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This algorithm is key to space travel, GPS, VR and more, and it is over 50 years old 21

Posted by Lisa Harvey,

Earlier this week, MIT Technology Review published an article “How an Inventor You’ve Probably Never Heard of Shaped the Modern World” which described Rudolf Kálmán’s contribution to modern-day science and technology, a recursive estimation algorithm that accurately predicts variables such as direction, speed, and location even in noisiest of environments.

Rudolf Kálmán first described the Kalman filter in technical papers in 1960, a mere 2 years after NASA was founded. One of the first applications of the Kalman filter was the navigation for the Apollo Project. It was used to estimate the trajectories of manned spacecraft taking the first astronauts to the Moon and back. Since then, it has been used in many technologies that affect our daily lives, or will in the near future.

Here’s a list of some of the modern technologies that use Kalman filters:

GPS

The entire satellite-based global positioning system (GPS) was described as “one enormous Kalman filter” in the engineering textbook Global Positioning Systems, Inertial Navigation, and Integration. According to an IEEE article on the applications of the Kalman filtering in aerospace, “This Kalman filter has a large system state vector, including the trajectories of the 24+ satellites, the drift rates and phases of all system clocks, and hundreds of parameters related to atmospheric propagation delay as a function of time and location.”

Image credit: Wikipedia

Wind turbines

Green technology is the focus of much research and commercial investment. In Europe, wind energy is rapidly gaining in adoption and Kalman filters are helping improve the efficiency of this technology.

Phys.org recently shared an article called “A software ‘detective’ for wind power generation” in which they described a new approach for prolonging the life of wind turbines by detecting wind anomalies such as wind shear and extreme gusts. The smart control software for the Windtrust project utilizes an extended Kalman filter for regression analysis.

Image credit: Vera Kratochvil, PublicDomainPictures.net

Weather forecasting

In April, the Washington Post reported the United States’ National Weather Service is working on two improvements to their Global Forecast System (GFS) forecast model. The first establishes a time stamp on the data points used to run the model, removing the assumption that the data points were collected simultaneously. The second upgrade makes use of a variation on the Kalman algorithm. “The second addition was an ensemble Kalman filter, or EnKF, which essentially throws out bad data that would result in a poor forecast.”

Image credit: An animated image of GFS simulation, NOAA.

Advanced Driver Assistance Systems (ADAS)

While self-driving cars top many newsfeeds, a simplified view of ADAS is a navigation system for our roads similar to the system Apollo used in space. ADAS systems will eventually be responsible for providing navigational guidance for autonomous vehicles. According to Paul Whytock’s article Why should car drivers love Kalman filtering, “The reason why drivers should love it is simple enough, it increases the efficiency of advanced driver assistance systems (ADAS) and makes vehicle control operations like blind spot detection, stability and traction control, lane departure detection and automatic braking in emergency situations a lot safer and more effective.”

adas

Virtual Reality (VR)

In VR, predictive tracking is used to forecast the position of an object and its trajectory. Kalman filters are a common choice for this application. An MIT Press Journal article that tracks the history of using Kalman filters in VR applications states, “In recent years there has been an explosion in the use of the Kalman filter in VR/AR. In fact, at technical conferences related to VR these days, it would be unusual to see a paper on tracking that did not use some form of a Kalman filter, or draw comparisons to those that do.”

vr

VR example from Mathworks.com

MATLAB and Kalman Filters

Kalman filters have many applications, and there are multiple MATLAB resources available to show you how to use them in your designs.

  • Computer vision systems regularly rely on Kalman filters for object tracking, particularly when tracking multiple objects are required. Here is a short video on the topic.
  • Here’s an example that shows how to perform automatic detection and tracking from a moving camera. This example contains several additional algorithmic steps including people detection, customized non-maximum suppression, and heuristics to identify and eliminate false alarm tracks.
  • Kalman filters are commonly used in GNC systems, such as in sensor fusion, where they synthesize position and velocity signals by fusing GPS and IMU (inertial measurement unit) measurements. A case study using Kalman filters for controls systems can be seen here.
  • Here’s an example of using Kalman filters to estimate the position and velocity of a vehicle in that can move freely in the two-dimensional space without any constraints.

There are many more examples using Kalman filters. Please post a comment and let us know how you’ve utilized Kalman filters in your design.

