Analysis of 5G Smart Communication Base Station Doppler-Smoothed Pseudorange Single-Point Geodesic Positioning Accuracy

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station [5,6]. However, due to the infuence of the smart terminal chip process and antenna, the observation noise and multipath error during base station positioning are large, resulting in low positioning accuracy, so how to improve the positioning accuracy of smart devices has become a research hotspot in recent years [7,8].
Doppler observation has better observation accuracy and is not easily disturbed by multipath errors [9,10]. Te study [11] analyzed the diference between multipath errors in 5G smart communication base station and geodetic receivers. A study [12] showed that using Doppler combined with pseudorange observation for localization is better than using pseudorange observation alone. Te study [13] investigated the feasibility of Doppler smoothing pseudorange. Te study [14] used Doppler observations for pseudorange smoothing to improve the accuracy and stability of localization. Since the antennas of 5G smart communication base stations are diferent from those of geodetic receivers, 5G smart communication base stations are more likely to track satellite signals, but the signal-to-noise ratio is lower than that of geodetic receivers, and the multipath efect of 5G smart communication base stations is an order of magnitude higher than that of geodetic receivers [15,16]. Tis is one of the main reasons for the poor positioning accuracy of 5G smart communication base stations, and these research works have been done by many scholars and will not be discussed here [17,18].
To address the problem of low positioning accuracy of 5G smart communication base stations, this paper makes full use of the feature that Doppler observations are not afected by multiple paths to carry out research on the application of Doppler observation smoothing pseudorange for smart terminals, carries out research on coarse diference rejection and broad value setting in the process of Doppler smoothing, and preprocesses measurement data according to the analysis results to achieve the purpose of improving positioning accuracy [19,20].

Doppler Positioning Architecture
Te target positioning method of a single satellite is as follows: acquire the coordinates of the satellite's hypostasis; acquire the incoming wave direction angle of the target and the zenith angle from the satellite to the target; establish the frst spherical triangle on the Earth's surface with the hypostasis, the target, and the pole as the vertices; the pole is the South Pole of the Earth or the North Pole of the Earth; determine the coordinates of the target B and the pole N based on the relationship between the sides and angles of the frst spherical triangle. Based on the coordinates of the frst spherical triangle, the coordinates of the substar point A, the incoming wave direction angle, and the sky bottom angle, the position of the target B and the pole N are determined. Based on the position of the target B and the pole N, the coordinates of the target B are determined. When the satellite fies over the target radiation source, the single-satellite positioning process is carried out, and its radius l acceleration changes continuously during the motion. Based on the correspondence between the radial acceleration and the target position, the radial acceleration of the target is measured at several moments, and then combined with the constraint of the target position on the Earth, the coordinates of the radiation source position can be located (see Figure 1). STK (Satellite Tool Kit), or Satellite Simulation Kit, was developed by AGI, USA, to quickly and efectively analyze missions in complex environments such as land, sea, and air, and to support the whole process of space missions, including design, test, launch, operation, and mission. Terefore, it is widely used in the aerospace industry and in science and technology felds. In this paper, we choose the STK version 10 environment and build a motion scenario including a ground radiation source, motion satellite, and on-board receiver with the powerful and realistic analysis capability of STK. Te communication simulation module of STK is used to analyze the reception of ground radiation source signals by the on-board receiver. Te simulation fow of single-star passive positioning is shown in Figure 2.
Positioning based on Doppler information mainly refers to the use of Doppler frequency and Doppler frequency change rate to determine the positioning surface, multiple measurements to obtain multiple positioning surfaces, and intersection position as the target's positioning point. Generally, the target is on Earth's surface or at a relatively low height, and two-dimensional plane analysis is used. As shown in Figure 3.

Coarse Difference Detection and Doppler
Smoothing Algorithm GNSS pseudorange observations contain various errors caused by observation equipment, propagation paths, relativity, satellite ephemeris, etc. Terefore, the single-point positioning results are afected by satellite ephemeris errors and atmospheric refraction errors. Due to the infuence of the 5G smart communication base station itself, the measurement results are not as stable as those of earth-based receivers, and the observations contain large, coarse differences. By using pseudorange observations for real-time dynamic positioning, we can avoid the problems of resolving ambiguity and dealing with circular jumps, and the accuracy of the obtained positioning results can meet the single-solution needs of most navigation users. However, pseudorange observation is susceptible to multipath efects, nonvisual distance, and signal occlusion, which makes dynamic localization using pseudorange in complex scenarios less efective. Due to the efect of the duty cycle, it is difcult for intelligent terminals to obtain ideal carrier phase observations, so Doppler observations can be used to smooth the pseudorange and improve the satellite positioning accuracy of intelligent terminals. When there is no duty cycle limitation, the smoothed pseudorange of carrier phase observation can obtain more reliable satellite positioning results from the smart terminal. In this paper, we detect ephemeris elements containing coarse diferences by calculating quadratic diferences between ephemeris elements, removing the ephemeris elements, and restarting the smoothing calculation.

