Efficient Cost-Effective Static-PPP Using Mixed GPS/Glonass Single-Frequency Observations (KSA)

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Figure 9.

Static-PPP accuracy variation with observation duration from single-frequency observations (active ionosphere) (GPS day 21,820) (station NB03)

Duration of observations	GLONASS			GPS			Mixed GPS/GLONASS
	Lat. (m)	Long. (m)	Ellip. height (m)	Lat. (m)	Long. (m)	Ellip. height (m)	Lat. (m)	Long. (m)	Ellip. height (m)
15 min	2.551	3.361	8.322	1.404	1.384	3.096	1.336	1.336	3.117
30 min	2.007	2.594	2.594	1.172	1.384	2.180	1.132	1.336	2.259
1 h	1.200	1.725	2.844	0.777	1.231	1.273	0.642	0.981	1.150
2 h	0.702	0.816	1.607	0.331	0.678	0.628	0.297	0.507	0.577
4 h	0.310	0.376	0.726	0.155	0.367	0.386	0.129	0.242	0.309
6 h	0.203	0.356	0.490	0.106	0.317	0.272	0.091	0.216	0.224
8 h	0.125	0.306	0.352	0.107	0.322	0.255	0.088	0.224	0.211
10 h	0.137	0.295	0.384	0.119	0.314	0.284	0.094	0.213	0.231
12 h	0.145	0.275	0.400	0.135	0.324	0.315	0.100	0.204	0.247
14 h	0.137	0.266	0.373	0.140	0.309	0.329	0.098	0.196	0.243
16 h	0.125	0.258	0.337	0.130	0.269	0.307	0.091	0.189	0.222
18 h	0.128	0.254	0.337	0.117	0.249	0.282	0.088	0.182	0.212
20 h	0.122	0.233	0.317	0.106	0.229	0.256	0.081	0.170	0.195
22 h	0.113	0.220	0.293	0.099	0.208	0.240	0.075	0.158	0.181
24 h	0.104	0.204	0.269	0.090	0.187	0.219	0.070	0.147	0.169

The characteristics of the two tested days related to ionosphere activity (SILSO, 2021; STCE, 2021; GFZ, 2021)

Ionosphere state of activity	Date	GPS day	SSN	VTEC (TECu)	Kp	F10.7obs
Quiet	03-01-2021	21,390	0	15	0.333	80.4
Active	31-10-2021	21,820	68	29	4	102.7

Static-PPP accuracy variation with observation duration from single-frequency observations (active ionosphere) (GPS day 21,820) (station RY99)

Duration of observations	GLONASS			GPS			Mixed GPS/GLONASS
	Lat. (m)	Long. (m)	Ellip. height (m)	Lat. (m)	Long. (m)	Ellip. height (m)	Lat. (m)	Long. (m)	Ellip. height (m)
15 min	2.492	2.695	8.157	1.274	1.509	2.898	1.290	1.429	3.246
30 min	1.774	2.220	4.843	1.608	1.509	2.136	1.081	1.431	2.374
1 h	1.451	1.974	3.308	0.766	1.360	1.277	0.649	1.061	1.148
2 h	0.676	0.839	1.526	0.332	0.658	0.635	0.299	0.516	0.588
4 h	0.382	0.518	0.790	0.146	0.320	0.409	0.130	0.252	0.342
6 h	0.224	0.494	0.583	0.123	0.330	0.359	0.105	0.247	0.283
8 h	0.202	0.502	0.587	0.148	0.410	0.411	0.122	0.305	0.319
10 h	0.225	0.477	0.646	0.215	0.534	0.579	0.155	0.342	0.414
12 h	0.261	0.489	0.728	0.231	0.518	0.604	0.172	0.345	0.453
14 h	0.256	0.489	0.712	0.243	0.502	0.641	0.177	0.341	0.464
16 h	0.253	0.476	0.691	0.225	0.443	0.600	0.169	0.321	0.435
18 h	0.249	0.463	0.670	0.216	0.408	0.572	0.164	0.311	0.415
20 h	0.245	0.453	0.653	0.193	0.367	0.515	0.151	0.297	0.381
22 h	0.236	0.439	0.619	0.181	0.333	0.476	0.142	0.282	0.352
24 h	0.210	0.391	0.545	0.161	0.303	0.423	0.129	0.258	0.320

