Declared Operational
The last in the series of eight modernized Global Positioning System IIR satellites, GPS IIR-21(M), was declared operational Thursday for military and civilian users worldwide, just 10 days after launching from Cape Canaveral Air Force Station. More....
PRN01/SVN49: Another GPS Satellite Anomaly
From monitoring at the University of New Brunswick and elsewhere around the globe, it appears that normal signals from the L1 and L2 transmitters on the GPS satellite PRN01/SVN49 were unavailable for more than two hours on the morning of September 4. More....
More problems with GPS and the end for Loran (not too wise since redundant navaids enable easy detection by comparison when GPS is being interfered with) can be found at the following link: http://www.gpsworld.com/gnss-system/out-front-rocky-road-robustness-9424 .
An INS-based Tracking device the size of a pin head:
TeK Associates’ motto : “We work hard to make your job easier!”