Journal of Computer Networks and Communications
For the calendar element k, the pseudorange observation equation can be expressed as the following equation: where s is satellite number; c is the speed of light; ρ s k is the pseudorange observation; R s k is true satellite ground distance from the receiver; δt k is the receiver clock diference; δt s k is the satellite clock diference; δρ s k, trop , δρ s k, ion are tropospheric delay error and ionospheric delay error; δρ s k,rel is the relativistic efect; δρ s k,sagnc is the Earth's rotation error; ε s ρ,k is the unmodeled error such as multipath and measurement noise.
Te single diference between epoch k + 1 and epoch k of (1) can eliminate or weaken the efects of tropospheric delay error, ionospheric delay error, relativistic efect, and Earth rotation error. Since the satellite clock is more stable, the single diference between pseudorange ephemeris elements is a smooth curve when no large jump occurs in the receiver clock. Ten, the double diference between the ephemeris is a straight line tending to 0. According to error theory, (an error is an experimental scientifc term that refers to the extent to which the measurement results deviate from the true value. Mathematically, the measured value or other approximate value and the diference between the true value of the error. Te error theory is the study of the error in the experiment of a theory; error theory is the test technology, instrumentation, and engineering experiments and other felds' indispensable and important theoretical basis; it plays an important role in science and production practice.) Tree times, a medium error is selected as the limit diference for coarse diference rejection.
Because of the increased more week-hopping of 5G smart communication base station carrier phase observations, the pseudorange smoothing efect is not good, so this paper uses Doppler smoothing pseudorange, which is not afected by week-hopping and whose algorithm is more   For the calendar element k, the carrier phase observation equation can be expressed as the following equation: where φ s k is the carrier phase observation; λ is the corresponding carrier wavelength; N s is the whole-period ambiguity; ε s φ,k is the unknown carrier phase measurement noise; rest parameters have the same meaning as equation (1).
In the initial epoch, let the initial smoothing pseudorange be equal to initial epoch pseudorange observation, i.e., ρ k � ρ k , then the conventional equation of carrier smoothing pseudorange is in the following equation: where the frst coefcient on the right side of the equation ω k+1 � 1/(K + 1) is usually called the weighted smoothing factor, which is equivalent to the following equation: Combining equations (2)-(4), it can be seen that the use of carrier smoothing pseudorange is independent of wholeperiod ambiguity, and the result obtained from φ k+1 − φ k is a high-precision pseudorange change rate, while a high-precision pseudorange change rate can be directly obtained in the 5G smart communication base station.
According to a white paper published by the European GNSS Agency (GSA), Doppler observations are derived from pseudorange rates of change, and the relationship is given in the following equation: where PsdR denotes the pseudorange variation rate, whose value can be obtained from Google's open GNSS raw data API interface; α is a constant, which can be expressed as α � c/f i ; c is the speed of light; f i is the central frequency of the signal (e.g., L1 � 1575.42e6 Hz); and Doppler shift is the Doppler observation value. Because Doppler observations have better observation accuracy and are not disturbed by multipath errors, the relationship between pseudorange change rate and Doppler observations can be known from equation (5), and pseudorange change rate PsdR is used instead of φ k+1 − φ k for pseudorange smoothing in cell phone Doppler smoothing pseudorange, which can be expressed as the following equation:

