Performance Monitoring for Galileo High Accuracy Service and Reliable Galileo Service Operations ^†

Abstract

In this paper, we present the performance reporting of one of the selected Galileo services, namely the HAS. Specifically, we present the evolution of the monitored Galileo HAS correction quality and availability as well as the HAS-derived user positioning accuracy at selected Galileo Sensor Stations (GSSs).

1. Introduction

One of prerequisites for high-accuracy GNSS user positioning is the availability of precise satellite orbit, clock offset and code bias products. Galileo is the world’s first global navigation satellite system to broadcast high-accuracy corrections to satellite orbit and clock offset relative to the respective values computed using Galileo “Open Service” (OS) broadcast ephemerides from the INAV navigation message, see [1,2]. Galileo High Accuracy Service (HAS) corrections are broadcast through both signal-in-space (SiS) as well as through the Internet (commonly called Internet data dissemination or IDD). In either case, a Galileo user, subject to assumptions in the Galileo HAS service definition document (SDD) (see [3] pg. 23 and §2.4), is able to use the Galileo HAS corrections in real time for precise positioning, which turns out to be a huge benefit compared to other expensive means of subscribing to real-time corrections from commercial correction service providers. Until recently, precise point positioning (PPP) was only possible when other limited sources of real-time precise GNSS products were available, or it was generally required to wait until a so-called “rapid” reference products from scientific agencies such as the International GNSS Service (IGS) were made available, which had a typical accuracy of decimeters and latency in the order of few hours to a few days (see [4]) so that the GNSS measurements could be post-processed. There have been recent developments from the IGS and other scientific agencies to provide real-time correction (most notably the IGS Real-Time Service (see, e.g., [5,6]) through the NTRIP protocol [7]. However with Galileo HAS, GNSS users (user receivers who comply with the assumptions made for receiving equipment for using Galileo HAS corrections, as described in the Galileo HAS SDD [3]) have the possibility to use precise GPS and Galileo corrections in real time reliably without additional expense. Precise GNSS orbit and clock offset corrections are also motivated by the ever-increasing user requirements in various applications for higher accuracy in real time compared to that using the GPS Standard Positioning Service (SPS) or Galileo OS broadcast navigation data (BRDC), which typically delivers a signal-in-space range error (SISRE) on the order of decimetres to meters, see, e.g., [8]. Accordingly, EUSPA, a Galileo service provider, with the support of Spaceopal, a Galileo service operator, have ensured that Galileo HAS meets the minimum performance levels (MPLs) defined in the Galileo HAS SDD [3] and regularly reported on the obtained performances since the Galileo HAS service declaration in January 2023. One of the main objectives of this paper is to describe the Galileo HAS operational performance reporting and highlight its adherence to MPLs, thereby ensuring a high degree of reliability in Galileo service operations. Reliability is achieved by ensuring continuous service performance monitoring and prompt intervention when required to resolve operational challenges.

2. Galileo Services and HAS

“The Galileo High Accuracy Service (HAS) is an open access and free of charge service based on the provision of precise corrections (orbit, clock, biases) transmitted in the Galileo E6 signal (E6-B, data component) and via internet (RTCM—SSR like format)” [9], which can be received by E6-B tracking capable receivers subject to compliance to assumptions made for the user receiver, as described in the Galileo HAS SDD [3]. For the scope of this paper, hereafter we will refer to such a user receiver as the “HAS-enabled receiver” for better readability. Subject to the usage described in the HAS ICD [9], HAS SDD [3] and HAS Internet Data Distribution (IDD) ICD, available under registration, HAS-enabled receivers can achieve a typical HAS positioning performance to decimeter-level accuracy. Other studies that have used Galileo HAS for positioning, e.g., [10,11,12], have consistently reported user performance similar to the typical HAS positioning performance. Moreover, the Galileo HAS service has been proposed for precise orbit determination (POD) of satellites in low Earth orbit (LEO), see [13].

