Analysis of GPS P(Y) signal power enhancement based on the observations with a semi-codeless receiver

Abstract

The Global Position System (GPS) satellites of Block IIR-M and later versions can turn on the signal power enhancement if needed. In recent years, this power enhancement has been triggered several times when the U.S force was involved in local conflicts, which was observed by the monitoring receivers at International GNSS Service (IGS)/international GNSS Monitoring and Assessment System (iGMAS) stations or the high-gain antennas at monitoring ground stations. The specific power enhancement magnitudes with these two observation methods are different. The observations of L1/L2 P(Y) power with a high-gain antenna are accurate, while the observations at IGS/iGMAS stations contain biases. This paper analyses the reasons for the observation biases with monitoring receivers at IGS/iGMAS stations and proposes a method verifying the accurate relation between the observed carrier-to-noise ratio (C/N₀) data and the real power enhancement magnitudes. When the power enhancement event happens, the observed L1/L2 P(Y) C/N₀ data at IGS/iGMAS stations can be corrected using the model proposed in this paper. In the analysis, this paper concludes that the power of L1P(Y) increases by about 4.3–5.3 dB and the power of L2P(Y) by about 4.6–5.2 dB in power enhancement events, which matches the designed capability of GPS satellites as well. The results are also verified by the data of high-gain antennas.

Introduction

In order to improve the anti-jamming capability of the navigation service in conflict environments, the power enhancements of GPS L1 P(Y) signal and L2 P(Y) signal were used many times. The power enhancement of GPS signals and its influence on GNSS services were reported and studied (Fan et al., 2012; Jiménez-Baños et al., 2011). The latest enhancement event in Syria was also analysed in many works (Thoelert et al., 2018; Xie et al., 2021). In these studies, the data from International GNSS Service (IGS) stations are used. However, at these stations, as long as most non-military users, the real power increment of each signal component cannot be obtained by its observed C/N₀, because the P(Y) signals are received with semi-codeless methods.

The semi-codeless and codeless methods of receiving GPS L1P(Y) and L2P(Y) signals are widely discussed (Betz & Cerruti, 2020; Liao et al., 2006; O'Driscoll & Curran, 2017; Soloviev et al., 2012; Zeng et al., 2017). Montenbruck et al. (2006) compared the performance of three different dual-frequency receivers equipped with semi-codeless receiving algorithms. The research indicates that the complexity and the accuracy of tracking are various in these three receivers. Woo (2000) also compared the performance of several codeless and semi-codeless tracking receivers. The result shows that the z-track has the least C/N₀ loss among them. Borio (2011) analysed the performance of squaring and cross-correlation in the tracking of GPS L2P(Y) signal and proposed a generalized codeless PLL structure. Borio et al. (2013) and Borio (2019) also developed the method of codeless processing of the BOC (Binary Offset Carrier) signal, and other researchers analysed the performance of most codeless and semi-codeless tracking algorithms (Bakholdin et al., 2020; Betz & Cerruti, 2020). Besides, the voting modulation method used in GPS III satellites may influence the performance of codeless tracking method and was analysed in Allen et al. (2020). Based on these analyses, most tracking stations nowadays adapt the z-track method for L1P(Y) and L2P(Y) signal tracking because of its better C/N₀ performance.

The signal power enhancement events are also studied by several works. Jiménez-Baños et al. (2011) analysed the change in signal power level during September 7 to September 12, 2010. Thoelert et al. (2018) analysed the signal power distribution of L1P(Y) between February 7 and 8 2017 using the data of GNSS receivers combined with high-gain antennas. The result shows that during the enhancement period the signal power of different components is redistributed for all GPS IIR-M satellites so that the power of L1P signal increases while the L1M decreases. Sun et al. (2011) analysed the influence of signal power increment in positioning performance and gave the upper bound for power increment. In addition, some researchers have also analysed the authorized signals of GNSS systems using the data from high-gain antennas (He et al., 2020; Lestarquit et al., 2012; Xiao et al., 2018; Yan et al., 2019). However, in these papers, the model calculating power increment of L1P(Y) and L2P(Y) is based on the approximate evaluation of frequency spectrum magnitudes, but this evolution is not authentically precise.