21 CommentsOldest to Newest

Umamaheswari replied on : 2 of 21
We used kalman filter successfully in a real time project for anti blur and smear process in digital image processing
Saeed Masoomi replied on : 3 of 21
Kalman filter have a many applications in our life that I will mention some of them that I used in my works 1- It's really good for filtering in digital signal processing for some application of robotics such as quadcopter's GPS and logging data from sensor 2- I use in some application for moving-average filter(for some data that have a Gaussian noise, remember that in theory Kalman filter proofs for this type of noise) 3- in Surveillance system and object tracking , for example in object tracking maybe you want to use Gaussian mixture model for your work IN obtaining foreground objects but in labeling maybe some target lose(because of gamma correction or combining blobs or other reasons) and in some frame labeling be a bewildering but using from kalman filter assure that your program have a nice prediction for lost object. 4- Navigation (two or more GPS) 5 - combining two or more sensor data's for precision.(GPS and acceleration sensor) and so on...sorry for my English I'm not good in English
Abdulmajid Mrebit replied on : 4 of 21
Kalman Filter has many applications in the control system, image tracking and target tracking in the radar system in both civilian and military. In a control system is used to predict unobservable state. Moreover, It has been used financially in the stock market to predict the future stock price. The Kalman has different types Kalman filter, Extended Kalman filter, Time-varying Kalman Filter. A particle filter is another technique that can be used for estimation. Particle filters design does not depend on the system equation like the Kalman filter case, it relays on the states' weight which can be updated with iteration.
tomkerr replied on : 5 of 21
I was involved with D-1 Trident and C-4 back-fit Poseidon SSBN SINS/ESGM navigation development from 1973-1979 (where I developed an original automated failure detection algorithm for the ESGM as a Kalman filter real-time accoutrement involving Two Confidence Regions: 1; Kerr, T. H., “Failure Detection Aids for Human Operator Decisions in a Precision Inertial Navigation System Complex,” Proceedings of Symposium on Applications of Decision Theory to Problems of Diagnosis and Repair, Keith Womer (editor), Wright-Patterson AFB, OH: AFIT TR 76-15, AFIT/EN, Oct. 1976, sponsored by Dayton Chapter of the American Statistical Association, Fairborn, Ohio, June 1976. 2. Kerr, T. H., “Real-Time Failure Detection: A Static Nonlinear Optimization Problem that Yields a Two Ellipsoid Overlap Test,” Journal of Optimization Theory and Applications, Vol. 22, No. 4, August 1977. 3. Kerr, T. H., “Statistical Analysis of a Two Ellipsoid Overlap Test for Real-Time Failure Detection,” IEEE Transactions on Automatic Control, Vol. 25, No. 4, August 1980. 4. Kerr, T. H., “False Alarm and Correct Detection Probabilities Over a Time Interval for Restricted Classes of Failure Detection Algorithms,” IEEE Transactions on Information Theory, Vol. 28, No. 4, pp. 619-631, July 1982. 5. Kerr, T. H., “Examining the Controversy Over the Acceptability of SPRT and GLR Techniques and Other Loose Ends in Failure Detection,” Proceedings of the American Control Conference, San Francisco, CA, 22-24 June 1983.  (an expose) 6. Kerr, T. H., “Comments on ‘A Chi-Square Test for Fault Detection in Kalman Filters’,” IEEE Transactions on Automatic Control, Vol. 35, No. 11, pp. 1277-1278, November 1990. 7/ Kerr, T. H., “A Critique of Several Failure Detection Approaches for Navigation Systems,” IEEE Transactions on Automatic Control, Vol. 34, No. 7, pp. 791-792, July 1989.  (an expose of sorts) 8/ Kerr, T. H., “On Duality Between Failure Detection and Radar/Optical Maneuver Detection,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 25, No. 4, pp. 581-583, July 1989. 9. Kerr, T. H., “Comments on ‘An Algorithm for Real-Time Failure Detection in Kalman Filters’,” IEEE Trans. on Automatic Control, Vol. 43, No. 5, pp. 682-683, May 1998. (an expose of sorts) 10. Kerr, T. H., “Integral Evaluation Enabling Performance Trade-offs for Two Confidence Region-Based Failure Detection,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 29, No. 3, pp. 757-762, May-Jun. 2006.
