Effect of satellite availability and time delay of corrections on position accuracy of differential NavIC

1.1 Differential NavIC

A typical Differential NavIC architecture is shown in Figure 1. Differential NavIC consists of a reference station which is located at a known location (which is a well-surveyed location) and a mobile receiver (also called a rover). The reference station estimates the range corrections (difference between pseudo-range and true range) for each NavIC satellite in view, which are transmitted to the rover. The errors that are common to the reference station and the rover can be eliminated as the same set of NavIC satellites are visible to both the receivers. Using these corrections, the rover’s position accuracy is improved (Parkinson 1996, Misra and Enge 2001).

Figure 1

Differential NavIC architecture.

The equation for pseudo-range at the rover receiver (equation (1)) and reference receiver (equation (2)) is

where R _m and R _ref are true ranges (meters) of the rover and reference station, respectively, c is the speed of light in m/s, δ t ref , δ t m are receiver clock errors (in seconds) for reference station and rover receiver, δ t s is satellite clock error in seconds, T ref , T m are errors due to tropospheric delay (in meters) for the reference station and rover receiver, respectively, I ref , I m are errors due to ionospheric delay (in meters) for reference receiver and rover respectively, m p ref , m pm are errors due to multipath (in meters) for reference station and rover receiver, respectively, and v pref , v pm are errors in pseudo-range (in meters) due to receiver noise for the reference receiver and rover receiver, respectively (Naveen Kumar et al. 2014, Madhu Krishna and Naveen Kumar 2023).

The true range R _ref is calculated from the known satellite position and predetermined position of the reference station.

where (x _sat, y _sat, and z _sat) is the satellite position (in meters), (x _ref , y _ref, and z _ref) is the fixed position of the reference receiver (in meters).

The differential correction is known by subtracting the true range from the pseudo-range at the reference receiver. The differential correction (Δ_D) is

This differential correction is transmitted by the reference station to the rover receiver.

The corrected pseudo-ranges ρ ˆ r for the rover at the epoch of observation are,

The above equation is the range correction equation for the rover using which the accuracy of the rover is improved by eliminating the errors which are in common and reducing the other errors (Parkinson 1996).

1.2 Factors affecting satellite availability and its impact on GNSS users

The period of time that a navigation system’s services are available to the user receiver or navigator is referred to as the satellite availability of the navigation system (Seeber 2003, Dutt et al. 2009). Satellites are now an essential component of our contemporary world, facilitating communication, navigation, and data transmission on a global scale. However, a number of factors must be taken into account which can affect the availability of satellite services (Parkinson 1996). Understanding these factors is crucial for the users who rely on satellite technology for their operations.

One key factor affecting satellite availability is orbital congestion. As more satellites are launched into space to meet the growing demand for connectivity, the limited space in certain orbits can become crowded. This congestion can lead to interference and reduced signal quality and has an impact on the availability of satellite services (Misra and Enge 2001, Pan et al. 2019). Atmospheric conditions are another factor. Rain, snow, and storms are examples of weather conditions that can attenuate or scatter satellite signals as they travel through the Earth’s atmosphere. This can result in signal degradation or complete loss of connectivity during severe weather events (Hofmann Wellenhof et al. 1992, Naveen Kumar et al. 2014).

Geographical location also plays a role in satellite availability. Satellites operate within specific coverage areas known as footprints. The size and shape of these footprints vary depending on factors such as satellite altitude and beam characteristics. Therefore, areas located at the edge or outside of a satellite’s footprint may experience weaker signal strength or no coverage at all (Santra et al. 2019, Pan et al. 2022). Technical issues and equipment failures are additional factors that can affect satellite availability. Satellites are complex systems with numerous components that must work together seamlessly to provide reliable services. Any malfunction or failure in these components can disrupt service availability until repairs or replacements are made. Lastly, regulatory restrictions and licensing agreements can impact satellite availability in certain regions or countries (Vasudha and Raju 2017). Governments may impose limitations on frequency bands or require operators to obtain specific licenses before providing services within their jurisdiction.

Therefore, several factors influence the availability of satellite services including orbital congestion, atmospheric conditions, geographical location, technical issues, and regulatory restrictions. Understanding these factors and taking them into account when planning for satellite-based operations or services enable reliable connectivity and minimize disruptions caused by external influences (Sharma et al. 2019).

1.3 Impact of satellite availability on GNSS users

The availability of satellite signals from Global Navigation Satellite Systems (GNSS) like GPS (Global Positioning System), GLONASS (Global Navigation Satellite System), Galileo, and BeiDou and Regional Navigation Satellite Systems (RNSS) like IRNSS and Quasi-Zenith Satellite System, respectively, can significantly impact GNSS and RNSS users in various ways (Rao 2010).