In order to monitor the operational high-accuracy service performance, several key performance indicators and metrics are defined together with EUSPA. These parameters are time- as well as space-dependent and in some cases satellite-specific as well as dependent on the the individual signal frequency and modulation type. These have to be routinely computed, monitored in near real time and compared against the MPLs defined in the SDD [3]. The performance of these parameters are published quarterly by European Union in their Galileo HAS performance report (see, e.g., [14]) on the EGNSS Service Center (E-GSC) website https://www.gsc-europa.eu/ accessed on 18 August 2025. Two examples of such parameters are Galileo HAS correction accuracy and Galileo HAS-enabled typical position accuracy. In the following sections we will describe what specifically these two parameters contain, how they are defined and how the correction accuracy as well as position accuracy are computed. These are operational activities by Spaceopal in Galileo service operation provision and are ensured by executing, as part of routine operations, the following (among others):

• Collecting Galileo HAS corrections as well as raw GNSS ranging measurements globally at the GSS as part of continuous 24/7 operations.
• Obtaining the most recent reference dataset for the routine comparison and quality monitoring of the Galileo HAS corrections.
• Generating PPP solution(s) with an EU-approved HAS user algorithm (HAS-UA) (see [3], pg. 38 and Appendix E) with multiple signal/frequency/constellation combinations routinely (with daily restarts) using Galileo HAS-generated precise GNSS products and the collected GSS raw measurements. This allows the monitoring (identification and isolation) of any potential anomalies on the receiver side or the broadcast HAS corrections themselves.
• Ensuring that the performance of Galileo HAS correction accuracy meets the MPL provided in the Galileo HAS SDD [3] as well as ensuring that the PPP performance at the GSS meets the typical HAS positioning performance in the Galileo SDD [3], pg. 39 and Appendix E.
• Computing the Galileo HAS correction availability at the average and worst user location (AUL/WUL) in the globe.

In this paper we will define, as in the HAS ICD and SDD, and quantify the HAS service operation performance and also present selected examples of user performance for selected user receivers in static PPP mode. We will show that the correction quality performance is well bound by the MPL. Similar performance studies have been reported in [15,16,17]. We will show that in line with the Galileo HAS ICD [9] and SDD [3], the precise corrections and the code biases when processed by a user algorithm (UA) yield a navigation PVT solution in real time with decimeter-level accuracy in horizontal and vertical dimensions. The daily positioning performance in both horizontal and vertical dimensions after convergence will be cumulatively analyzed to compare with the typical HAS positioning accuracy as described in the Galileo HAS SDD [3].

3. Service Operations for Galileo HAS

The Galileo HAS corrections are applied to the satellite orbit and clock offsets provided through the Galileo Open Service broadcast navigation messages (INAV) [1] and the GPS Standard Positioning Service (SPS) navigation data (LNAV) [18]. MPLs specified in the HAS SDD [3] have global service area coverage with selected regions excluded, as described in [3], pg. 26 and §3.1. HAS users in the excluded areas may still use the Galileo HAS service, albeit without the MPL applicability. Specifically for this paper we refer to the set of constraints as described in the SDD [3]. (These constraints listed here in this paper in Equation (1) should be considered as a subset and simplified representation, for the sake of better readability of this paper, of the overall conditions and constraints substantiated in the Galileo HAS ICD [9] and SDD [3].) These are defined as follows:

