Научный вестник МГТУ ГА (May 2017)
LAW DISTRIBUTION APPROXIMATION ON EIGENSTATE ERRORS OF ADS-B BASED ON CUMULANT ANALYSIS OF ADS-B-RAD SYSTEM DATA DISPARITY
Abstract
The article deals with a new approximation method for enhanced accuracy measurement system errors distribution. The method is based upon the mistie analysis of this system and a more robust design data. The method is considered on the example of comparison of Automatic Dependent Surveillance - Broadcast (ADS-B) with ground radar warning system used at present. The peculiarity of the considered problem is that the target parameter (aircraft swerve) value may drastically change in the scale of both measurement systems errors during observation. That is why it is impossible to determine the position of the aircraft by repeatedly observing it with ground radar warning system. It is only possible to compare the systems’ one-shot measurements, which are called errors here. The article considers that the distribution of robust measurement system errors probability density (the system that has been continuously in operation) is known, the histogram of errors is given and it is needed to obtain an asymptotic estimate of errors occurrence distribution for a new improved measurement system.This approach is based on cumulant analysis of measurement systems error distribution functions. The approach allows us to carry out the reduction of corresponding infinite series properly. The author shows that due to measurement systems independency, their errors distribution cumulants are connected by a simple ratio, which allow to calculate the values easily. To reconstruct distribution initial form one should use Edgeworth’s asymptotic series, where a normal distribution derivative is used as a basis function. The latter is proportional to Hermitian polynomial, thus the series can be considered as an orthogonal decomposition.The author reveals the results of coordinate error component distribution calculation; the error is measured when the normal line lies towards aircraft path, using error statistics experimental information obtained in ”RI of Aeronavigation” Branch of FSUE SRI of Civil Aviation.
