I.A. Tsikin - Dr. Sc. (Eng.), Professor, Department «Radio Engineering and Telecommunication Systems», Peter The Great St.Petersburg Polytechnic University E-mail: tsikin@mail.spbstu.ru E.A. Shcherbinina - Assistant, Department «Radio Engineering and Telecommunication Systems», Peter The Great St.Petersburg Polytechnic University E-mail: lizspbstyle@gmail.com

In the attitude determination based on global navigation satellite systems there are two approaches of obtaining maximum likelihood estimations. The first one consists in the likelihood function construction based on navigation signals directly on antenna array elements. In the second approach the likelihood function is formed on the basis of signals phase difference measurements on array elements pairs from each of the navigation spacecraft. On the other hand, there is the third approach, which is based on R function maximization. The third one is more implementation simple and more accurate in working range of signal to noise ratio in comparison with the second approach. It is interesting to carry out the comparative analysis of angles estimations accuracy for maximum likelihood approach provid-ing a potential attitude parameters accuracy and approach based on R function. The paper deals with the likelihood function formation based on the statistics of analyzed processes multidimensional samples, when GPS signals are being received. The maximization of obtained function for the unknown parameters vector leads to the desired value of angles estimations by maximum likelihood. The third approach described in this paper is based on the consideration of the attitude determination problem as inverse to direction finding problem and is to maximize the R function representing a trigonometric functions combination on the distinctions between the measured and the reference phase differences. The maximization of the likelihood function and R function is accomplished using reference phase differences method. These reference phase differences for each navigation spacecraft represent the values of phase differences between signals on array elements, which are calculated before or during measurement procedure for specific navigation spacecraft location and any possible navigation object spatial orientation. The comparative analysis of two algorithms is carried out by simulation in Matlab. The simulated signals from different navigation spacecraft correspond to the real GPS constellation. The antenna array with small number of elements which is necessary for a unique solution attitude determination problem and typical, for example, for small unmanned aerial vehicles is considered in the paper. The angles estimations standard deviations obtained using the first and third approaches for different signal to noise ratio are investigated. Analysis of these standard deviations shows no appreciable difference in the accuracy within the work area of the signal to noise ratio values.

 

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