$$\begin{array}{cc}\hfill C_{corr,acc}& : \mathrm{C}\mathrm{o}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{s} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{H}\mathrm{A}\mathrm{S} \mathrm{c}\mathrm{o}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s} \mathrm{a}\mathrm{c}\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{a}\mathrm{c}\mathrm{y} \mathrm{M}\mathrm{P}\mathrm{L}.\hfill \\ \hfill C_{corr,ava}& : \mathrm{C}\mathrm{o}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{s} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{H}\mathrm{A}\mathrm{S} \mathrm{c}\mathrm{o}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s} \mathrm{a}\mathrm{v}\mathrm{a}\mathrm{i}\mathrm{l}\mathrm{a}\mathrm{b}\mathrm{i}\mathrm{l}\mathrm{i}\mathrm{t}\mathrm{y} \mathrm{M}\mathrm{P}\mathrm{L}\hfill \\ \hfill C_{pos,acc,Gal}& : \mathrm{C}\mathrm{o}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{s} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{t}\mathrm{y}\mathrm{p}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{l} “\mathrm{G}\mathrm{a}\mathrm{l}\mathrm{i}\mathrm{l}\mathrm{e}\mathrm{o} \mathrm{o}\mathrm{n}\mathrm{l}\mathrm{y}” \mathrm{H}\mathrm{A}\mathrm{S} \mathrm{p}\mathrm{o}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{a}\mathrm{c}\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{a}\mathrm{c}\mathrm{y}.\hfill \\ \hfill C_{pos,acc,GPS+Gal}& : \mathrm{C}\mathrm{o}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{s} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{t}\mathrm{y}\mathrm{p}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{l} “\mathrm{G}\mathrm{a}\mathrm{l}\mathrm{i}\mathrm{l}\mathrm{e}\mathrm{o} + \mathrm{G}\mathrm{P}\mathrm{S}” \mathrm{H}\mathrm{A}\mathrm{S} \mathrm{p}\mathrm{o}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{a}\mathrm{c}\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{a}\mathrm{c}\mathrm{y}.\hfill \\ \hfill C_{pos,ava}& : \mathrm{C}\mathrm{o}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{s} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{t}\mathrm{y}\mathrm{p}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{l} \mathrm{H}\mathrm{A}\mathrm{S} \mathrm{p}\mathrm{o}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{a}\mathrm{v}\mathrm{a}\mathrm{i}\mathrm{l}\mathrm{a}\mathrm{b}\mathrm{i}\mathrm{l}\mathrm{i}\mathrm{t}\mathrm{y}.\hfill \end{array}$$

(1)

3.1. Galileo HAS Correction Accuracy

Our objective in this section is to obtain a measure of Galileo HAS correction accuracy from the instantaneous HAS correction errors (as a function of time) using the recommended procedure outlined in the SDD [3]. This procedure is presented further in this section. For the scope of this paper, we specifically define the set

$$x^s\in \left\{{\mathit{r}}_c^s,{\tau }_c^s,b_c^{s,m}\right\}$$

(2)

of three correction types currently supported in Galileo HAS, namely (1) the orbit correction ${\mathit{r}}_c$, (2) the clock offset correction ${\tau }_c$ and (3) the code bias $b_c^m$. (The bold font in the orbit corrections ${\mathit{r}}_c^s$ denotes that it is a vector, whereas the remaining two are scalars). Whereas the superscript s denotes the satellite index, the additional superscript m in the code bias denotes a particular signal type. Specifically, the currently supported signal types in the HAS code bias are provided in the HAS SDD [3], pg. 23 and §2.4.1. The subscript c in the correction types on the right-hand-side parenthesis of Equation (2) signifies that these are corrections. In future, additional correction types, such as phase biases and ionospheric corrections, are also foreseen, see [3], pg. 5 and §1.5. To evaluate the Galileo HAS correction quality, we define the set

$$x_{ref}\in \left\{{\mathit{r}}_{REF}^s,{\tau }_{REF}^s,b_{REF}^{s,m}\right\}$$

(3)

of reference products as well as the set

$$x_{BRDC}\in \left\{{\mathit{r}}_{BRDC}^s,{\tau }_{BRDC}^s\right\}$$

(4)

of satellite positions and clock offsets from broadcast ephemerides. Galileo HAS correction quality analysis is summarized in the following steps:

1.

In the first step, the HAS corrections are decoded from the GSS E6B binary data and consolidated.

2.