Nowadays, researchers adopt the increase in C/N₀ estimation as the actual power enhancement of GPS signals. But this may introduce a bias related to the structure of the z-track algorithm, which is widely adopted for the receivers at IGS stations in receiving P(Y) signals. For example, Table 2 demonstrates the C/N₀ increments observed at different stations. Take ARUC station as an example, the C/N₀ observation of GPS L2P(Y) of PRN1 increased by 9.1070 dB during the operation. However, the research (Li et al., 2011) tells that GPS Block II-F satellites do not have the capability to achieve a power enhancement greater than 7 dB. Hence, if the change in C/N₀ observation is adopted as the power enhancement, there will be a bias in the estimation. Besides, these IGS stations are not equipped with high-gain antennas especially parabolic antennas. There are no reliable Power Spectrum Density (PSD) observations at these stations to make any analysis. Thus, an unbiased method to estimate the power enhancement of P(Y) signal is needed.

The better understanding of GPS power enhancement strategy may guide developers to make better receivers and provide the suggestions for other GNSS to improve their power enhancement capability. To reduce the bias of power enhancement estimation using the z-track method and to provide an accurate estimation when a high-gain antenna is not available, this paper refines the power increment result by analysing the model of semi-codeless receiving, and then proposes the equations showing the accurate relation between the observed C/N₀ data and the real power enhancement magnitudes. The signal data from tracking stations and high-gain antennas are used to verify the proposed model.

The rest of this paper is arranged as follows. First, the z-track model is analysed and the method to evaluate the power modification from the z-track results is proposed in “Model and signal power evaluation method of the z-track” section. Then in “Observation data from tracking stations” section, the observation data of various ground stations are analysed, which is the primary conclusion obtained through the theoretical result of the in “Model and signal power evaluation method of the z-track” section. In “Signal data from a high gain antenna” section, the data of high-gain antennas are used to verify the result. In “Discussion and application potential” section, the application and other features in the proposed analyse method is discussed. Finally, the conclusion is drawn in “Conclusion” section.

Model and signal power evaluation method of the z-track

GPS satellites broadcast signals of three frequencies, namely L1, L2, and L5. Although several new signal branches have been developed these years, the L1C/A, L1P and L2C L2P are kept in use on all the working satellites. Among them, L1P and L2P are both modulated by P code only with the difference that P code on L2P is a delayed version of L1P. The P code on GPS L2P(Y) is publicly available, but an additional code is modulo-2 added to P code for the purpose of Anti-Spoofing (AS). This code is known as W code, while the combination of P code and W code is called P(Y) code. The generation of W code is not published but its chip rate is known as 0.5115 MHz.

Since P code and W code are the same in L1 and L2 signals, it is possible to generate P code and track L2P(Y) signal via L1 signal. Based on this assumption, there are many methods to receive GPS L1P(Y) and L2P(Y) signals for non-authentic users, including codeless methods and semi-codeless methods (Wang et al., 2012). In 1992, Ashtech researched how to track L1P(Y) and L2P(Y) signals after Y code is added to the original P code (Ashjaee & Lorenz, 1992). Woo (2000) developed the receiving structure of the z-track for L1P(Y) and L2P(Y) which outperforms the other methods because of its less C/N₀ loss, and the structure of the z-track is shown as Fig. 1. Ashtech used this tracking technique in its receivers. Nowadays, many IGS stations are equipped with Ashtech receivers using the z-track technique (IGS Station Information).

Fig. 1

Digital signal processing structure of the z-track method. Spreading code of L2P(Y) is estimated and accumulated through stable tracking of L1C/A signal

From the upper part of Fig. 1, the z-track utilizes the signal energy of both L1P(Y) and L2P(Y). Since the P(Y) code on L1P signal is partially known, it leads to C/N₀ loss when recovering the carrier. Hence L1C/A is tracked to recover the carrier. After that, L1P is correlated with local P code and integrated into baseband. It should be noticed that L1P is integrated at the rate of W code, which means that the coherent integration length is equal to the time length of W code. Hence W code is recovered from the integration result based on hard decision.