RNSS receivers are intricately linked to satellite availability. The number and positioning of satellites directly impact the precision of location information, with more visible satellites allowing for better triangulation and enhanced accuracy (Nageena Parveen and Siddaiah 2019, Kuter and Kuter 2010). However, in scenarios with limited satellite visibility, such as urban canyons or areas obstructed by tall buildings, signal reliability may diminish due to multipath interference, potentially leading to degraded navigation performance (Specht 2020). The time required for GNSS or RNSS receivers to establish an initial position, known as Time to First Fix (TTFF), can also be prolonged in such conditions (Sundara and Raju 2022). Moreover, the implications extend to safety-critical applications like aviation, where reduced satellite availability may compromise GNSS integrity, risking inaccuracies in navigation information and potentially affecting timing applications crucial for synchronization in various industries (Sivaraj et al. 2017). Therefore, addressing challenges related to satellite visibility is paramount for ensuring the robustness and reliability of GNSS and RNSS systems across diverse applications.

Overall, the impact of satellite availability on GNSS and RNSS users varies depending on the application, location, and the specific GNSS and RNSS constellation being used. GNSS and RNSS users should be aware of potential limitations and consider using alternative positioning technologies or augmentation systems (e.g., Wide Area Augmentation System, European Geostationary Navigation Overlay Service) in areas where satellite availability is limited or compromised.

As per the literature, it is observed that the satellite availability of a standalone navigation system (GNSS or RNSS) has been analysed and no significant work has been carried out on the effect of satellite availability on the position accuracy of differential NavIC. In this article, the effect of satellite availability is analysed for user receiver accuracy of differential NavIC, and the effect of time delay of corrections on position accuracy is analysed for differential NavIC. This work will be helpful to assess the performance of differential NavIC over NavIC service areas.

2.1 At base station

The steps in computing the corrections at the base station (Figure 3) initially involve data extraction. Here, the raw data are converted to RINEX and CSV format from which the required parameters are extracted; then, the satellite positions are estimated and the user position of the base station receiver is computed. For estimation of pseudorange corrections well surveyed location is required which is obtained by taking the average of estimated position of the base station receiver for 72 h. The geometric range is calculated using the satellite position of each NavIC satellite and the surveyed location of the base station. Using the above parameters, the range corrections are estimated for all visible satellites and then transmitted to the user receiver (Madhu Krishna and Naveen Kumar 2023).

2.2 At user receiver

The steps in computing the corrections at the user receiver (Figure 4) initially involve data extraction. The raw data is converted to RINEX and CSV format from which the required parameters for the calculation of satellite position and user position of user receiver are extracted. Here, the differential NavIC analysis is carried out for three cases. Case I: all visible IRNSS satellites (here six visible satellites), Case II: five visible satellites (thee GSO and two GEO), Case III: five visible satellites (three GEO and two GSO). For the above three cases, standalone NavIC 2D accuracy CEP, DRMS, and 2DRMS are computed. Using the range corrections transmitted from the base station receiver, the accuracy is estimated based on the minimum Geometric Dilution of Precision (GDOP) and plotted for all three cases. Further, the position accuracies of standalone NavIC and differential NavIC are compared.

Figure 4

Steps showing calculations at user receiver.

3.1 Effect of satellite availability on position accuracy of differential NavIC

The effect of satellite availability on position accuracy of differential NavIC is analysed by selecting the different combinations of the satellite by considering minimum GDOP as discussed in the following sections.

3.1.1 Case I: All (six) satellites in view

In the first case, all (six) satellites are visible; the corresponding satellite path and GDOP are shown in Figures 5 and 6, respectively. For all the visible satellites, the satellite positions are plotted in Figure 5. In this figure, the satellite positions of six satellites, of which, three are GEO satellites and three are GSO satellites.

Figure 5

NavIC Satellites path for all (6) visible satellites.

Figure 6

Variation of GDOP for all (six) visible satellites.

Figure 6 shows the GDOP for six visible NavIC satellites in orbit. GDOP is calculated and plotted for 24 h duration, and it is observed that at about 12 and 24 h time, GDOP is higher because of the poor satellite geometry (Rathore 2017). The minimum GDOP value is observed to be 3.72 (at about 5 and 18 h), and the maximum is 4.52 (at about 12 and 24 h). The average value of GDOP is noted to be 3.98.

The position accuracy of standalone NavIC and differential NavIC is plotted in Figure 7(a) and (b), respectively, by considering east error on the x-axis and north error on the y-axis in meters. An East–North-Up (ENU) system is used to represent the NavIC accuracy in terms of east error and north error in meters. The east error and north error are considered to represent the horizontal position error. The data considered are of 24 h duration. Accuracy is plotted with the horizontal accuracy parameters CEP, DRMS, and 2DRMS (Vasudha and Raju 2017).

Figure 7

Position accuracy of user receiver for Case I: (a) standalone NavIC, and (b) differential NavIC.