tomkerr replied on : 6 of 21
I posed and solved the problem of SSBN external navaid fix utilization while evading enemy surveillance as a “cat-and-mouse” game of “sensor schedule optimization” within a natural Kalman Navigation filter context. Publications constituting significant development in submarine navigation trade-off considerations between frequency of external navaid usage (to maintain sufficient navigation accuracy in case a launch is ordered) versus exposure to enemy surveillance: 1. Kerr, T. H., “Preliminary Quantitative Evaluation of Accuracy/Observables Trade-off in Selecting Loran/NAVSAT Fix Strategies,” TASC Technical Information Memorandum TIM-889-3-1, Reading, MA, December 1977 (Confidential). 2. Kerr, T. H., “Improving C-3 SSBN Navaid Utilization,” TASC TIM-1390-3-1, Reading, MA, August 1979 (Secret). 3. 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 (reprinted in Navigation: Journal of the Institute of Navigation, Vol. 28, No. 4, pp. 263-285, Winter 1981-82). 4. Kerr, 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 (an update).
tomkerr replied on : 7 of 21
I have published results for several other diverse Kalman filter applications relating to use of Kalman-like filters for Early Warning Radars to track enemy RV's: 1. Kerr, T. H., “Angle-Only Tracking,” slide presentation for Reentry Systems Program Review, Lincoln Laboratory, Lexington, MA, 10 Jan. 1989. 2. Kerr, T. H., “An Analytic Example of a Schweppe Likelihood Ratio Detector,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 25, No. 4, pp. 545-558, Jul. 1989. (closed-form analytic solution) 3. Kerr, T. H., “Streamlining Measurement Iteration for EKF Target Tracking,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 27, No. 2, Mar.1991. 4. 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, pp. 1173-1188, 20-23 Sep. 1994. 5. Kerr, T. H., “Assessing and Improving the Status of Existing Angle-Only Tracking (AOT) Results,” Proceedings of the International Conference on Signal Processing Applications & Technology, Boston, pp. 1574-1587, 24-26 Oct. 1995. (an expose) 6. Kerr, T. H., “Extending Decentralized Kalman Filtering (KF) to 2-D for Real-Time Multisensor Image Fusion and/or Restoration,” Proceedings of SPIE Conference, Vol. 2755, Orlando, pp. 548-564, 8-10 Apr. 1996. 7. Kerr, T. H., “Extending Decentralized Kalman Filtering (KF) to 2D for Real-Time Multisensor Image Fusion and/or Restoration: Optimality of Some Decentralized KF Architectures,” Proceedings of the International Conference on Signal Processing Applications & Technology, Boston, MA, 7-10 Oct. 1996. 8. Kerr, T. H., “Developing Cramer-Rao Lower Bounds to Gauge the Effectiveness of UEWR Target Tracking Filters,” Proceedings of AIAA/BMDO Technology Readiness Conference and Exhibit, Colorado Springs, 3-7 August 1998.   9. Satz, H. S., Kerr, T.  H., “Comparison of Batch and Kalman Filtering for Radar Tracking,” Proceedings of 10th Annual AIAA/BMDO Conference, Williamsburg, VA, 25 Jul. 2001 (Unclassified, but Conference Proceedings are SECRET).
tomkerr replied on : 8 of 21
My publications that combine the ideas of failure detection with those of decentralized Kalman Filtering to yield a rigorous basis for system reconfiguration and redundancy management: 1. 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.  (an expose) 2. Kerr, T. H., “Decentralized Filtering and Redundancy Management for Multisensor Navigation,” IEEE Trans. on Aerospace and Electronic Systems, Vol.23, No. 1, pp. 83-119, Jan. 1987.   (an expose)
tomkerr replied on : 9 of 21
Also see: "Introduction to the Special Section on Industrial Applications and Implementation Issues of the Kalman Filter" François Auger; Josep M. Guerrero; Mickaël Hilairet; Seiichiro Katsura; Eric Monmasson; Teresa Orlowska-Kowalska IEEE Transactions on Industrial Electronics, 2012, Volume: 59, Issue: 11, Pages: 4165 - 4168.
