Application of the bifurcation theory to the quality analysis of measurement data

One of the essential drawbacks of the classical approach to the classification of measurement errors lies in the theoretically pure division of them into random and systematic ones. The measurement errors are mixed and they cannot exist in the other way. We consider the problem of navigational measurement errors. Let the position of a moving object be fixed by n+l isolines in such a way that they form a simplex of errors oriented in the n-dimensional space. Upon repeating measurements and making appropriate corrections this simplex diminishes but it retains its orientation. After numerous measurements and corrections the situation continues to remain the same until the simplex reaches quite a definite size, then the simplex starts to fluctuate. We consider that the vector of the local systematic error is a vector preventing the simplex from inversions at the interval of two consecutive measurements, and the vector of global systematic error we understand as a vector preventing simplex from inversions within block of measurements. So we can see two different in quality types of simplex behaviour. In other words, different types of simplex behaviour demonstrate different quality of navigation data. The method described gives us an attractive view on measurements errors classification with applied bifurcation theory as of the most advanced and natural methods. Such a classification enables us to extract dangerous systematic errors and as a result to lower the level of navigation disasters