## Question

Do any of the position calculation applications ouput an accuracy for each epoch? If not, does anyone know of another way?

-- DominicFuller - 02 Apr 2009 If you answer a question - or have a question you asked answered by someone - please remember to edit the page and set the status to answered. The status is in a drop-down list below the edit box.

The problem in computing accuracy is that it is dependent on a variety of factors that may not be available to the solution process. For example, how noisy is your range data? How much multipath is present? What is the accuracy of the ephemeris data? How good is your tropospheric correction? Am I tracking a real SV or a spoofed signal? Many receivers/position solutions will show you a PDOP and a FOM. These are just numbers. The smaller they are typically the better your solution. However they are not a quantitative measure of accuracy. When we want to measure accuracy, we usually compare the computed position to an outside measure of truth. This could be a surveyed benchmark or a differential solution. There are indirect ways of doing the same measurement multiple times on multiple days and comparing the consistency of the results. Does this help?

-- RickMach - 17 Apr 2009

Hi Dominic!

As Rick explained, the issue of providing an error figure is very complex (or, at least, to provide an error figure that makes sense).

An approach to achieve a reasonable value is to use an observable model that not only estimates the biases affecting the observations (tropospheric and ionospheric biases, ephemeris errors, etc.), but also provides standard deviation estimates (sigmas) for each of those modeled biases.

Those sigmas may be combined and used to assign a "weight" to each of the equations build from the observations. Such weights usually are the inverse of the variance (1/(sigma*sigma)) and make up a "weight matrix" (the inverse of the covariance matrix). Please take a look at class "MOPSWeight" for an example of this procedure.

Such weights matrix, when used in the solver (WMS, Kalman filter, etc.), will aid to get a better solution, but will also allow to compute a covariance matrix of the solution.

The diagonal of this covariance matrix contains the variances associated with each of the estimated parameters (position, clock, etc.), and those variances are called the "formal errors".

Be aware, however, that formal errors are NOT the real errors. Formal errors are a good approximation only if the variances computed during the modeling phase are right, and no additional problems (like some of the ones pointed out by Rick) happened.

Best regards,

Dago

-- DagobertoSalazar - 11 Sep 2009 No such template def TMPL:DEF{PROMPT:supportquery}