tomkerr replied on : 10 of 21
A related Cramer Rao Lower Bound (CRLB) computational methodology for evaluating and gauging the efficacy of using Kalman-filter-like "Extended Kalman filters" for nonlinear estimation applications.
tomkerr replied on : 11 of 21
For a quick summary of standard approximations invoked and utilized within many Kalman filter implementations and to provide some closed-form analytic solutions that can be useful in verifying/validating the correctness of a Kalman filter software implementation, please see: 1. Kerr, T. H., “Numerical Approximations and Other Structural Issues in Practical Implementations of Kalman Filtering,” a chapter in Approximate Kalman Filtering, edited by Guanrong Chen, World Scientific, NY, 1993. 2. Kerr, T. H., “Exact Methodology for Testing Linear System Software Using Idempotent Matrices and Other Closed-Form Analytic Results,” Proceedings of SPIE, Session 4473: Tracking Small Targets, pp. 142-168, San Diego, 29 July-3 Aug. 2001. (closed-form analytic solutions)
tomkerr replied on : 12 of 21
Also see the excellent book by Bruce P. Gibbs (contributed to by many of my TASC cohorts from the 1970's and other illustrious contemporaries):  Gibbs, B. P., ADVANCED KALMAN FILTERING, LEAST-SQUARES AND MODELING: A Practical Handbook, John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada, 2011.
tomkerr replied on : 13 of 21
Here are some technical notes on the subject of operations counts of SVD or Eigenvalue Eigenvector decomposition and other approaches to establishing Positive definiteness/semidefiniteness of symmetric matrices (as routinely arise in implementing Kalman filters):: Kerr, T. H., “Testing Matrices for Definiteness and Application Examples that Spawn the Need,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 10, No. 5, pp. 503-506, Sept.-Oct., 1987. Kerr, T. H., “On Misstatements of the Test for Positive Semidefinite Matrices,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 13, No. 3, pp. 571-572, May-Jun. 1990. (as occurred in Navigation & Target Tracking software in the 1970’s & 1980’s using counterexamples) Kerr, T. H., “Fallacies in Computational Testing of Matrix Positive Definiteness/Semidefiniteness,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 26, No. 2, pp. 415-421, Mar. 1990. [Lists fallacious algorithms that the author found to routinely exist in U.S. Navy submarine navigation and sonobuoy software in the late 1970’s and early 1980’s using counterexamples to point out the problems.] The third one has the most relevance in the last Section VII. My endorsement for use of Beirman's and Thornton's U-D-U^T squareroot Kalman filter formulation in Section VII was OK for its time (1990 and before). By the late 1990's, computers were built differently and computation of the scalar square root was no longer iterative and so time consuming. Consequently, Neal Carlson's squareroot filter has the least computations or operations counts even though it uses explicit computation of scalar square roots (now handled by logarithms and anti-logarithms).
tomkerr replied on : 14 of 21
Certain errors previously existed within the methodology for how various aerospace companies computed the matrix exponential (as used for the transition matrix for Linear Time-Invariant [LTI] systems) as associated with using mathematical norms: 1.Kerr, T. H., “A Simplified Approach to Obtaining the Steady-State Initial Conditions for Linear System Simulations,” Proceedings of the Fifth Annual Pittsburgh Conference on Modeling and Simulation, 1974. 2.Kerr, T. H., “An Invalid Norm Appearing in Control and Estimation,” IEEE Transactions on Automatic Control, Vol. 23, No. 1, February 1978. 3.Kerr, T. H., “Three Important Matrix Inequalities Currently Impacting Control and Estimation Applications,” IEEE Transactions on Automatic Control, Vol. 23, No. 6, December 1978. 4.Kerr, T. H., “The Principal Minor Test for Semidefinite Matrices-Author’s Reply,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 13, No. 3, p. 767, Sep.-Oct. 1989. 5.Kerr, T. H., “The Proper Computation of the Matrix Pseudo-Inverse and Its Impact in MVRO Filtering,” IEEE Transactions on Aerospace and Electronic Systems, Vol. AES-21, No. 5, September 1985. 6.Kerr, T. H., and Satz, H., S., “Applications of Some Explicit Formulas for the Matrix Exponential in Linear Systems Software Validation,” Proceedings of 16th Digital Avionics System Conference, Vol. I, pp. 1.4-9 to 1.4-20, Irvine, CA, 26-30 Oct. 1997. The situation is much better today thanks to the eternal vigilance of numerical analysts and application engineers (such as those at The MathWorks, who recognize its importance)!