After these procedures, the recovered W code from L1P(Y) is used for tracking L2P(Y) as shown in the bottom part of Fig. 1. L2P(Y) signal is first correlated with P code and integrated at the rate of W code. The integration result of L2P is expressed in Eq. (1), in which the carrier tracking error on L2P is temporarily neglected for convenience:

$$\begin{aligned} I_{{{\text{nt}}2\_i}} & = \frac{1}{{T_{{\text{M}}} }}\int\limits_{{t = \left( {i - 1} \right)T_{{\text{M}}} }}^{{iT_{{\text{M}}} }} {S_{2} \left( t \right)P_{{{\text{2\_l}}}} \left( t \right){\text{d}}t} \\ & = \frac{1}{{T_{{\text{M}}} }}\int\limits_{{t = (i - 1)T_{{\text{M}}} }}^{{iT_{{\text{M}}} }} {\left( {P_{2} \left( t \right){\text{W}}_{2} \left( i \right) + n} \right)P_{{{\text{2\_l}}}} \left( t \right){\text{d}}t} \\ & = W_{2} \left( i \right) + N_{i} \\ \end{aligned}$$

(1)

where $T_{M}$ is the chip length of W code, $S_{2} \left( t \right)$ is the signal of L2P(Y), $P_{{2{\text{\_l}}}} \left( t \right)$ is the locally generated P code of L2P, n is white noise, $W_{2} \left( i \right)$ is the ith chip of W code with the amplitude of + 1 or − 1, and $N_{i}$ is the noise after integration.

It should be noted that the correlation loss caused by carrier frequency error and code phase error is ignored since it is not significant when the track loop converges.

Then the integration result is correlated with the W code recovered from L1P(Y) and accumulated. However, the recovered W code from L1P may contain bit errors because of a low C/N₀ of satellite signal. Therefore, the result of accumulation is expressed as Eq. (2) when considering error bits:

$$\begin{aligned} A_{{{\text{cc}}2}} & = \frac{1}{K}\sum\limits_{i = 0}^{K - 1} {I_{{{\text{nt}}2\_i}} W_{1} \left( i \right)} \\ & = \frac{1}{K}\sum\limits_{i = 0}^{K - 1} {\left( {W_{2} \left( i \right) + N_{i} } \right)W_{1} \left( i \right)} \\ & = \frac{1}{K}\sum\limits_{i = 0}^{K - 1} {W_{2} \left( i \right)W_{1} \left( i \right)} + \sum\limits_{i = 0}^{K - 1} {N_{i} } M_{1} \left( i \right) \\ & = \frac{1}{K}\left( {K_{{{\text{Ws}}}} - K_{{{\text{Wd}}}} } \right) + \sum\limits_{i = 0}^{K - 1} {N_{i} } M_{1} \left( i \right) \\ \end{aligned}$$

(2)

Here $K$ is the number of accumulated integration results, K_Ws is the number of correctly recovered W code chips and K_Wd is the number of wrongly recovered W code chips.

Statistically, the number of error chips of W code is determined by the C/N₀ of L1 signal. And this number can be calculated through the Bit Error Rate (BER) of BPSK modulation. These flipped W codes will reduce the correlation result in L2 signal, which finally cause the loss in C/N₀ of L2. If L_C chips are involved in the correlation, the base correlation result should equal to L_C in case no error chip. When the number of error chips is less than L_C/2, every single error chip would reduce the correlation result by 2 (+ 1 shift to − 1). This loss of correlation result can be calculated as ${\text{E}}[R_{{{\text{CNloss}}}} ] = 20\log_{10} (1 - 2R_{{{\text{BE}}}} )$. The BER can be calculated through BPSK modulation as $R_{{{\text{BE}}}} = Q(\sqrt {2R_{{{\text{CN}}1}}^{{}} T_{{\text{M}}} } )$. According to the above analysis the expected accumulation loss can be expressed as follows:

$${\text{E}}\left[ {R_{{{\text{CNloss}}}} } \right] = 20\log_{10} \left( {1 - 2Q\left( {\sqrt {2R_{{{\text{CN}}1}}^{{}} T_{{\text{M}}} } } \right)} \right)$$

