The true value of inertial navigation: an interview with Brad Parkinson

The U.S. Secretary of Defense once predicted that eventually navigation would be based on inertial devices that were installed at the factory, and then always knew where they were. A recently published study reported steps in this direction. However, according to navigation expert Brad Parkinson, the prospects are not as bright as some may think.

RNT Foundation President Dana A. Howard recently discussed the issue with him.

Howard: Dr. Parkinson, you are well known for your contributions as the chief architect of the global positioning system. But you’re not just casually familiar with inertial systems, are you?

Parkinson’s: I do. Long before I got into radio navigation, I was the chief analyst of all the U.S. Air Force on inertial navigation systems testing. I received my master’s degree from Doc Draper’s Inertial Laboratory at MIT in 1961. I am a major supporter and advocate of inertial systems. I also deeply understand their limitations.

Howard: Have you followed the latest media reports about the achievements of inertial systems?

Parkinson’s: I enjoy reading about these advances in physical devices. At the same time, I’m a little impatient with articles in the media that don’t appreciate the differences between creating a device that measures specific power (or feels rotation) and a working inertial navigation system.

Howard: What are some of the inherent limitations of these systems?

Parkinson’s: I find it interesting that some articles suggest that they can replace GPS and other GNSS. Inertial navigation system can not ensure its exact position (say, better than 10 meters) after long periods (from hours to days). In fact, achieving an accuracy of better than 200 meters in a few hours will be very difficult in a moving vehicle.

Today, farmers demand even more accuracy from GPS. They typically use GPS for operations in rows accurate to a few inches. The economic value is indirectly measured by the purchase of such equipment by farmers – the agricultural market for GPS equipment is much more than a billion dollars a year. Therefore, a total GPS replacement should provide centimeter accuracy.

Howard: So what is it about inertial systems that prevents them from becoming standalone GPS replacements?

Parkinson’s: There are some very simple and fundamental reasons why inertial positioning systems cannot count on such a possibility.
First, force sensors are not accelerometers because they cannot sense gravity. To find the acceleration, a gravity vector must be added to their outputs. But gravity, or the force g, varies greatly at the micro-g levels, and inaccuracies are fed to the double integration that creates the position. Errors increase as time or time is squared and, without external reset, are essentially unlimited. The physical devices described in some of these articles are certainly devices that Doc Draper called “specific force sensors”.

What we loosely call the force g, or simply g, is actually a backlash to the maintenance of stationarity on Earth. G is defined as the centrifugal force caused by the rotation of the Earth, which varies greatly depending on the latitude – the radius of the carousel, called the Earth. Mountains and abysses affect local g. In addition, it is a vector quantity: its direction can change locally for many angular seconds. In other words, down usually does not point to the center of the Earth. Gravity gradiometers can bring limited help, but they are very large and not designed for dynamic conditions.

In a nutshell, acceleration estimation requires calculating and adding gravity to a three-dimensional specific gravity sensor.

Second, to use these devices for advanced navigation, coordinate frames must be defined and stable to milli-arc seconds. All instruments must have input axes and calibrated to appropriate levels of cross-axial sensitivity. Typically, this problem is ignored in many laboratory projects.

Third, for inertial navigation sensors to work, they need to know exactly their original position. Any errors in the initial velocity or position will increase with time.

Fourth, the vertical position axis is inherently unstable and diverges exponentially.
Physicists have been fascinated by instruments that can use atoms to sense a certain force and rotation. Despite scientific interest, even ideally they cannot overcome these challenges.

Howard: But inertial systems still play a role in navigation, right? How good are they and what are the applications?

Parkinson’s: I suspect that the best inertial systems today (which are in nuclear submarines) can maintain an accuracy of about 0.1 nautical miles or about 200 meters in a matter of days. I’m sure the real figure is secret. These systems are very large, expensive and complex. They rely on very low acceleration and are periodically reset by GPS. In addition, they probably use gravitational gradiometry to calculate local variations in first-order gravity. They do not calculate the vertical position, but use the water density and knowledge of the local geoid to keep the vertical axis stable.

An aircraft with inertia can to some extent keep vertical dimensional errors limited, provided it has knowledge from other locations about the settings of local sea level barometers and taking adiabatic pressure changes.

I strongly support the marriage of inertial / GPS / directional antennas for users who want to guarantee PNT. Aviation is a good option for this. Inexpensive inertial components (so-called microelectromechanical systems, or MEMS) can improve the jamming resistance of a GPS receiver by 15 dB or more. This step alone can reduce the effective failure area of ​​the line-of-sight muffler by more than 95%.

Howard: Thus, inertia may be a good part of the solution, but is not necessarily the whole solution.

Parkinson’s: That’s right. Although some media outlets may publish to attract readers.