For standalone NavIC and differential NavIC, the CEP value is observed to be 5.31 and 1.21 m, respectively, which contain the position estimates with a probability of 50%. The DRMS values observed are 7.36 and 1.56 m, which is the radius of the circle with the position estimates with the probability of 65%. The 2DRMS is twice the DRMS value and is observed to be 14.72 and 3.09 m, which is the radius of the circle with the position estimates with a probability of 95% (Madhu Krishna and Naveen Kumar 2023).

3.1.2 Case II: (5 Satellites (three GSO, two GEO))

For case II, the NavIC satellites considered are 3 GSO and 2 GEO satellites. There are three combinations of NavIC satellites are identified which are, combination 1, with PRNs [2 4 5 6 7], combination 2, with PRNs [2 3 4 5 7]. and for combination 3, PRNs are [2 3 4 5 6]. The mean GDOP for these three combinations is 6.76, 7.11, and 4.9, respectively. For these combinations, the satellite path and corresponding GDOP (Figure 8(a) and (b) respectively) are calculated, and the satellite geometry with minimum mean GDOP is considered and used for the analysis. Here, the selected combination of satellites based on minimum GDOP is [2 3 4 5 6].

Figure 8

(a) NavIC Satellites path for five (three GSO, two GEO) visible satellites (PRN [2 3 4 5 6]), (b) GDOP for five visible satellites (PRN [2 3 4 5 6]).

The user receiver accuracy of differential NavIC for Case II is plotted in Figure 9(b). The observed accuracy parameters CEP, DRMS, and 2DRMS values are 1.71, 2.19, and 4.38 m, respectively. From the above-observed value, it can be stated that the user position accuracy is improved using the differential positioning technique.

Figure 9

Position accuracy of user receiver for Case II: (a) standalone NavIC, (b) differential NavIC.

3.1.3 Case III: (five Satellites (three GEO, two GSO))

For Case III, the NavIC satellites considered are 3 GEO and 2 GSO satellites. For these satellites, these are three combinations of NavIC satellites are identified which include, for combination 1 the PRNs are [3 4 5 6 7], combination 2, the PRNs are [2 3 5 6 7], and for combination 3, the PRNs are [2 3 4 6 7]. The mean GDOP for these three combinations is 5.41, 4.31, and 4.37, respectively. For these combinations, the satellite path and corresponding GDOP (Figure 10(a) and (b) respectively) are calculated, and the satellite geometry with minimum mean GDOP is considered and used for the analysis. Here, the selected combination of satellites is [2 3 5 6 7].

Figure 10

(a) NavIC Satellites path for five (three GEO, two GSO) visible satellites (PRN [2 3 5 6 7]), (b) GDOP for five visible satellites (PRN [2 3 5 6 7]).

The user receiver accuracy of differential NavIC for Case III is plotted in Figure 11(b). The observed accuracy parameters CEP, DRMS, and 2DRMS values are 1.22, 1.54, and 3.08 m, respectively. From the above-observed values, it can be stated that the user position accuracy is improved using the differential positioning technique.

Figure 11

Position accuracy of user receiver for Case III: (a) standalone NavIC, (b) differential NavIC.

The comparison (Table 2) of the accuracy of user receiver for standalone and differential NavIC is represented for Case I, Case II, and Case III. It is observed that, with the satellite availability in Case I (six visible satellites) and Case III (five visible satellites), the rover receiver accuracy is approximately the same. In Case III, even if the available satellites are five, the accuracy of the rover is comparable to the accuracies in Case I.

Table 2

Comparison of accuracy parameters of rover receiver for standalone and differential NavIC for Case I, Case II, and Case III

Accuracy Parameters	Case I 6 visible satellites		Case II 3 GSO, 2 GEO		Case III 3 GEO, 2 GSO
	Standalone (m)	Differential (m)	Standalone (m)	Differential (m)	Standalone (m)	Differential (m)
CEP	5.31	1.21	7.05	1.71	5.33	1.22
DRMS	7.36	1.56	9.56	2.19	7.44	1.54
2DRMS	14.72	3.09	19.13	4.38	14.88	3.08

3.2 Effect of time delay on position accuracy of differential NavIC

To observe the effect of time delay (delay in transmission of range corrections) on the rover position, IRNSS data are collected with the epochs of 1 s. Further, to avoid the effect of residual errors and to focus only on time-delay effects, NavIC data of the same day and time are considered for the base station as well as the rover receiver. The steps involved in the estimation of range corrections and other calculations at the base station and the calculations at user receivers are depicted in Figure 12.

Figure 12

Steps showing calculations at base station and at user receiver.

With respect to different time delay values (0, 5, 10, 20,……300 s), error in rover position is estimated for the epochs under consideration. For differential GPS, the standard delay of 3–4 s is considered (Wang et al. 2016).

For different values of time delay, the position accuracy of the rover is estimated and plotted (Figure 13). It is observed that when the time delay is increased, the accuracy of the rover position is degraded (Table 3).

Figure 13

Time delay vs Accuracy parameters (CEP, DRMS, and 2DRMS).