Results
Due to the high power consumption of GNSS modules in long-term continuous operation, 5G smart communication base station manufacturers have introduced a "duty cycle" mechanism within the base station to ensure the low power consumption of the GNSS module, which causes discontinuous carrier phase tracking, resulting in circular jumps in the phase observations of the front and rear ephemeris. Te base station can turn on the option to force full tracking of GNSS measurements to eliminate the efect of the "duty cycle." Table 1 shows the felds of raw observations available for 5G smart communication base stations. Before pseudorange smoothing, data are frst preprocessed to detect jumps between Doppler and pseudorange observations by making a primary diference between observed Doppler and pseudorange values and then a second diference between epochs to determine a reasonable reading value. Table 2 shows an error in the double-diference value of an observable satellite.
From Table 2, we can see that the Doppler observation data are relatively stable, and the double diference can refect that some satellites contain coarse diferences while the pseudorange observation data vary more through the double diference, so it is easy to fnd the coarse diferences through the double diference and eliminate them. Obviously, G11 and G32 are normal observations because the observation epoch of the G11 satellite is relatively small, so satellite 32 is selected as a reference, and 0.9 Hz (3 times the medium error) is set as the reading value of the Doppler double diference and 15 m (3 times the medium error) is set as the ranking value of the pseudorange double diference.
Te satellites G11, G32, G22, and G23 are selected for detailed analysis, where G11 and G32 are normal observations without jump, and the single and double diferences of the observed satellite Doppler and pseudorange observations are observed and calculated by epoch elements, and the comparison results are shown in Figure 4. Figure 4 shows single and double diferences between Doppler and pseudorange observations of the G11 satellite, calendar element by calendar element. It can be seen that Doppler observations contain small jumps, while pseudorange observations do not have jumps. 99.5% of the absolute values of single diferences between Doppler observations are within 2 Hz, and 985% of the absolute values of double diferences between ephemerides are within 1 Hz. Te single diference between calendar elements of the pseudorange observation value varied smoothly, and the absolute value of the double diference between calendar elements did not exceed 15 m. Figure 4 refects variation rate of Doppler and pseudorange variation when a 5G smart communication base station tracks satellites normally, which provides data support for setting coarse diference rejection broad value. Figure 5 shows single and double diferences between Doppler and pseudorange observations of the G32 satellite, calendar element by calendar element. It can be seen that Doppler observations contain small jumps, while pseudorange observations do not have jumps. 99.9% of the absolute values of single diferences between Doppler observations and double diferences between ephemerides are within 2 Hz, and 98.6% of the absolute values of double diferences between ephemerides are within 1 Hz. Te single diference between the ephemerides of pseudorange observations   varied smoothly, and the absolute value of the double difference between the ephemerides did not exceed 25 m. Figure 6 shows single and double diferences between Doppler and pseudorange observations of the G22 satellite, calendar element by calendar element. It can be seen that there is no jump in Doppler values; 99.9% of the absolute values of single diferences between Doppler values are within 2 Hz, and most of the absolute values of double diferences between ephemerides are within 1 Hz. For most of the pseudorange observations, the single diference between ephemerides varied smoothly, but there were frequent jumps between 1000 and 3000 ephemerides, and the absolute value of the double diference between ephemerides exceeded 200 m, which was larger than the broad value. Figure 7 shows single and double diferences between Doppler and pseudorange observations of the G23 satellite on an ephemeris-by-ephemeris basis. It can be seen that there are seven Doppler single diferences greater than 2 Hz between 7000 and 11000 epochs and many double diferences greater than 2 Hz between 10 000 and 11 000 epochs, while pseudorange observations have a large coarse diference of 300 km jumps between 8000 and 9000 epochs.
Te GPS L1 single-frequency data were smoothed with a satellite cut-of altitude angle of 15°and a signal-to-noise ratio reading of 30 dB-Hz, and smoothing windows of 50, 100, 120, and no smoothing were selected for comparison. After the test, accuracy was signifcantly improved, and the test results are shown in Table 3.
As can be seen from Table 3, RMS values of smoothed single-point localization results become smaller in all directions, and the accuracy of smoothed window 100 improves by 11.0% in the E direction, 10.0% in the N direction, and 4.0% in the U direction over smoothed window 50 results; the accuracy of smoothed window 100 improves by 67.9% in the E direction, 64.8% in the N direction, and 65.5% in the U direction over unsmoothed results. Although the solution accuracy of smoothed window 120 is improved over that of smoothed window 100, improvement is limited.
As can be seen from Table 4, pseudorange observations contain coarse errors when data are not preprocessed, which leads to no results in data solution, and after star picking, the data solution rate reaches 100%, which verifes the necessity of coarse error removal before smoothing pseudorange. In summary, it is especially important to remove the Doppler jump and deal with the pseudorange observation jump before Doppler smoothing pseudorange, and Doppler jump and the pseudorange jump are not related, so they should be handled separately in coarse error rejection. If the wrong value is introduced, it will afect smoothed pseudorange observations and continue to afect subsequent localization results on an epoch-by-epoch basis. Based on the abovementioned analysis, 0.9 Hz is selected as the reading value for the double diference between Doppler ephemeris elements, and 15 m is selected as the reading value for the double diference between pseudorange ephemeris elements.

Conclusion
Tis paper frst introduces the principle of GNSS pseudorange single-point positioning, then introduces carrier phase smoothing pseudorange and Doppler smoothing pseudorange according to the poor quality of smartphone pseudorange observations, and compares and analyzes the three strategies of pseudorange single-point positioning, pseudorange single-point positioning after carrier phase smoothing, and pseudorange single-point positioning after Doppler smoothing. Te experimental results show that Doppler smoothing pseudorange can improve the positioning accuracy. When the smoothing window is 100, the pseudorange single-point localization strategy with carrier phase smoothing improves the localization results by 67.9% in the E direction, 64.8% in the N direction, and 65.5% in the U direction compared with the pseudorange single-point localization strategy without carrier phase smoothing. Te original pseudorange observations with carrier phase and Doppler smoothing can efectively reduce the noise efect and thus improve accuracy.

Data Availability
Te experimental data used to support the fndings of this study are available from the corresponding author upon request.

Conflicts of Interest
Te authors declare that they have no conficts of interest.