Subsequently, the orbit and clock offset are obtained (as intermediate products) by applying the corresponding Galileo HAS corrections (2) to the values from the broadcast ephemerides (4). These are shown for orbit and clock offset in Equation (5b) and Equation (6b), respectively.

3.

In a second step these intermediate products (from Step 1 above) are subtracted from the corresponding reference values (3) after applying the appropriate coordinate transformations (see [9], pg. 41 and §7.2 for orbit correction and pg. 42 and §7.3 for clock correction) to ensure consistency. These are summarized in Equations (5a) and (6a) for orbit and clock, respectively. Although not explicitly described in this paper, a similar procedure is used to evaluate the code bias accuracy.

The instantaneous ranging error vector ($\delta {\mathit{r}}_c^s\left(t\right)$)

$$\begin{array}{cc}\hfill \delta {\mathit{r}}_c^s\left(t\right)& ={\mathit{r}}_{HAS}^s\left(t\right)-{\mathit{r}}_{REF}^s\left(t\right),\mathrm{with}\hfill \end{array}$$

(5a)

$$\begin{array}{cc}\hfill {\mathit{r}}_{HAS}^s\left(t\right)& ={\mathit{r}}_c^s\left(t\right)+{\mathit{r}}_{BRDC}^s\left(t\right)\hfill \end{array}$$

(5b)

to a given satellite indexed by superscript ’s’ and at an epoch ’t’ is computed using the HAS-corrected satellite position vector ${\mathit{r}}_{HAS}^s$, which results from applying the HAS orbit correction vector ${{\mathit{r}}_{\mathbf{c}}}^s$ to the respective satellite position ${\mathit{r}}_{BRDC}^s$ computed from broadcast ephemeris of the INAV navigation message using the necessary transformations, leading to a homogeneous coordinate reference system, as described in [9], pg. 41 and §7.2. It shall be noted that the Galileo HAS orbit corrections refer to the satellite’s ionosphere-free antenna phase center, as described in [9], pg. 41 and §7.1. Similarly, the instantaneous error

$$\begin{array}{cc}\hfill \delta {\widehat{\tau }}_c^s\left(t\right)& ={\tau }_{HAS}^s\left(t\right)-{\tau }_{REF}^s\left(t\right)\mathrm{with}\hfill \end{array}$$

(6a)

$$\begin{array}{cc}\hfill {\tau }_{HAS}^s\left(t\right)& ={\tau }_c^s\left(t\right)+\Delta t_{rel}^s+{\tau }_{BRDC}^s\left(t\right)\hfill \end{array}$$

(6b)

in the HAS-corrected clock offset ${\tau }_{HAS}\left(t\right)$ results by applying the Galileo HAS clock offset correction ${\tau }_c$ to the corresponding ionosphere-free broadcast clock offset ${\tau }_{BRD}$ of the INAV navigation message, as described in [9], pg. 42 and §7.3. Furthermore the transformation

$$\delta {\tau }_c^s\left(t\right)={\widehat{\tau }}_c^s\left(t\right)-\left[{\displaystyle \frac{1}{N_{sat}}}\sum _{s=1}^{N_{sat}}\delta {\widehat{\tau }}_c^s\left(t\right)\right]-\delta {\tilde{\tau }}_c^s\left(t\right)$$

(7)

is applied, where the instantaneous constellation average over $N_{sat}$ satellites as well as the daily average per satellite ${\tilde{\tau }}_c^s\left(t\right)$ are removed. It shall be noted that both the clock offset terms in Equation (6a) are defined with respect to Galileo System Time (GST), as described in the HAS ICD [9]. The terms in Equations (6a) and (6b) are ensured to be in consistent units, i.e., either in units of time (e.g., nanoseconds) or in units of range (e.g., meters). However, as shown in Equation (6b), the relativistic correction term $\Delta t_{rel}$ is excluded in the satellite clock offset calculation from broadcast ephemerides following [1] and added separately instead. This is also explained in the Galileo HAS ICD [9] in Equation (23) in §7.3. The application of Galileo HAS correction to broadcast ephemerides (orbit and clock offset), as shown in Equations (5b) and (6b), follows the Galileo HAS ICD [9], pg. 41–42 and §7.3–§7.4 for orbit and clock, respectively. For each supported signal type (see Galileo HAS SDD [3], pg. 23 and §2.4.1) denoted by superscript m and satellite indexed by superscript s at epoch t, the instantaneous error

