Why do smart bracelets always overestimate the distance you run?

Have you ever had this experience: on a 400-meter track, not long after you finish two laps, the pedometer app or smart bracelet on your phone reminds you, "Complete 1 kilometer," even though you are still some distance away from the halfway point of the third lap.

Is it a miscalculation? Or is the manufacturer of the smart bracelet trying to please you?

Neither. The reason your smart tracker always overestimates your running distance is the method used by GPS to calculate distance. Yes, this is a very strange story.

GPS calculates distance by collecting a series of coordinates along the entire route, then calculating the distance between each adjacent coordinate, and finally adding up the length of each segment to get the complete distance.

The calculation method is simple and intuitive, but why does it always appear inaccurate? You may analyze that most routes in reality are not straight lines, and GPS calculates the straight-line distance between every two coordinates and finally adds them up to get the approximate distance of the entire route. But if this is the case, the distance calculated by GPS should be smaller than the actual distance, so why is it just the opposite in reality?

By the way, GPS will have errors when collecting coordinates. Each coordinate point on the entire route may deviate from the actual route. Although the current GPS accuracy is very high, there is an offset between every two points, which will also affect the final result. But if the coordinate points are offset, is it possible that the distance will be shortened? If the offset is random, then the probability that the distance finally counted by GPS is greater or less than the actual distance is the same?

Despite your careful consideration, you are still wrong. Recently, researchers from the University of Austria, Delft University of Technology (Netherlands) and the independent research institute Salzburg Forschungsgesellschaft conducted a series of measurements and found that regardless of the distribution of the error, the distance between two points measured by GPS is always greater than the actual distance, unless the error value between the two points is exactly the same.

This is because the straight line between two points is the shortest. Only when the positions of the two points are simultaneously offset along this straight line, the distance measured by GPS will be less than the actual distance. However, in fact, according to the researchers' measurements, this situation rarely occurs. Since the total distance is the sum of the distances between each two points, the data measured by GPS is always greater than the actual distance.

The researchers also created a formula to calculate how much the distance measured by GPS is offset (OED, Over Estimate of Distance):

Among them, d0 is the actual distance, var is the variance of the GPS offset value, and C is the autocovariance between the offset values. The final calculated result is always a positive number, that is, the data measured by GPS is always greater than the actual distance.

In addition to theoretical calculations, the researchers also conducted experiments. They found a 10-meter square site, marked it every 1 meter, and the surveyors walked around the site and read the GPS value at each marked point.

They found that the actual distance was 1 meter to 5 meters, while the GPS measured data was 1.2 meters to 5.6 meters, with an error of between 12% and 20%.

So, next time your wristband tells you that you have run 5 kilometers, don't believe it. However, this is not a big problem for you, and it can also satisfy your vanity. However, professional athletes are sometimes distressed by this because GPS equipment always overestimates their status, which is not good for scientific training.

Is there a way to solve this problem? This may involve more professional issues. According to the researchers' proposal, in simple terms, it is to change the GPS measurement method and use speed multiplied by time to calculate distance. This data is more accurate, and the error is random, so the measured distance will not always be greater than the actual distance.

As a winner of Toutiao's Qingyun Plan and Baijiahao's Bai+ Plan, the 2019 Baidu Digital Author of the Year, the Baijiahao's Most Popular Author in the Technology Field, the 2019 Sogou Technology and Culture Author, and the 2021 Baijiahao Quarterly Influential Creator, he has won many awards, including the 2013 Sohu Best Industry Media Person, the 2015 China New Media Entrepreneurship Competition Beijing Third Place, the 2015 Guangmang Experience Award, the 2015 China New Media Entrepreneurship Competition Finals Third Place, and the 2018 Baidu Dynamic Annual Powerful Celebrity.