Measurement Techniques, Vol. 45, No. 12, 2002

APPARATUS AND METHOD FOR CHECKING THE RECEPTION INDICATORS OF GLOBAL NAVIGATIONAL SATELLITE SYSTEMS

V. I. Kokorin and Yu. L. Fateev

UDC 629.783

Methods and equipment are described for measuring the parameters of radio-navigational apparatus and for checking it at different stages of its development and production. Several components in the error of measuring the coordinates and the spatial orientation of an object are considered. Key words: radio-navigational apparatus, satellite systems, measurement errors, spatial orientation of an object.

The range of application of satellite radio-navigational systems is constantly increasing. Such systems provide high accuracy in measuring the coordinates and velocity of an object and also form a reference frequency and time marker tied to the State standard of time and frequency. Using phase methods for measuring the information parameters, the apparatus makes it possible to determine the spatial orientation of objects and also the coordinates of an object relative to a reference station with decimetric and centimetric accuracy. There is particular experience at the Scientific-Research Institute of Radio Engineering of the Krasnoyarsk State Technical University and at the FGUP Radiosvyaz’ Scientific Production Enterprise in creating and checking phase radio-navigational apparatus [1]. In 1998, a test sample of an MRK-11 user navigational apparatus was developed providing reception of signals to three spatially separated antennas simultaneously of up to nine navigational spacecraft. The MRK-11 navigational apparatus determines the geophysical coordinates and also the spatial orientation of an object. Since 1998, the FGUP Radiosvyaz’ Scientific Production Enterprise has undertaken series production of MRK-15 and MRK-17 navigational devices which are intended for use in systems for controlling ground-based mobile objects. At the present stage of the use of radio-navigational systems, demands are increasing as regards the accuracy and reliability of determining the parameters of motion of objects. An urgent problem is that of investigating the instrumental errors when measuring radio-navigational parameters [2]. The methods of checking radio-navigational systems which are used at present in practice are based on the deployment of user navigational apparatus at points having known coordinates. A disadvantage of these methods is their considerable unwieldiness, including that associated with the difficulty of geodesically locating reference points having a given accuracy (of the order of 1 m) and with the low accuracy of measuring the instrumental errors of products resulting from the fact that a multiplicity of parameters which are not related to the navigational apparatus influence the results of the measurements. These are the influence of the ionosphere and troposphere, the errors of determining the epheremides of navigational spacecraft, etc. Undoubtedly, a resulting measurement error which includes all the components is the principal parameter of the apparatus considered, although under factory conditions there is interest in developing methods which provide for a high accuracy of determining the instrumental error component. In addition, these methods must be simple to implement in practice and must make provision for the possibility of automating the checking process. For the purposes of resolving questions of the metrological assurance of developed and serial production devices, a GLONASS and GPS signal simulator has been created which forms the signal of any navigational spacecraft of the Translated from Izmeritel’naya Tekhnika, No. 12, pp. 6–8, December, 2002. Original article submitted June 13, 2002. 1210

