Later in the 70’s Gerald J. Bierman from JPL did a bunch of work on stable factorization algorithms for Kalman filtering. Some of his work is described in
- Thornton, C. L., & Bierman, G. J. (1976). A numerical comparison of discrete Kalman filtering algorithms: An orbit determination case study (No. NASA-CR-148278).
- Bierman, G. J. (1977). Factorization methods for discrete sequential estimation. Academic Press, Inc., New York.
Notably, the routines Gerald Bierman and his brother Keith used in their consultancy company, Factorized Estimation Applications, Inc., were made available via Netlib:
1. a/esl.tgz
for: estimation and smoothing by UDU**T and square root information filter SRIF for Kalman filtering
by: Keith and Gerald Bierman
lang: Fortran
ref: “Factorization Methods for Discrete Sequential Estimation”, Academic Press 1977. Republished by Dover
You can read in one of the Fortran source comments:
C Introduction
C
C The Estimation Subroutine Library (ESL) was originally authored by Gerald J.
C Bierman and Keith H. Bierman. The algorithms largely correspond closely
C to those found the Research Monograph "Factorization Methods for Discrete
C Sequential Estimation" originally published by Academic Press. It has
C been reprinted by Dover with ISBN-10: 0486449815 and ISBN-13: 978-0486449814
C
C Originally published as commerical software by Factorized Estimation
C Applications Inc. it has largely been unavailable to the general public
C for over 20 years. This library is now licensed under the Creative Commons
C Attribution 3.0 Unported License.
C To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/
C or send a letter to Creative Commons, 171 Second Street, Suite 300,
C San Francisco, California, 94105, USA.
C
C As most are aware, Gerald J. Bierman (Ph.D., IEEE Fellow) died suddenly in
C his prime in 1987. This library is re-released in his memory.
C
C Keith H. Bierman 2008
C khbkhb@gmail.com
C Cherry Hills Village, CO
For those interested, I’ve been able to locate the in memoriam for Gerald Jack Bierman. I would also bring to your attention his involvement in the Voyager orbit determination at Jupiter (1983). As he wrote there:
Numerous tests were made throughout the mission to
test estimate consistency and accuracy of the SRIF/SRIS
and U-D algorithm implementations. The navigation
estimation software performed flawlessly. Indeed, the
estimation software performed so well that most of the
time it was taken for granted by the navigation team, and
that is the ultimate compliment.
I would note that Voyager 1 & Voyager 2 remain in contact with Earth. Maybe Bierman’s Fortran factorizations are still doing their job on some NASA computer just like they did 50 years ago?