(3)

where $R_{{{\text{CNloss}}}}$ is the C/N₀ loss caused by the error bits, and the $R_{{{\text{CN}}1}}^{{}}$ is the C/N₀ of L1P. Q(x) is expressed as follows:

$$Q\left( x \right) = \int_{x}^{ + \infty } {\frac{1}{{\sqrt {2\uppi } }}\exp \left( { - \frac{1}{2}t^{2} } \right){\text{d}}t}$$

(4)

Therefore, one can see that the observed C/N₀ of L2P is affected by the C/N₀ of both L1P(Y) and L2P(Y).

The GPS satellites have the capability to increase the transmitting power of signals. The designed transmitting power of different GPS signals in different satellites can be found in Li et al. (2011). It is known from Li’s research that the GPS IIR satellites do not have the capability of increasing signal power while GPS IIRM/IIF in both L1P and L2P do have. In the next part of the evaluation, the C/N₀ increment of L1P and L2P are analysed according to the observation of L2P signal. From the calculation power enhancing capability of GPS IIF L1 and L2 are 6.9 dB and 5.3 dB, respectively.

Based on the analysis in “Model and signal power evaluation method of the z-track” section, if the correlation loss caused by code phase error and carrier frequency error is ignored, the observed C/N₀ of L2P can be expressed as:

$$R_{{{\text{CN2Obs}}}} = R_{{{\text{CN2}}}} - R_{{{\text{CNloss}}}}$$

(5)

Hence the change of the estimated C/N₀ of L2P signal is determined by the changes of $R_{{{\text{CN2}}}}$ and $R_{{{\text{CNloss}}}}$, which is expressed as Eq. (6).

$$\begin{aligned} G_{{{\text{2Obs}}}} & = \left( {R_{{{\text{CN2}}}} - R_{{{\text{CNloss}}}} } \right)_{2} - \left( {R_{{{\text{CN2}}}} - R_{{{\text{CNloss}}}} } \right)_{1} \\ & = \left( {R_{{{\text{CN2}}}} } \right)_{2} - \left( {R_{{{\text{CN2}}}} } \right)_{1} - \left( {\left( {R_{{{\text{CNloss}}}} } \right)_{2} - \left( {R_{{{\text{CNloss}}}} } \right)_{1} } \right) \\ \end{aligned}$$

(6)

Here the subscripts 1 and 2 stand for the observations before and after the power increment, respectively. Figure 2 shows the relation between $R_{{{\text{CNloss}}}}$ and the C/N₀ of L1P.

Fig. 2

The relation of loss in tracking C/N₀ vs the C/N₀ of L1P. Loss of tracking C/N₀ drops with the increasement of L1P C/N₀ because there will be fewer bit error when L1P C/N₀ increases

It is known from Fig. 2 that the change of $R_{{{\text{CNloss}}}}$ is approximately linear with the change of L1P C/N₀, which is between 25 and 55 dB·Hz. The relation is expressed as follows:

$$R_{{{\text{CN2loss}}}} = 2.62 \, + \left( {55 - R_{{{\text{CN1}}}} } \right) \times 0.944$$

(7)

Substituting Eq. (7) into Eq. (6), the G_L2PObs can be expressed as Eq. (8).

$$\begin{aligned} G_{{{\text{2Obs}}}} & = \left( {R_{{{\text{CN2}}}} } \right)_{2} - \left( {R_{{{\text{CN2}}}} } \right)_{1} \\ & \quad + \left( {\left( {R_{{{\text{CN1}}}} } \right)_{2} - \left( {R_{{{\text{CN1}}}} } \right)_{1} } \right) \times 0.944 \\ & = G_{2} + 0.944 \times G_{1} \\ \end{aligned}$$

(8)

Here $G_{{{\text{2Obs}}}}$ is the observed C/N₀ increment of L2P, $G_{2}$ is the real C/N₀ increment of L2P, and $G_{1}$ is the actual C/N₀ increment of L1P. When the receiving condition does not drastically change, the C/N₀ increment reflects the enhancement of transmitting signal power on the satellite.