$$\delta b_c^{s,m}\left(t\right)=b_{HAS}^{s,m}\left(t\right)-b_{REF}^{s,m}\left(t\right),$$

(8)

between the Galileo HAS-disseminated code bias $b_{HAS}$ and the corresponding reference bias $b_{REF}$ (e.g., obtained from reference service provider such as GRSP, see, e.g., [19]) is computed.

In the next step, we will obtain a measure of accuracy from the instantaneous error values obtained from Equations (5a)–(8). The Galileo HAS orbit correction accuracy is the statistical characterization evaluated as the instantaneous constellation average (computed as the RMS) of $\delta {\mathit{r}}_c\left(t\right)$ from Equation (5a) over a reference period of time T, as defined in [3]. The Galileo HAS clock correction accuracy is the statistical characterization evaluated as the instantaneous constellation average (computed as the RMS) of $\delta {\tau }_c^s\left(t\right)$ from Equation (6a) over T. The computed Galileo HAS orbit and clock correction accuracies for March 2024 are shown in Figure 1a and Figure 1b, respectively. Galileo HAS code bias accuracy for E1C and E5Q signals during March 2024 are shown in Figure 2a and Figure 2b, respectively. The corresponding correction accuracy for GPS and Galileo over the period from January to March 2024 is summarized in

Table 1. Summary of GPS LNAV and Galileo INAV orbit and clock correction accuracy ¹ (95%ile) as well as that of C1C code bias for January–March 2024.

Month	GPS Orbit Correction (cm)	GPS Clock Correction (cm)	GPS Code Bias (C1C) (cm)	Galileo Orbit Correction (cm)	Galileo Clock Correction (cm)	Galileo Code Bias (C1C) (cm)
January 2024	16.4	10.1	25.1	15.7	7.0	6.7
February 2024	15.3	10.0	20.7	15.9	7.3	7.9
March 2024	18.3	10.0	17.5	17.7	8.1	9.5

¹ See [3] pg. 28 Table 6 and §3.2.2 subject to the conditions defined in $C_{corr,acc}$.

. We have used the HAS corrections broadcast from SiS for the evaluation of the correction quality in this paper. For the scope of this work, we assume without loss of generality that the reference products in the set $x_{REF}$ shown in Equation (3), i.e., ${\mathit{r}}_{REF}$, ${\tau }_{REF}$ and $b_{REF}$, are “error-free” and are well characterized in the literature. We refer the readers to studies [8,20] regarding the SISRE of GPS and Galileo satellites.

3.2. Galileo HAS Correction Availability

The availability $A_{HAS,corr}$ of HAS corrections $c(t,g)$ (such that $c\in x$) at grid point g (with $g\in G$ the set of grid points) and at time epoch t is computed individually for the correction types in the set x defined in Equation (2), i.e., for orbit and clock offset correction as well as code bias, see Equation (10), by defining a “validity operator” V

$$V\left(c(t,g)\right)=\left\{\begin{array}{cc}1,\hfill & \mathrm{i}\mathrm{f} c(t,g) \mathrm{m}\mathrm{e}\mathrm{e}\mathrm{t}\mathrm{s} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{s} C_{corr,acc}\hfill \\ 0,\hfill & \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{w}\mathrm{i}\mathrm{s}\mathrm{e}.\hfill \end{array}\right.$$