tomkerr replied on : 15 of 21
Besides merely limiting one's attention to the Kalman filter algorithm itself and its mechanization in software, one must occasionally branch out and fix glitches made by others in models to be used, as occurred by someone attempting to handle numerical gravity data non-rigorously, as corrected in: 1.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, pp. 1214-1215, Jul.-Aug. 2007. (Two counterexamples are provided where claimed conditions are not satisfied.) Simplifying a test proposed by others for two ellipsoid overlap, when the ellipsoids are not necessarily related (as they are in the CR2 failure detection approach above in Item 5 of 16), as availed in: 2.Kerr, T. H., “Comments on ‘Determining if Two Solid Ellipsoids Intersect’,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 28, No. 1, pp. 189-190, Jan.-Feb. 2005. By simplifying a GPS-related optimization problem by revealing that it has a directly calculated closed-form solution as: 3.Kerr, T. H., “Comment on ‘Low-Noise Linear Combination of Triple-Frequency Carrier Phase Measurements’,” Navigation: Journal of the Institute of Navigation, Vol. 57, No. 2, pp. 161, 162, Summer 2010. Frequently having to deal with principles of operation of the actual hardware and identifying likely vulnerabilities way before others saw them and started fixing them: 4.Kerr, T. H., “Further Critical Perspectives on Certain Aspects of GPS Development and Use,” Proceedings of 57th Annual Meeting of the Institute of Navigation, pp. 592-608, Albuquerque, NM, 9-13 Jun. 2001. (An expose of several loose ends in GPS development that needed [and have now received] further attention before unabated and unabashed reliance upon GPS, as had been the claimed plan in the late 1990's for Battlefield 2000.)
tomkerr replied on : 16 of 21
I looked into decentralized Kalman filter stability for navigation, as used in U.S. Navy Joint Tactical Information Distribution Systems (JTIDS)-RelNav: 1. Kerr, T. H., “Stability Conditions for the RelNav Community as a Decentralized Estimator-Final Report,” Intermetrics, Inc. Report No. IR-480, Cambridge, MA, 10 Aug. 1980, for NADC (Warminster, PA). 2. Kerr, 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 Dec. 1980. 3. Kerr, T.H., and Chin, L., “The Theory and Techniques of Discrete-Time Decentralized Filters,” in Advances in the Techniques and Technology in the Application of Nonlinear Filters and Kalman Filters, edited by C.T. Leondes, NATO Advisory Group for Aerospace Research and Development, AGARDograph No. 256, Noordhoff International Publishing, Lieden, pp. 3-1 to 3-39, 1981. 4. Kerr, T. H., “Extending Decentralized Kalman Filtering (KF) to 2D for Real-Time Multisensor Image Fusion and/or Restoration: Optimality of Some Decentralized KF Architectures,” Proceedings of the International Conference on Signal Processing Applications & Technology (ICSPAT96), Boston, MA, 7-10 Oct. 1996. For the U.S. Navy: 5. 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 Oct. 1982. For GPS (a representative partial listing): 6. Kerr, T. H., “Phase III GPS Integration; Volume 1: GPS U.E. Characteristics,” Intermetrics Report IR-MA-177, Cambridge, MA, Jan. 1983, for Navair. 7. Kerr, T.H., “GPS/SSN Antenna Detectability,” Intermetrics Report No. IR-MA-199, Cambridge, MA, 15 Mar. 1983, for NADC For U.S. Navy minesweeper navigation: 8. Kerr, T. H., and Rogers, R., “Report on PINS Filter Design Review (of Magnavox),” Intermetrics Memo, Cambridge, MA, 11 Aug. 1983, for NOSC (San Diego, CA). For DARPA: 9. 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 Sep. 1994. 10. Kerr, T. H., “A Critique of Neural Networks as Currently Exist for Control and Estimation,” Proc. of the International Conference on Signal Processing Applications & Technology (ICSPAT), Boston, MA, pp. 1434-1443, 24-26 Oct. 1995. 11. Kerr, T. H., “Critique of Some Neural Network Architectures and Claims for Control and Estimation,” IEEE Transactions on Aerospace and Electronic Systems, Vol. AES-34, No. 2, pp. 406-419, Apr. 1998. (Extends beyond prior version [10] above.)
