How to correct for random measurement error?

[moonman239]

I am building an iPhone app where the iPhone is just going to sit on my desk measuring the distance to Earth's core. I will build a calibration function into my app to reduce the variation in the estimate. How, then, should I go about calibrating it?

 

[Filip Larsen]

I did not know the iPhone came with a device to measure the distance to the core of the Earth - I'm impressed :tongue:

Seriously though, if you are "measuring" the distance by reading off the position of the GPS on the phone and you know (or measure) that the phone is not moving you should be able to get a more precise position by simply taking the average position over a long time.

Note however, that modern GPS receivers already do a heck of a job filtering the raw GPS position to give you the best possible position filtered towards a normal kinematic model so you may have to average for a along time (many hours or perhaps even days) before you can expect to see a significant improvement.

Also note, that not moving your GPS receiver mean that some systematic errors in the position (like multipath) will not average out leaving you with a precise but inaccurate position. To get a more accurate position in this case you could make the precise long time averaging measurement in a place that has clear sight of the sky and away from tall buildings.

Frankly, if it were me making an app, I'd be satisfied with the usual 5-10 meter precision delivered by the GPS receiver. In addition to position you may also have access to a measure for how precise the current position is which you can then transform into how precise you can know the distance to the center of the Earth so you can display to your users something like "Distance to core: 6378137 ± 9 meter".

 

[Stephen Tashi]

I'm curious if the GPS 3D coordinates for a location assume a particular geometric model for the Earth (like WGS84).

"Distance to the core" , I assume means distance to the "center of the earth". Or does it mean "distance to the edge of the core"? If it mean that, you would need a model for surface of the core.

 

[moonman239]

I mean distance to the center of Earth. It's certainly doable, the iPhone has a built-in accelerometer (and gyroscope, so I could probably figure out a way to account for sudden movements).

 

[blue_raver22]

There are a few steps you can take to calibrate your iPhone app and reduce random measurement error in your distance measurements to Earth's core.

1. Use a reference object: The most accurate way to calibrate your app would be to use a known distance as a reference object. This could be a ruler, tape measure, or any other object with a known length. Place the reference object at a known distance from your iPhone and use the app to measure the distance. This will allow you to compare the app's measurement to the actual distance and make adjustments accordingly.

2. Take multiple measurements: To account for any variability in your measurements, it is important to take multiple measurements and calculate an average. This will help reduce any random measurement error and provide a more accurate estimate of the distance to Earth's core.

3. Consider environmental factors: The environment in which you are taking measurements can also affect the accuracy of your app. Factors such as temperature, humidity, and electromagnetic interference can impact the performance of your iPhone's sensors. Make sure to take these factors into consideration and try to minimize their effects during calibration.

4. Use statistical analysis: After taking multiple measurements, you can use statistical analysis to identify and correct for any outliers or inconsistencies in your data. This will help improve the accuracy of your measurements and reduce random measurement error.

5. Regularly update the calibration: It is important to regularly update the calibration of your app as environmental conditions and other factors may change over time. This will ensure that your measurements remain accurate and reliable.

In summary, to correct for random measurement error in your iPhone app, it is important to use a reference object, take multiple measurements, consider environmental factors, use statistical analysis, and regularly update the calibration. By following these steps, you can improve the accuracy and reliability of your distance measurements to Earth's core.