(9)

that checks the Galileo HAS corrections for specific conditions and constraints, denoted $C_{corr,acc}$ and defined in Equation (1), as defined in [3] pg. 28, Table 7 in §3.2.4. Specifically, the operator V takes Galileo HAS corrections c (with $c\in x$) at time epoch t from grid point g (those in the service area for phase 1, see [3], pg. 26 and §3.1) as input and returns “1” when the corresponding correction $c(t,g)$ is valid and completely satisfies the constraints $C_{corr,acc}$. Further details are referred to see [3] pg. 28, §3.2.2 and Table 6. Accordingly for each correction in the correction type set x from Equation (2) and using Equation (9), we are able to compute an individual correction availability

$$\begin{array}{c}\hfill {\left[\begin{array}{ccc}{A}_{Orbit,HAS}\left(g\right)& A_{Clock,HAS}\left(g\right)& A_{CodeBias,HAS}\left(g\right)\end{array}\right]}^T=\\ \hfill {\left[{\displaystyle \frac{1}{N}}\sum _{t=0}^{N-1}V\left({\mathit{r}}_c(t,g)\right){\displaystyle \frac{1}{N}}\sum _{t=0}^{N-1}V\left({\tau }_c(t,g)\right){\displaystyle \frac{1}{N}}\sum _{t=0}^{N-1}V\left(b_c(t,g)\right)\right]}^T\end{array}$$

(10)

at grid point g over a reference period of time T, during which we assume a total of N samples, and further the computed availability is expressed as the percentage of time in which valid HAS corrections for the satellite/signal are available at each grid point g. (In general, there could be a different number of correction samples per satellite over a period of time due to receiver–satellite relative geometry and other operational reasons. In the scope of this paper, for simplicity we assume and use a common nominal number of correction samples across all satellites.) For more details, we refer to the reader to the HAS SDD [3], especially to Figure 6 therein. The full operational service availability of all three correction types is cumulatively evaluated epoch-wise

$$A_{HAS,corr}=\underset{g\in G}{min}\left({\displaystyle \frac{1}{N}}\sum _{t=0}^{N-1}\left[V\left({\mathit{r}}_c(t,g)\right)\wedge V\left(\delta t_c(t,g)\right))\wedge V\left(\delta b_c(t,g)\right)\right]\right)$$

(11)

over the set G of the grid points as the availability at the worst user location (WUL). The operator ∧ denotes logical conjunction, which returns 1 only when all the operands are 1, and otherwise returns 0. The measured HAS data broadcast availability is shown in Figure 3a,b. Specifically here, “35” in left sub-figure refers to a scenario with at least five HAS-corrected and valid (see [3], pg. 22 and §2.3) Galileo-only satellites in view and “38” in the right sub-figure refers to that with at least eight HAS-corrected and valid (see [3], pg. 22 and §2.3) GPS + Galileo satellites in view.

3.3. Galileo HAS Typical Positioning Accuracy

HAS user position error vector is defined as the instantaneous difference

$$\Delta {\mathit{r}}_{user}={\mathit{r}}_{user,GalileoHAS}-{\mathit{r}}_{user,REF}$$

(12)

between the estimated user position with Galileo HAS ${\mathit{r}}_{user,GalileoHAS}$ and the reference position of the user receiver ${\mathit{r}}_{user,REF}$ in the Galileo terrestrial reference frame (GTRF) at any time after convergence has been achieved, with the respective position vectors defined with the same datum definition or coordinate reference frame. The user position errors are commonly projected into the horizontal ($\Delta {\mathit{r}}_{user,Horz}$) and vertical ($\Delta {\mathit{r}}_{user,Vert}$) dimensions using orthogonal decomposition $\Delta {\mathit{r}}_{user}(t,g)={\left[\begin{array}{ccc}\Delta E(t,g)& \Delta N(t,g)& \Delta U(t,g)\end{array}\right]}^T$ in a local-level topocentric coordinate system such that

$$\Delta {\mathit{r}}_{user}(t,g)={\left[\begin{array}{cc}\Delta r_{user,Horz}(t,g)& \Delta r_{user,Vert}(t,g)\end{array}\right]}^T$$