tomkerr replied on : 17 of 21
For the U.S. Air Force: 1. Carlson, N. A., Kerr, T. H., Sacks, J. E., “Integrated Navigation Concept Study,” Intermetrics Report No. IR-MA-321, 15 Jun. 1984, for ITT (Nutley, NJ). 2. Kerr, T. H., “Decentralized Filtering and Redundancy Management for Multisensor Navigation,” IEEE Trans. on Aerospace and Electronic Systems, Vol. AES-23, No. 1, pp. 83-119, Jan. 1987 (minor corrections appear on p. 412 of May and on p. 599 of Jul. 1987 issues of same journal). 3. Kerr, T. H., “Comments on ‘Federated Square Root Filter for Decentralized Parallel Processes’,” IEEE Transactions on Aerospace and Electronic Systems, Vol. AES-27, No. 6, Nov. 1991. For U.S. Navy sonar and sonobuoy tracking filters: 4. 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. 5. Kerr, T. H., “Assessment of the Status of the Current Post-Coherent Localization Algorithm,” Intermetrics Report No. IR-MA-319, 31 May 1984, for NADC. For U.S. helicopter missile warning system (MWS): 6. Kerr, T. H., “Update to and Refinement of Aspects of Pattern Recognition Principles Used in the Missile Warning System (AN/AAR-47),” Intermetrics Report No. IR-MA-362, 15 Sep. 1983, for Honeywell Electro-Optical.
tomkerr replied on : 18 of 21
For BMDO: 1. Kerr, T. H., “Multichannel Shaping Filter Formulations for Vector Random Process Modeling Using Matrix Spectral Factorization,” MIT Lincoln Laboratory Report No. PA-500, Lexington, MA, 27 Mar. 1989 (BSD [previously BMO]). 2. Kerr, T. H., “Emulating Random Process Target Statistics (using MSF),” IEEE Trans. on Aerospace and Electronic Systems, Vol. 30, No. 2, pp. 556-577, Apr. 1994. 3. Kerr, T. H., “Multichannel AR Modeling for the Active Decoy (U),” MIT Lincoln Laboratory Report No. PA-499, Lexington, MA, Mar. 198 (Secret). 4. Kerr, T. H., “Angle-Only Tracking,” slide presentation for Reentry Systems Program Review at Lincoln Laboratory, Lexington, MA, 10 Jan. 1989. 5. Kerr, T. H., “Assessing and Improving the Status of Existing Angle-Only Tracking (AOT) Results,” Proc. of the International Conf. on Signal Processing Applications & Technology (ICSPAT), Boston, MA, pp. 1574-1587, 24-26 Oct. 1995. 6. Kerr, T. H., “Rationale for Monte-Carlo Simulator Design to Support Multichannel Spectral Estimation and/or Kalman Filter Performance Testing and Software Validation/Verification Using Closed-Form Test Cases,” MIT Lincoln Laboratory Report No. PA-512, Lexington, MA, 22 Dec. 1989 (BSD [previously BMO]). 7. Kerr, T. H., “Numerical Approximations and Other Structural Issues in Practical Implementations of Kalman Filtering,” a chapter in Approximate Kalman Filtering, edited by Guanrong Chen, 1993. 8. Kerr, T. H., “Streamlining Measurement Iteration for EKF Target Tracking,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 27, No. 2, Mar. 1991 (minor correction appears in Nov. 1991 issue). 9. Kerr, T. H., NMD White Paper on Designated Action Item, MITRE, Bedford, MA, Jan. 1998. 10. Kerr, T. H., “Status of CR-Like Lower bounds for Nonlinear Filtering,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 25, No. 5, pp. 590-601, Sep. 1989 (Author's reply in Vol. 26, No. 5, pp. 896-898, Sep. 1990). 11. Kerr, T. H., “Cramer-Rao Lower Bound Implementation and Analysis for NMD Radar Target Tracking,” TeK Associates Technical Report No. 97-101 (for MITRE), Lexington, MA, 26-30 Oct. 1997. 12. Kerr, T. H., “Cramer-Rao Lower Bound Implementation and Analysis: CRLB Target Tracking Evaluation Methodology for NMD Radars,” MITRE Technical Report, Contract No. F19628-94-C-0001, Project No. 03984000-N0, Bedford, MA, Feb. 1998. 