The GNSS standard positioning solution determines the coordinates of the GNSS receiver and the receiver clock offset from measurements of at least four pseudoranges. For GNSS positioning, a direct solution was derived for five and ten observed satellites without linearisation of the observation equations and application of the least squares method. The article presents the basic principles of methods for solving the positioning problem, the formulas and their derivation. The numerical examples with simulated pseudorange data confirm the correct performance of the proposed algorithm. The presented algorithms should be further tested with real measurements in other domains of positioning and navigation as well.
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