(13)

where $\Delta r_{user}(t,g)=\parallel \Delta {\mathit{r}}_{user}(t,g)\parallel$ is the magnitude of the position error vector, $\parallel ·\parallel$ denotes the vector L2 norm operator and ${\left[\begin{array}{ccc}{\mathit{u}}_E& {\mathit{u}}_N& {\mathit{u}}_U\end{array}\right]}^T$ denotes the topocentric coordinate system unit vector along the dimensions east (E), north (N) and up (U), respectively. (Strictly speaking, the unit vector is also time- and space-varying, but for the sake readability, the time and grid point indices are dropped from the unit vectors.) The HAS horizontal and vertical positioning accuracy are the statistical characterization of the respective horizontal and vertical position error (13) over a reference period of time T, during which there are a total of Q estimated positioning solution samples (Only the samples after convergence are considered for availability computation. In general, there could be a different number of samples per GSS station over a period of time due to operational reasons. In the scope of this paper, for simplicity we assume and use a common nominal number of positioning solution samples across all stations.). In order to characterize the availability of positioning accuracy from Equations (12) and (13), we define

$$W\left(\Delta {\mathit{r}}_{user}(t,g)\right)=\left\{\begin{array}{cc}1,\hfill & \mathrm{i}\mathrm{f} \Delta {\mathit{r}}_{user}(t,g) \mathrm{satisfies} \mathrm{contraints} \mathrm{in} C_{pos,acc,GPS+Gal}.\hfill \\ 0,\hfill & \mathrm{otherwise}.\hfill \end{array}\right.$$

(14)

which takes the position error $\Delta {\mathit{r}}_{user}$ at time epoch t from grid point g (those in the service area for phase 1, see [3], pg. 26 and §3.1) and compares it against $C_{pos,acc,GPS+Gal}$, which is one set of conditions and constraints from (1), within which the HAS typical positioning performance is characterized, see [3], pg. 40, Appendix E.2. Using Equations (13) and (14), we compute

$$A_{pos}=\underset{g\in GSS}{max}\left\{{\displaystyle \frac{1}{Q}}\sum _{t=0}^{Q-1}W(\Delta r_{user}(t,g))\right\}$$

(15)

which is the HAS-enabled positioning availability as the worst case value across the GSS of the individual position solution availability. The horizontal and vertical position accuracy as well as their distribution (E1 + E5a) over selected GSSs from January to March 2024 are shown in Figure 4.

4. Summary

The Galileo HAS SiS performance has been excellent in terms of availability and correction quality, in compliance with MPLs defined in the SDD [3]. User positioning performance with a Galileo HAS-enabled receiver (subject to the receiver assumptions made in the HAS SDD [3], pg. 24 and §2.4) with the signal combinations (listed in the SDD, see [3] pg. 23 and §2.4.3) also meets the typical positioning performance (see HAS SDD [3], Appendix E). Monthly HAS correction accuracy and availability has been consistently above the MPL target values for correction accuracy since the service declaration of Galileo HAS in January 2023. The results presented in this paper are consistent with the findings of Galileo HAS SiS performance reported in [20,21]. The positioning performance has been determined with the HAS performance characterization user algorithm (HAS-UA). (The reader is referred to the disclaimers in the SDD [3] regarding the assumptions made for the positioning performance and the assumptions of the underlying receiver type used.) The performance is conditioned upon assumptions substantiated in the Galileo HAS SDD (see [3] pg. 23, §2.3) regarding the use of the HAS corrections and the HAS performance characterization user algorithm (HAS-UA), see [3], pg. 38 and Appendix D. The impact of certain types of errors, as shown in the Galileo HAS SDD [3] pg. 25 and §2.5, are not considered in the computation of the MPLs and typical performance. The operational details and challenges in data pre-processing or treatment of specific operational challenges in near real time are not in the scope of this paper.