13. Kerr, T. H., “Developing Cramer-Rao Lower Bounds to Gauge the Effectiveness of UEWR Target Tracking Filters,” Proceedings of AIAA/BMDO Technology Readiness Conference and Exhibit, Colorado Springs, CO, 3-7 Aug. 1998. 14. Kerr, T. H., UEWR Design Notebook-Section 2.3: Track Analysis, TeK Associates, Lexington, MA, (for XonTech, Hartwell Rd, Lexington, MA), XonTech Report No. D744-10300, 29 Mar. 1999. 15. Kerr, T. H., and Satz, H. S., “Evaluation of Batch Filter Behavior in comparison to EKF,” TeK Associates, Lexington, MA, (for Raytheon, Sudbury, MA), 22 Nov. 1999. 16. Satz, H. S., Kerr, T. H., “Comparison of Batch and Kalman Filtering for Radar Tracking,” Proc. of 10th Annual AIAA/BMDO Conference, Williamsburg, VA, 25 Jul. 2001 (Unclassified paper but Conference Proceedings are SECRET).
tomkerr replied on : 19 of 21
For Lincoln Laboratory of MIT: 1. Kerr, T. H., “Vulnerability of Recent GPS Adaptive Antenna Processing (and all STAP/SLC) to Statistically Non-Stationary Jammer Threats,” Proc. of SPIE, Session 4473: Tracking Small Targets, pp. 62-73, San Diego, CA, 29 Jul.-3 Aug. 2001. 2. Kerr, T. H., “New Lamps for Old: a shell game for generalized likelihood use in radar? Or this isn’t your father’s GLR!,” Proc. of SPIE, Session 4473: Tracking Small Targets, pp. 476-483, San Diego, CA, 29 Jul.-3 Aug. 2001. 3. Kerr, T. H., “Status of CR-Like Lower bounds for Nonlinear Filtering,” IEEE Transactions on Aerospace and Electronic Systems, Vol. AES-25, No. 5, pp. 590-601, Sep. 1989 (Author's reply in Vol. AES-26, No. 5, pp. 896-898, Sep. 1990). (Importance and utility of the above being endorsed by independent experts on page 9 of: http://www.tekassociates.biz/branko_05.pdf and in Section 5 of: https://www.ll.mit.edu/asap/asap_05/pdf/Presentations/01_vantrees.pdf) 4. http://www.tekassociates.biz/services.htm#HPEC
tomkerr replied on : 20 of 21
For General Electric Corporate R&D Center in Schenectady, N.Y.: Kerr, T. H., "ADA70 Steady-State Initial Value Convergence Techniques," Information Science and Engineering, Report No. 72CRD095, General Electric Company Corporate Research and Development, Schenectady, N.Y., Technical Information Series, CLASS 2, March 1972. In the above, ADA is "Automated Dynamic Analyzer", which was a more capable, jointly continuous-time and discrete-time, product response (for G.E. internal industrial simulations in the late 1960's and early 1970's) to IBM's earlier Continuous Systems Modeling Program (CSMP). An open question (existing for numerical analysts either at The MathWorks or elsewhere) that still needs a definitive answer pertains to the possible universal validity of an alternate approach to direct calculation of the pseudo-inverse matrix that is NOT based on invoking the Singular Value decomposition (SVD). A flow diagram of this alternate approach appears in: Kalman, R. E., Englar, T. S., "A User's Manual for the Automatic Synthesis Program (Program C)," NASA Contract Rep. NASA CR-475, June, 1966. A French researcher vouches for its validity in: Proceedings of the International Conference on Signal Processing Applications & Technology, Boston, MA, 7-10 Oct. 1996. The only limitation identified by this French researcher was that this alternative algorithm is not amenable to parallel implementations as a Systolic Array nor as a Cordic Algorithm; while SVD-based Pseudo-inverse calculation is amenable to such.
Thomas H. Kerr III replied on : 21 of 21
The algorithm discussed immediately above and mentioned there to be by French researchers appeared in O. Caspary and P. Nus, "Implementation of the Greville algorithm on a Motorola DSP96002 Application to Least-Squares problems," The Proceedings of the 7th International Conference on Signal Processing Applications & Technology (ICSPAT), Boston, MA, USA, pp. 142-145, 7-10 Oct. 1996. (It's Table 2 offers a short MatLab implementation of the Greville algorithm that is summarized as a flow chart in their Table 1, both Tables appearing on page 145.)

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