Applying spaced reception to measure geographical coordinates of near-earth spacecraft radiation source

Abstract

Differential distance algorithm is investigated to estimate the position of a near-earth radiation source in three-dimensional space for geographical (Greenwich geocentric) coordinate system. Radiation detectors travel with identical speed in space at 700 km altitude in polar orbits. There were obtained experimental dependences of geographical coordinates estimate accuracy of radiation source on the measuring accuracy of path difference value of the emitted signal for each  pair of receiving stations taking part in measurements, as well as  on the range from the central position to the source. The above named was obtained via simulation modeling of the algorithm under research. Besides, the effect of the estimate accuracy of detectors position and their quantity on the accuracy of radiation source geographical coordinates was evaluated.  It was found out as a result of the analysis of the dependences obtained through experiments that the receiving  channels quantity in measuring emitted signal path differences not only between central and each peripheral positions, but also between the neighboring peripheral receiving positions can be reduced to four that is minimum possible for three-dimensional measurements. The quantity of receiving positions has to be not less than five without additional measurements as with smaller quantity the Newton method used for finding estimates of radiation source geographical coordinates diverges. It also appeared that the mean square error of source coordinates measurement decreases with growth channels quantity without additional measurements of path difference, but when using additional measurements this reduction is not so essential and is practically is away with seven receiving stations. Besides, the mean square error of radiation source coordinates measurement decreases in proportion to growing signal bandwidth that determines measuring accuracy value of path difference and also it also decreases with growing measuring bases to the limit defined by direct visibility of the most remote receiving station and, of course, with shortening distance between a signal source and its receivers. Additional measurements of path between neighboring  peripheral receiving stations are used to identify uncorrelated radiation sources.