Supposing that the signal C/N₀ increments of L1P and L2P are the same (observed in PSD data from high-gain antenna), the $G_{2}$ would be identical to the $G_{1}$. Therefore, the power increment of L1P and L2P can be expressed as:

$$G_{{\left( {L1P,L2P} \right)}} = G_{{2{\text{Obs}}}} /\left( {1 + 0.944} \right)$$

(9)

Here $G_{{\left( {L1P,L2P} \right)}}$ is the power increment of L1P and L2P. Analyses of the power enhancement of GPS L1P(Y) and L2P(Y) signals will rely on this theoretical result in the rest of the paper.

Observation data from tracking stations

To verify the theoretical deduction, the observation data at different tracking stations are analysed. During the period from April 13 to April 17 in 2018, a signal power increment of L1P(Y) and L2P(Y) was observed at many stations. Hence the signal C/N₀ observations from International GNSS Service (IGS) tracking stations are analysed. During the period of time, an attack mission was operated by American Army and the time relationship between the power enhancement and attack mission is shown in Fig. 3.

Fig. 3

The power enhancement and attack mission in April 2018. Yellow and orange blocks indicate the period of power enhancement while the red block shows the time of the attack mission

As shown in Fig. 3, a preparation stage was from 06:01 to 18:36, afterwards the power enhancement was deployed and then the attack mission started. The chosen IGS tracking stations are shown in Table 1.

Table 1 Position of chosen IGS stations

The observation data of PRN 2, PRN1, and PRN7 are analysed, in which PRN2 satellite is GPS IIR while PRN 1 is GPS II-F satellite and PRN 7 is GPS IIR-M satellite.

The L2P(Y) signal C/N₀ of GPS PRN2 satellite observed at ANKR for 7 days is shown in Fig. 4, in which time is expressed in weeks while the decimal part is the time in week. The time can be converted to Gregorian calendar date by considering the start point of GPS time, which is 0 h UTC (midnight) of January 6th 1980. For example, day 6 of week 1996 corresponds to April 13, 2018. The figure shows that the C/N₀ of PRN2 remains almost the same, but the L2P(Y) signal C/N₀ of PRN7 increases from April 13, 2018 to April 17, 2018.

Fig. 4

The L2P(Y) signal C/N₀ observed at ANKR station in seven days; a PRN 2 satellite b PRN 7 satellite

Since the repeating period of GPS satellites is 23 h 56 min, the C/N₀ data is shifted by − 4 min every day to make time epoch aligned in Fig. 5. The L2P(Y) C/N₀ increment is obtained by calculating the difference between the observed C/N₀ in April 13 and that in April 12. To make the data more reliable, the observed C/N₀ is chosen based on the following principle:

• 1. The observed C/N₀ data should be taken between a constant tracking stage.

• 2. During the tracking stage, the satellite elevation should be above 15°.

Fig. 5

The PSD of GPS Block IIF-10 L1 signal. The PSD is observed from the samples of a high-gain antenna

When the these principles are satisfied, $G_{{\left( {L1P,L2P} \right)}}$ can also be calculated according to the Eq. (9). The C/N₀ increment values are obtained based on the data from different tracking stations considering both PRN 1 and PRN7, which is shown in Table 2. Some conclusions can be drawn from Table 2:

• 1. The observed C/N₀ increments at different stations vary from 8.5 to 10.4 dB for PRN1. The difference may be caused by the elevation angle of satellite or the C/N₀ estimation methods at different tracking stations. Hence the power increments of L2P are between 4.4 and 5.3 dB considering that the increment of L1P and L2P is identical.

• 2. The observed C/N₀ increment values at different stations vary from 9.0 to 10.15 dB for PRN 7, while the power increments of L2P are between 4.6 and 5.2 dB.

Table 2 C/N₀ increment observed from different stations

The analysis result basically matches the designed capability of satellites collected by Li et al. (2011). Besides we found Block IIR-M satellites had similar behaves as Block II-F satellites.