0543-1972/02/4512-1210$27.00 ©2002 Plenum Publishing Corporation

GLONASS and GPS systems, modifies the signal for delay and Doppler frequency shift, adds digital service information to the signal, and forms reference phase shifts in order to carry out and test the regime for determining the spatial orientation. The simulator implements a regime for adjusting phase measurements of the carrier frequency signals of satellites when they are received at the spatially separated antennas of the user navigational apparatus, for the purposes of determining the angular orientation of mobile objects. Provision is made in this regime for the formation of three signals of one and the same navigational spacecraft with a regulated phase shift between the signals. The simulator can be used both for the functional checking of an apparatus during serial production and in order to adjust and improve the signal processing algorithms. Provision is made for the simulator to operate from both internal and external reference oscillators. The simulator software makes it possible to form signals having a dynamically varying phase, delay, and frequency. This makes it possible to adjust the algorithms for measuring the signal parameters and to test apparatus mounted on highly maneuverable objects. The software simultaneously records the results of a measurement of the signal parameters of the navigational apparatus to whose input the simulator is attached and compares them with the true values. The use of a simulator of the signals of navigational satellites makes it possible to measure such apparatus parameters as the error of measuring the radio-navigational parameters, the maximum dynamics of the object, and the dynamic errors of measurements of the radio-navigational parameters. One of the basic metrological parameters of the MRK-11 apparatus is the root-mean-square error of measuring angular position. The error of measuring angular orientation has a number of components, both external and instrumental. The external error components, i.e., those which are not dependent on the apparatus, include: • the noise error of measuring phase shifts; • ionospheric and tropospheric components; • an error caused by reflections of the signals of the navigational spacecraft; • ephemeris errors. The instrumental components of the error of measuring angular orientation are as follows: • phase shift measuring errors caused by the nonidentical nature of the phase characteristics of the antennas resulting in a different deviation of the antenna phase centers depending on the direction of arrival of the signals and consequently an additional error in measuring the path difference. This error component is different for different navigational spacecraft and depends on the direction of the arrival of the signal, and it is therefore not possible to eliminate it by algorithmic methods. This error component can be taken into account by calibrating the antenna platform, i.e., by performing a preliminary plot of the dependence of the error on the direction of arrival of the signal; • measurement error due to differences of the signal delays in the angular measurement channels. It is identical for all navigational spacecraft and can be taken into account by introducing an additional variable into the system of equations. This component can be attributed to the error caused by delay differences in cables; • the measurement error caused by the mutual influence of the measurement channels on each other (the so-called fundamental error). The error caused by the mutual influence of the channels is manifested in the form of a phase–phase error, i.e., its value depends on the phase difference between the antennas. By using a simulator of the signals of a navigational spacecraft one can estimate the following parameters of the angular measurement channels of the MRK-11 device: • the noise component of the error in measuring the phase shift for different levels of input signal. This error component is measured with a constant phase shift between the antennas; • the phase–phase measurement phase shift error. Since the phase shifts are measured with a constant error one can use the simulator to estimate only the relative measurement accuracy, i.e., within the accuracy of a constant value. The following signals are taken from antennas of a user navigational apparatus: S0 = A0cos(ω0t + ϕ0); S1 = A1cos(ω0t + ϕ1), where A0 and A1 are the signal amplitudes, ω0 is the signal frequency; ϕ0 and ϕ1 are the instantaneous signal phases. 1211

Fig. 1. Structure of a phase–phase error.

On account of the mutual influence of the channels, signals from one channel are transferred to the other channels: S0* = S0 +k01S1; S1* = S1 +k10S0, where kij are the mutual influence coefficients of the channels. Let us consider the error caused by the mutual influence in the case of two antennas (see Fig. 1): ∆ϕ 01 = arctan

k01 sin ϕ1 ; 1 + k01 cos ϕ1

∆ϕ10 = arctan

k10 sin ϕ1 ; 1 + k10 cos ϕ1

tan ∆ϕ = tan ( ∆ϕ 01 + ∆ϕ10 ) =

tan ∆ϕ 01 + tan ∆ϕ10 . 1 − tan ∆ϕ 01 tan ∆ϕ10

We show that it can be expanded in the series

∆ϕ 01 = arctan

k2 k3 k01 sin ϕ1 ≈ k01 sin ϕ1 − 01 sin 2ϕ1 + 01 sin 3ϕ1 − ... = 1 + k01 cos ϕ1 2 3

∞

∑

( −1) n +1

n =1

n k01 sin nϕ1 . n

The maximum value of the error is found by taking the derivative of the expression obtained and equating it to zero: ′ 2  k sin ϕ1  k01 cos ϕ1 + k01 ∆ϕ ′01 =  arctan 01 . =  2 1 + k01 cos ϕ1  (1 + k01 cos ϕ1 ) + ( k01 sin ϕ1 )2  Hence cosϕ1 = –k01, ∆ϕ 01 max = arctan

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2 k01 1 − k01 2 1 + k01

.

Fig. 2. Phase–phase error of two channels of the MKR-11 user navigational apparatus.

For k01 << 1,

∆ϕ01max ≈ arctan(k01) ≈ k01.

