“How accurate is someone’s location?”… — against what?

When I am reading a question “How accurate is someone’s location?”, my first response would be: “Location against what?…”

Location is always against something

People subconsciously assume that there are some “real coordinates”; that there are some “real distances”:

• GPS coordinates are not “real” — they are just relative to a historically chosen point (Greenwich, for example) measured in historically chosen units (meters, degrees). There is nothing given by nature in such a coordinate system or chosen units — just some history behind it

Photo by Maxim Hopman on Unsplash

• Earth is not a center of the Universe or our “real” coordinates are constantly changing in the world. But they are not necessarily changing against our points of interest, for example, the Earth, desk, car. Thus, coordinates and position is always relative
• Even today, some countries are using completely different system than the metric one, for example. In broader terms, our coordinates may be defined in a way which is not easily translated to another coordinate system or measurement system
• The most common Cartesian coordinate system is not always the most convenient. Take, for example, quaternions in planes or drones; or approaching a charging station by a robot

Renatus Cartesius

Thus, before answering the question about accuracy of somebody’s location, we need to clearly understand against what we plan to localize the somebody or something.

Drastically different coordinate systems and reference points

There could be drastically different localization systems and different reference points for different situations and tasks:

• A ship’s position and direction Greenwich town/meridian
• A charging station against a robot
• View to a person from the robot’s coordinate system
• A space ship against a docking port of another space ship
• A mobile beacon against stationary beacons
• A human against a door
• An eagle against a rabbit

Photo by GeoJango Maps on Unsplash

Inside-out vs. Outside-in approach

We also need to define whether we are localizing the object externally or the object localizes itself against some external references. Outside-in and inside-out makes a huge difference in practical implementation.

Outside-in

• Better when you have multiple similar mobile objects: people or forklifts in a warehouse; swarm robots
• Can be easier to implement and more robust in practice — the system may be complex, per se, but per robot or unit — it is very simple and very inexpensive — with little intelligence (complexity) required on the mobile object. The mobile object may even has no intelligence at all (QR code tracked with external cameras and external intelligence)
• Has a single point of failure — a small error in the external tracking system could fail all mobile objects at once

Inside-out

• Better works for single objects or totally independent objects
• Complex (expensive, bulky, power hungry, etc.), because intelligence of localization must in the mobile object
• Independent from external intelligence and doesn’t suffer from an external point of failure

Better to “measure in elephants”

Imaging autonomous robots. A conclusion whether the robot is driving accurate enough or not depends on its size. For a multi-ton 10x10m industrial robot a few centimeters of positioning inaccuracy could would be very accurate, whereas for a tiny swarm robot of 5x5cm size the same accuracy would result in the robot trying to position itself on the place of another robot, i.e. it would be considered as highly inaccurate.

Therefore in practice, often, it is better to measure the accuracy in relative terms — in sizes of the objects we are localizing — to “measure in elephants” so to say — because many practical aspects of implementation of robots, for example, such as margins, covered distances, allowed errors would depend on the size of the “elephant”, i.e. robots.

Photo by Kaffeebart on Unsplash

Objects are not dots

When somebody wants to localize a person — and a person is pretty fuzzy and flexible object — what exactly are we localizing? Person’s head, nose, eye (left or right?), center of gravity, “his/her center” — what exactly?

Thus, for objects having sizes larger than our accuracy of localization, it is even difficult to give a universal definition of the position of such objects, particularly, when they can change their shapes, like people can do.

Photo by Alexander Redl on Unsplash

This is why, typically, we localize mobile phones, but not the person; mobile beacons, instead of the objects they are placed on, etc.

Conclusions and further thoughts

Location is always relative. Accuracy is practically better to measure in relative terms of the sizes of the objects we deal with as well.