The Mathematics Behind GPS: Dr Gladys West

Dr Gladys West is a pioneer in the use of complex mathematics and efficient programming to generate accurate, repeatable and global models of the Earth’s geoid that were eventually incorporated into the mapping functions of the Global Positioning System (GPS). This work required her to process early satellite data and use complex algorithms to account for variations in gravitational, tidal, and other forces that distort Earth's shape.

In this episode of Create the Future, we speak with Dr West about the methods she employed to calculate an accurate geodetic earth model using a room-sized computer. We discuss her early career, hear what it meant to be awarded the Royal Academy of Engineering’s Prince Philip Medal in 2021, touch on her continued passion for education, and ask whether she uses GPS today.

To hear more about the engineering behind the Global Positioning System, check out our episode with the winners of the 2019 Queen Elizabeth Prize for Engineering.

About the guest

Now aged 90, Dr West was born in Dinwiddie County, Virginia, and started her career as a maths and science teacher after graduating from Virginia State University in 1952. Four years later she was hired to work at the Naval Proving Ground in Dahlgren, Virginia, (now called the Naval Surface Warfare Center), where she was the second black woman ever hired and one of only four black employees. West was a programmer in the Naval Surface Warfare Center Dahlgren Division for large-scale computers and a project manager for data-processing systems used in the analysis of satellite data.

In the early 1960s, she participated in an award-winning astronomical study that proved the regularity of Pluto’s motion relative to Neptune. Subsequently, Dr West began to analyse data from satellites, putting together altimeter models of the Earth's shape. She became project manager for the Seasat radar altimetry project, one of the first satellites that could remotely sense oceans. Dr West introduced innovations, cutting her team's processing time in half, and was recommended for a commendation in 1979.

From the mid-1970s through to the 1980s, Dr West designed, developed, tested and then used computer programmes to deliver increasingly precise calculations to model the shape of the Earth – an ellipsoid with irregularities, known as the geoid. Generating an extremely accurate model required her to employ complex algorithms to account for variations in gravitational, tidal, and other forces that distort Earth's shape. Her data ultimately became an important enabler for the Global Positioning System (GPS).

In 1986, Dr West published Data Processing System Specifications for the Geosat Satellite Radar Altimeter, a 51-page technical report from The Naval Surface Weapons Center. The guide was published to explain how to increase the accuracy of the estimation of geoid heights and vertical deflection, important components of satellite geodesy. This was achieved by processing the data created from the radio altimeter on the Geosat satellite, which went into orbit on March 12, 1984.

Dr West worked at Dahlgren for 42 years, retiring in 1998. After retiring, she completed a PhD in Public Administration.

Episode highlights

• “To tell you the truth, we didn't know anything about computers. It was a long climb to get on board. But it was exciting. Everybody else was excited about all the capability that we had. You didn't take any chances of not doing your best to be able to programme in code.”
• “I was proud of receiving the Prince Philip Medal because it was in another country. And I got to talk to Princess Anne when she awarded it to me.”
• “We were using computers that occupied rooms. It was a big operation because it was new. Now I guess we have a little computer on out wrist that can do as much as those big computers did.”
• “Just understanding that math can apply to other thoughts, other discoveries, and other ways of looking at things. It is a powerful method of doing things. Math is, I feel, always so clean, logical and precise. There are a lot of advantages to using math.”
• “I keep changing my mind about the highlight of my career. I would think first, when I got that college degree and I knew that I was ready. Nowadays, I'm just thankful for being able to see the recognition that other people are giving me and how much I have affected other people. To me, that is a big thing.”
• “I do use GPS. I don't drive as much now as I did before, so I mainly use it when my husband or son-in-law takes me somewhere. But I’ve always said that I like see more and know more than where the GPS tells me to ‘turn right, turn left, in two miles turn this and that’.”
• “With computers today there's so much that I can't even comprehend. They are just so powerful. People understand so much, things are so fast, and everybody's getting used to it becoming a way of life. It's so much I can hardly imagine.”

Image: NASA