Similarly, ∆ϕ10max ≈ arctan(k10) ≈ k10. Consequently, we have ∆ϕmax = ∆ϕ01max + ∆ϕ10max ≈ k01 + k10 ≈ k. Thus, the mutual influence coefficient of the channels can be determined in terms of the maximum value of the error when the phase shift varies from 0 to 2π. The following procedure can be proposed for estimating the phase–phase error of measuring a phase shift. A phase shift of the signals in the range 0–360° in steps of 2–10° is established in the simulator. The duration of each measurement is 1–2 min. Readings of the measured phase shift are recorded from the output of the MRK-11. The average values of the measured phase shifts for each measurement are then calculated. The relative error of measuring the phase shift is calculated from the expression ∆ϕi = (ϕi – ϕ0) – ϕ0i, where ϕi is the average value of the measured phase shift for the initial measurement (for zero phase shift of the simulator) and ϕ0i is the value of the established phase shift of the shift simulator for the ith measurement. It is then possible to construct the dependence ∆ϕ(ϕ) and to calculate the mutual influence coefficient of the channels as the half-difference of the maximum and minimum values of this dependence: k = (∆ϕmax – ∆ϕmin)/2. By way of an example, Fig. 2 gives a graph of the phase–phase error of two channels of an MRK-11 user navigational apparatus. The phase–phase error is 3–3.5° which corresponds to a mutual influence coefficient of 25–30 dB. The phase–phase error is reduced to 0.5° for a 40 dB decoupling of the measurement channels. A rotating stand was developed and manufactured in order to provide comprehensive checking of the MRK-11 angular measurement apparatus. This made it possible to simulate the evolution of an object with an antenna system mounted on it in space while providing for a change in the position of the antenna system independently in its heading, roll, and pitch 1213

with an accuracy of better than 1′ [1–3]. The stand is remotely controlled and can be connected to a computer. Survey control of the rotating stand is carried out with an error of 1 m in order to check the accuracy of measuring the coordinates of the object and of its spatial orientation. The accuracy of measuring the angular orientation is determined by measuring the change in the angular position of the antenna system. Measurement of the absolute error of determining the angular orientation is possible by fixing the orientation of the rotating stand with respect to the true meridian. One of the important problems when regulating angle measuring navigational instruments is the fixing of the antenna system to the structural axes of the object, in the present case to the axes of the rotating stand. The fixing error is manifested not only in a constant systematic error of the measurements but also in a mutual influence of the measured angles of pitch and roll. For example, if there is an error of fixing the antenna system along the heading angle, then when the pitch of the object is changed there will be a change not only in the measured value of the pitch but also in that of the roll angle. A similar effect will also be observed when changing the roll angle of the object. In the case of an error of 90° in fixing the heading angle, the pitch and roll angles will change places, i.e., for a change in the pitch of the object there will be a change in the measured roll angle, and vice versa. This effect can be utilized in order to fix the antenna system to the structural axes of the object in the absence of standard instruments for measuring the angular orientation. The process of calibrating the antenna system and fixing it to the structural axes of the objects in the MRK-11 is split into two stages. In the first stage, the parameters of the antenna system are determined by prolonged measurements in particular of the base lengths, the angle between them, and the difference of the delays in the measurement channels. At this stage, provision is made for a preliminary fixing of the antenna system to the structural axes of the object. The measured parameters are recorded in the energy-independent memory of the user navigational apparatus. In the second stage, the accurate fixing of the antenna system to the structural axes of the objects is carried out. It is accomplished during the process of measuring the angular orientation by the method of introducing corrections to the angular position. The correction of the angular orientation does not require prolonged measurements since the parameters of the antenna system itself are known. Thus, the parameters are measured and the navigational apparatus is checked at all stages of its development and production.

REFERENCES 1. 2. 3.

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V. N. Avsievich et al., Giroskopiya i Navigatsiya, No. 4(31) (2000). V. I. Kokorin and Yu. L. Fateev, Proc. Intern. Sci. Tech. Conf. on Satellite Communication and Navigational Systems, Vol. 1 [in Russian], State Technical University, Krasnoyarsk (1997). A. M. Aleshechkin and V. I. Kokorin, Digital Radio Engineering Systems and Instruments [in Russian], Krasnoyarsk (1996), p. 41.