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I have three sets of data, measured by three different devices: A,B and C of air balloon whose fall is influenced by wind and each data sheet looks like;

A:

Longitude    Latitude    Altitude    Weight    Rotation(about main axis)   Time
    ...       ...           ...       ...       ...                         ...

B:

Longitude    Latitude    Altitude    Weight    Rotation(about main axis)   Time
    ...       ...           ...       ...       ...                         ...

and similarly for C.

Are there known standard techniques to compute the error in measurement of B and C with respect to A (considered standard)?.

Note that except time, all other parameter can both increase and decrease and longitude/latitude and rotation are only parameters that can be positive and negative.

The problem with regression is that I do not have independent/dependent variables. The method of error analysis I generally approach is calculate $Err_{x},Err_{y},Err_{z}$ and combine them suitably when I have a function explaining something. I do not have a function to propagate error from given quantities.

ADDED

By combining using a suitable function, I mean : computing error of all quantities individually and propagating the error.

I am trying to measure accuracy of the devices B (let's disregard C for now) taking A as standard.

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  • $\begingroup$ originally asked at crossvalidated.SE . It's not purely statistics. So I moved here. $\endgroup$
    – user59756
    Jul 17, 2013 at 10:55

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Your objective is not quite clear, however, as per my understanding, if you're just trying to express the errors of the balloon B and C w.r.t A, you shall have many simple models to your disposal like mean squared error within the estimation period, root mean squared error, white noise standard deviation etc.

If the noise is random, you may try Berkson Error Model Or you may also express the error as a probability distribution.

You may try explaining "combine them suitably when I have a function explaining something"... that will help others explain things better, perhaps.

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  • $\begingroup$ yes. the problem is that I get error in measurement of long,lat,time,weight... When someone asks me how accurate does b measure the data. I should say something like 92%. It would be boring to say something like it calculates longitude by 91% accuracy, latitude by 95% accuracy,... that is my concern. Since I do not have a function to propagate the errors, are there other methods to combine without a function, the errors? $\endgroup$
    – user59756
    Jul 17, 2013 at 12:06
  • $\begingroup$ So, basically you're trying to achieve a competitive fusion of the multiple sensors present in each balloon? You may look into a Bayesian approach of expressing a joint probability density function of all the parameters measured by the multiple sensors. If your sensor model adheres roughly to the Gaussian distribution, this will work well. Take a look at this for the basics: science.uva.nl/~arnoud/education/OOAS/fwi/Chap9.pdf (pg. 9-11, 9-12). $\endgroup$
    – metsburg
    Jul 17, 2013 at 12:24

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