Keywords

1 Introduction

The definition of the geoid is one of the main tasks of geodesy, gravimetry and oceanography. Geoid is a surface of equal gravitational potential on the Earth, containing a point taken as the beginning of the height count. The surface of the geoid coincides with the surface of the World Oceans in the absence of disturbing forces such as wind, ocean currents, tides and conditionally continues under the continents. The height of the geoid is the elevation of the geoid above the ellipsoid.

Currently, the method of active satellite altimetry is used to measure the height of the geoid on the oceans. This method is based on the use of radio altimeters placed on board special spacecraft for geodetic purposes.

Satellite altimetry measurements with improved accuracy and spatial resolution can come closer in accuracy and resolution to the results of marine gravity surveys.

2 Ways to Improve the Accuracy of Altimetry

To date, over 10 national and international satellite altimetry projects have been implemented. Foreign altimetry missions are shown in Table 1.

Table 1 Existing and future foreign altimetry missions
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To improve the spatial resolution of altimetry measurements in the medium term, it is necessary to use:

  • altimeter with one carrier frequency in the Ka-band;

  • aperture radar synthesis method;

  • interferometric method;

  • constellation of spacecraft;

  • method of bistatic GNSS-altimetry.

Satellite altimetry based on active monolocators has high measurement accuracy. However, the following disadvantages of active satellite altimetry can be identified:

  • the onboard radio altimeter consumes more power;

  • only one observation track of the current altitude profile in one pass of the spacecraft is realized.

It is suggested that GNSS-R be used to eliminate the disadvantages of active altimetry. GNSS-R is a remote sensing method of the Earth that uses GNSS signals reflected from the water surface, allowing simultaneous observations at several points in a wide band. This method is promising for mesoscale altimetry. GNSS altimetry advantages:

  • many simultaneously processed altitudes (number of visible GNSS satellites 20–30) (Sahno et al. 2009);

  • low power consumption and low weight of on-board equipment;

  • opportunity to determination of the speed and direction of the near-surface wind (Awange 2018);

  • presence of algorithms for signal processing (Jin and Komjathy 2010).

3 Operating Principle

The GNSS altimetry bistatic system is based on the reception of direct signals from navigation satellites by an antenna directed at the zenith. Signals reflected from the ocean surface in the specular zone are received by an antenna directed to the “nadir”, The operating principle is presented in Fig. 1 (Zavorotny and Voronovich 2000; Gleason et al. 2005). To solve the problem of determining the height to the reflecting surface, it is necessary to determine the difference in the propagation time of the direct and reflected signals, the coordinates and speeds of the receiver and the satellite. The accuracy of determining the height depends on the noise of the equipment, the accuracy of accounting for the ionospheric delay, tropospheric delay, processing algorithms, etc. (Camps et al. 2017; Li et al. 2016).

Fig. 1
figure 1

Principle of operation of bistatic GNSS-R altimeter

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4 Methods of Bistatic GNSS-Altimetry

Today we can talk about four methods:

  1. (1)

    Code method. Code method can be called traditional. Receivers of bistatic altimetry system determine pseudorange and pseudodoppler frequency bias for direct and reflected signals, as well as commercial receivers. The received direct and reflected signals are correlated with a replica of the open code signal generated in the receiver. The method ignores the encrypted signal components, thereby reducing the achievable accuracy of bistatic GNSS altimetry (Zavorotny et al. 2014).

  2. (2)

    Interferometric method. An interference method can be used to improve measurement accuracy (Martín-Neira 1993). It is based on mutual correlation processing of direct and reflected signals from one satellite, received by two antennas with a large gain. Such antennas are used for spatial selection of received signals;

  3. (3)

    Method of SNR. The SNR method analyzes the change in the ratio of the signal (sum of direct and reflected signals) power level to the noise power depending on the satellite elevation angle, the signal wavelength, and the height of the receiving antenna (Löfgren and Haas 2014). Measurements by this method can be implemented using a single antenna to receive direct and reflected GNSS signals. The dependence of the SNR value on the height of the receiving antenna in accordance with (1)

$$ SNR(t)=\mathrm{Acos}\left(\frac{4\pi }{\lambda }h\cos \left(\theta (t)\right)+{\varphi}_o\right), $$
(1)

where θ(t)—elevation angle of the satellite at time t, λ—signal wavelength, h—height to the reflecting surface, φ o—initial phase, A—amplitude of the total signal. Unknown parameters are h, φ o, A.