Signal data from a high-gain antenna

The signal data from a high-gain antenna with 40 m calibre at National Time Service Centre of Chinese Academy of Sciences is used to verify the analysis result. The power gain of a parabolic antenna can be calculated with

$$G = \eta \left( {\frac{{\uppi D}}{\lambda }} \right)^{2}$$

(10)

Here $\eta$ is the effectiveness of the antenna, $D$ is the calibre, and $\lambda$ is the wavelength of the working frequency. For $\eta = 0.65$ and calibre $D = 40$, the antenna has a 26.32 dB gain for GPS L1 in the direction of main lobe. The $R_{{{\text{CN}}}}$ of GPS L1C/A signal is shown as

$$R_{{{\text{CN}}}} = \frac{{P_{{\text{s}}} G_{{\text{a}}} }}{kT} = 73.3\;{\text{dB}}\,{\text{Hz}}$$

(11)

In tracking L1C/A signal, the C/N₀ is estimated and shown in Fig. 6.

Fig. 6

The C/N₀ estimation of L1C/A signal of GPS Block IIF-10 in high-gain antenna samples. The samples were recorded on 15 March, 2018 and 16 April, 2018

From the Fig. 6 we confirm that the quality of the samples from the high-gain antenna meets the theoretical results. Figure 5 shows the PSD of L1 obtained from the high-gain antenna before and after the signal power is increased. From Fig. 5, the signal power of L1C/A is almost the same in these two days with the signal power of L1P(Y) increased by about 5 dB (Steigenberger et al., 2019).

To get the actual increment of signal power, the PSD is integrated while the signal power of L1C/A is excluded. Hence the PSD is integrated between ($f_{1}$ − 20.46 MHz, $f_{1}$ − 1.023 MHz) and ($f_{1}$ + 1.023 MHz, $f_{1}$ + 20.46 MHz) where $f_{1}$ is the carrier frequency of L1 signal. As is known, L1P(Y) is a BPSK modulated signal that the shape of PSD can be described as sinc(.) function. According to the consistence of the sinc(.) function in the whole frequency interval, one can use the PSD between ($f_{1}$ − 20.46 MHz, $f_{1}$ − 1.023 MHz) and ($f_{1}$ + 1.023 MHz, $f_{1}$ + 20.46 MHz) to represent the PSD of the whole L1P(Y) signal. In other word, the spectrum between interval (f₁ − 1.023 MHz, f₁ + 1.023 MHz) will increase or decrease in the same scale as in the interval between ($f_{1}$ − 20.46 MHz, $f_{1}$ − 1.023 MHz) and ($f_{1}$ + 1.023 MHz, $f_{1}$ + 20.46 MHz).

The signal power increment can be expressed as

$$G_{1} = \int\limits_{{f \in f_{{{\text{span}}}} }}^{{}} {\left( {P_{{{\text{SD}}}} } \right)_{{{\text{day2}}}} {\text{d}}f} /\int\limits_{{f \in f_{{{\text{span}}}} }}^{{}} {\left( {P_{{{\text{SD}}}} } \right)_{{{\text{day1}}}} {\text{d}}f}$$

(12)

where f_span is the PSD integration frequency range shown above, while $\left( {P_{{{\text{SD}}}} } \right)_{{{\text{day}}1}}$ and $\left( {P_{{{\text{SD}}}} } \right)_{{{\text{day2}}}}$ are the PSDs of two days of signals. It can be calculated that $G_{1}$ is about 4.47 dB.

Figure 7 shows the PSD of L5 and L2 obtained from the high-gain antenna. It is known from the figure that the PSD of L5 is almost the same in these two days. But for L2, whose signal modulation changes from L2C + L2P + L2M to L2C + L2P, the power of L2C remains the same in two days while the power of L2P significantly increases.

Fig. 7

The PSD of GPS Block IIF-10 L5 and L2 signal. The PSD is observed from samples of high-gain antenna

The same method in Eq. (12) is used to calculate the power increment of L2P. In order to avoid the influences of L2M and L2C, the PSD integration frequency span is ($f_{2}$ − 5.115 MHz, $f_{2}$ − 1.023 MHz) and ($f_{2}$ + 1.023 MHz, $f_{2}$ + 5.115 MHz), and the calculated $G_{L2P}$ is about 4.078 dB.

