A.Yu. Vostrov1

1 JSC «Concern «Sozvezdie» (Voronezh, Russia)

The known algorithms for determination of spatial orientation for vehicles by signals of the Global Navigation Satellite Systems are based on the phase measurements. In each pairs of antenna elements rigidly connected with antenna array vehicle signal phase difference of visible navigation spacecraft are measured. Then considering the known coordinates of the center for receive antenna array and the navigation spacecraft in the earth-based coordinate system, the known coordinates of antenna components in the coordinate system associated with the vehicle and the known geometric dependences of phase difference from direction of wave falling within the pair of the spaced antennas, overdetermined system of equations is drawn up, which pseudosolution gives directional cosines for axes of the coordinate system associated with the vehicle in the earth-based coordinate system after solving ambiguousness of phase measurements.

This method specifies the severe requirements for design and arrangement of the receive antenna array. Influence on the antenna components together with the direct wave passing from the navigation spacecraft of the same wave reflected by the components of the vehicle design and adjacent antenna components causes distortion of phase run up and errors when determining the angular orientation of the vehicle.

In the article it is suggested to measure mutual energy of signals received by the pair of spaced antennas instead of phase difference for the same signals, and vector complex pattern (dependence of the vector for complex gains for conversion of plane wave field strength complex amplitude in the centre of antenna array into complex amplitudes of strengths at its outputs from direction of plane radio wave arrival) previously calculated or experimentally measured for this antenna array for this vehicle instead of reference dependence of phase differences from direction of undistorted radio wave arrival direction.

An expression of the decisive function depending on the matrix of measured mutual signal energy for the visible navigation spacecraft, vector complex pattern, noise covariance matrix in channels of radio receiver of optic direction cosines to the navigation spacecraft and Euler angles for the vehicle characterizing its orientation in the earth-based coordinate system has been obtained. Maximization of this function in the space of Euler angles within the limits of a priori range of possible values for these angles for this vehicle by the known methods of multiextremal function optimization allows obtaining maximum reasonable evaluation of Euler angles.

A block diagram of a multichannel GNSS radio receiver that allowing to implement the proposed algorithm is given.

A mathematical apparatus allowing forecasting the obtainable accuracy for evaluation of vehicle angular orientation depending on the form of the vector complex pattern, configuration of the visible stellar pattern, object actual angular orientation, field strength amplitude in the area of the antenna array and signal/noise ratio in radio receiving channels has been developed.

Vostrov A.Yu. Maximum likely evaluation of object angular orientation by GNSS signals received by a multichannel radio with an antenna system of arbitrary configuration. Radiotekhnika. 2023. V. 87. № 5. P. 172−183. DOI: https://doi.org/10.18127/j00338486-202305-18 (In Russian)

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