Bearing Error and the Central Limit Theorem
Abstract
Bearings are frequently computed as the average of the number of readings. Most of fixing theory assumes that the bearing error is normally distributed. Averages are usually much closer to bearing normally distributed than individual readings. The amount closer to normally depends on the amount of independence between readings and on the number of readings: (1) If the readings are 100% dependent, then they are the same and hence the distribution of the average is no closer to normality than the original readings; If the readings are 100% independent, then the convergence to normality is very fast as is shown in the accompanying examples. The exact speed of convergence depends on the shape of the original curve but not very much (This convergence is predicted by the Central Limit Theorem but the Central Limit Theorem does not address speed of convergence, hence the graphs provided here). As a first approximation one may assume that some of the sources of error would be dependent and some independent. The independent error of the readings would get smaller and closer to normality as the number of readings being averaged increases. The dependent error of the readings would remain. The amount of the error that is independent could be judged using the standard deviation of the readings in comparison with the angular standard deviation. (Note: In order to compare the two, the standard deviation of the readings would need to be averaged). The method used to analyze the speed of convergence is demonstrated.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 24, 1987
- Accession Number
- ADA197837
Entities
Organizations
- California Institute of Technology