  1. (4)

    Phase method. Phase measurements have higher accuracy than code measurements, but such measurements are ambiguous due to the uncertainty of the initial integer number of phase shift periods (Semmling et al. 2014). However, if it is necessary to determine the change (increment) in height to the reflecting surface, the phase measurements can be used as more accurate on condition that there are no cycle slips. The change in height from time t j to t i is proportional to the change in the pseudophase difference:

$$ \varDelta h=\frac{\varDelta \varphi \left({t}_i\right)}{2\sin \left(\theta \left({t}_i\right)\right)}-\frac{\varDelta \varphi \left({t}_j\right)}{2\sin \left(\theta \left({t}_j\right)\right)}, $$
(2)

where Δφ—difference between the pseudophases of the direct and reflected signals.It is necessary that the measurements satisfy the Rayleigh criterion reference required. The Rayleigh criterion is fulfilled at low elevation angles of the spacecraft or at a small surface roughness. The accuracy of phase measurements can be centimeters.

5 Experimental Verification of the Methods

Experimental measurements were performed to test bistatic GNSS altimetry methods from a bridge over a reservoir. In the first case, the GNSS altimetry code method was tested. The place of measurements is shown in Fig. 2. The receiving antennas were located at point 1. The results of measurements of the height to the reflecting surface are preceded in Fig. 3. From the measurement results, we can conclude that the optimal elevation angles of satellites for this method are 30°–90°, and the measurement error may be less than 1 m.

Fig. 2
figure 2

Place of experiment p.1—place of measurements with the code method; p.2—place of measurements with the SNR method

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Fig. 3
figure 3

Height measurement results using the code method, true height from reflective surface 19.2 m

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The SNR method was tested in measurements at p. 2, the real and measured height of which to the reflecting surface was 17.1 m, Fig. 4. Such a noticeable difference between the heights of p.1 and p.2 is associated with the difference in the height of the bridge and different levels of the reservoir’s water in different seasons in which measurements were taken.

Fig. 4
figure 4

Results of height measurements using the method of SNR (blue—L1, green—L2)

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An anechoic shielded chamber was chosen for testing the phase method. The measurement scheme is shown in Fig. 5. Providing the necessary roughness of the reflecting surface and the necessary elevation angles of the satellite is not always a feasible task for field measurements.

Fig. 5
figure 5

The scheme of the experiment in an anechoic chamber

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Semi-natural modeling using a GNSS simulator in anechoic chamber conditions allows (Frolov et al. 2017):

  • to minimize reflections of radio signals from obscuring objects;

  • to form a spatial navigation field of GNSS signals;

  • to change the signal power level;

  • perform measurements both on the code and phase delay of the signal.

Antennas receiving direct and reflected signals were located on a mast with a variable height. GNSS satellites signals were simulated by a simulator manufactured by Navis. The results of measuring the difference between the pseudophases of the direct and reflected signals with a decrease and a further increase in mast height are shown in Fig. 6. The standard deviation of measurements was no more than 0.2 cm.

Fig. 6
figure 6

The scheme of the experiment in an anechoic chamber

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The phase altimetry measurements with the CYGNSS bistatic GNSS system over two independent passages above Qinghai Lake are shown in (Li et al. 2018). As the water surface of the lake approaches the equipotential surface of gravity, altimetry measurements above the lake can give an independent estimate of the height of the geoid along the track. The measurement data are relative due to an unknown integer number of phases. The measurements obtained after introducing all the necessary corrections were compared with the EGM2008 model along the track. The measurement results well repeat EGM2008, but anomalies of ± 10 cm are distinguished, which are repeated in time for different GNSS satellites.

6 Summary and Conclusions

Thus, the experiments show the consistency known methods of the bistatic GNSS-altimetry. An anechoic chamber and a GNSS signal simulator can be used to simulate the operation of a GNSS altimetry system using any of four known methods. The highest requirements for a GNSS signal simulator are imposed during phase measurements. The accuracy of determining the height can reach less than 0.1 m with space placement of a bistatic GNSS altimeter.