By using the values of $G_{1}$ and $G_{2}$, $G_{{2{\text{Obs}}}}$ can be calculated as 8.30 dB. This result matches the results in Table 2 considering the statistical errors in calculating the power increment by the data of the high-gain antenna.

In the above analyses we find there is a about 5 dB of enhancement in P(Y) signals while the power of C/A signals are not influenced. Besides, the signals carrying M code disappeared in the whole process of enhancement. From these results we can speculate that the satellite of GPS IIR-M and later version has an ability to adjust its modulation and power distribution among all components of its transmission. In the Syrian example, we observed the phenomenon that the power of M code signal may be transferred to P(Y) signal. The long-term observation of GPS III satellites may also discover that the power of P(Y) signal can also be transferred to M code signals if needed.

Discussion and application potential

The PSD from a high-gain antenna, especially parabolic antennas is usually used to estimate the signal power of military GNSS signals (Thoelert et al., 2018). However, very few GNSS stations all over the world are equipped with high-gain antennas especially parabolic antennas. For example, IGS stations monitor the GNSS signals via an omnidirectional antenna (e.g., Leica AR10 antenna in ANKR station provides a maximum of 10 dB gain at zenith direction) through C/N₀ observations in tracking channels.

If we want to estimate the power enhancement of P(Y) signals at these stations, the typical method is to observe the change in C/N₀ estimation in tracking channels using the z-track method. However, this estimation method will lead to a bias in the result when power of P(Y) signal increases in both L1 frequency and L2 frequency as we have analysed in “Model and signal power evaluation method of the z-track” section. Our work provides an unbiased estimation of the actual power increase scale via C/N₀ estimations in the z-track. This method can provide the capability of estimating the power enhancement for those stations without high-gain antennas. This can give the potential for a global observation network to monitor any power enhancement events in real-time and in every beam of any satellite.

In future, modernized satellites will have more flexible power enhancement capability. Since the power enhancement can occur in just a narrow beam of the satellite, it is possible that no high-gain antenna happens in the beam and is able to receive the enhanced signal. This scenario makes the analysis of signal power possible with no reliable data from high-gain antenna. However, the dense stations of IGS or other observation networks are quite possible to be covered in the enhanced beam and a real-time C/N₀ estimation can be obtained. With the proposed method in this work, an unbiased result such as that derived from high-gain antennas can be drawn just from these C/N₀ observations. This can have a great application potential. Another application of the proposed method is to correct the C/N₀ estimation of P(Y) signal in the existing stations. Influenced by the estimation error of W code, there is a bias in C/N₀ estimation at the existing stations. Initially calibrated via the data from high-gain antennas, these stations will have the capability to continually obtain the unbiased estimation of C/N₀ of P(Y) signal using the proposed method.

Conclusion

Based on the analysis of the z-track method of L1P and L2P, the accurate relation between the observed C/N₀ and the actual power increment magnitude is shown in the paper.

It is known from the signal data of L1P(Y) and L2P(Y) at IGS stations that the power of Block IIR satellites did not change while the signal power of Block IIF satellites increases. By using the proposed relation equation, one can calculate that the power of L1P(Y) increases by about 4.3–5.3 dB and the power of L2P(Y) by about 4.6–5.2 dB. The reason for this result is that the power enhancement in L1P did not reach its capacity (6.9 dB) at that time, mainly intends to make an evenly increase in both L1P and L2P. The signal data of a high-gain antenna is also used to analyse the signal power increment, which shows that the signal power increment of L1P(Y) is about 4.47 dB while that of L2P(Y) is about 4.078 dB.

It can be concluded that the analysis result based on the accurate model proposed in this paper matches the results of the high-gain antenna considering the statistical errors as for the power increment capability of satellites, which matches the designed capability of GPS satellites as well. We also find the flexibility of GPS satellites in power distribution. Hence, the results verify the correctness of the proposed method to analyse the real C/N₀ increment by using C/N₀ observations based on the z-track method.