Static-PPP accuracy variation with observation duration from single-frequency observations (active ionosphere) (GPS day 21,820) (station NJ04)

Duration of observations	GLONASS			GPS			Mixed GPS/GLONASS
	Lat. (m)	Long. (m)	Ellip. height (m)	Lat. (m)	Long. (m)	Ellip. height (m)	Lat. (m)	Long. (m)	Ellip. height (m)
15 min	2.619	2.649	7.834	1.808	2.182	4.205	1.588	1.763	4.009
30 min	1.983	2.437	4.855	1.482	2.051	3.254	1.189	1.568	2.704
1 h	1.266	1.638	2.479	0.845	1.473	1.554	0.702	1.085	1.312
2 h	0.629	0.925	1.413	0.388	0.791	0.771	0.330	0.600	0.680
4 h	0.345	0.534	0.767	0.160	0.398	0.469	0.143	0.305	0.389
6 h	0.212	0.496	0.545	0.177	0.493	0.534	0.137	0.332	0.368
8 h	0.177	0.475	0.481	0.165	0.486	0.484	0.126	0.338	0.334
10 h	0.160	0.374	0.432	0.151	0.444	0.434	0.115	0.286	0.305
12 h	0.160	0.339	0.437	0.141	0.391	0.397	0.109	0.255	0.294
14 h	0.145	0.329	0.411	0.152	0.392	0.428	0.107	0.251	0.295
16 h	0.147	0.329	0.412	0.143	0.365	0.410	0.107	0.250	0.288
18 h	0.147	0.327	0.401	0.136	0.338	0.383	0.105	0.247	0.278
20 h	0.150	0.332	0.401	0.125	0.314	0.352	0.100	0.242	0.261
22 h	0.144	0.322	0.374	0.118	0.286	0.325	0.095	0.229	0.242
24 h	0.130	0.290	0.345	0.105	0.252	0.289	0.086	0.208	0.223

Static-PPP accuracy variation comparing true coordinates for different observation duration from single-frequency mixed GPS/GLONASS observations (active ionosphere) (GPS day 21,820) for the three tested stations

Duration of observations	Station (NB03)			Station (RY99)			Station (NJ04)
	Lat. (m)	Long. (m)	Ellip. height (m)	Lat. (m)	Long. (m)	Ellip. height (m)	Lat. (m)	Long. (m)	Ellip. height (m)
15 min	0.166	−0.048	−0.718	−0.74	0.614	−0.403	0.252	0.018	−0.834
30 min	0.153	−0.048	−0.55	−0.508	0.556	−0.072	0.161	−0.02	−0.612
1 h	0.01	−0.026	−0.231	−0.201	0.259	−0.123	0.031	−0.039	−0.232
2 h	−0.014	−0.012	−0.176	−0.084	0.032	−0.068	0.02	−0.115	−0.097
4 h	−0.017	−0.057	−0.087	−0.011	−0.019	−0.126	−0.002	−0.046	−0.069
6 h	−0.026	−0.06	−0.065	−0.017	−0.033	−0.11	−0.004	−0.049	−0.094
8 h	−0.025	−0.046	−0.05	−0.021	−0.023	−0.088	0.009	−0.033	−0.102
10 h	−0.022	−0.065	−0.056	−0.025	−0.05	−0.069	0.006	−0.028	−0.095
12 h	−0.016	−0.087	−0.038	0.001	−0.155	−0.081	0.005	−0.028	−0.087
14 h	−0.015	−0.079	−0.034	0.015	−0.117	−0.125	0.01	−0.031	−0.091
16 h	−0.018	−0.074	−0.034	0.017	0.007	−0.087	0.008	−0.036	−0.075
18 h	−0.026	−0.073	−0.021	0.018	−0.047	−0.086	0.005	−0.023	−0.066
20 h	−0.027	−0.07	−0.03	0.014	−0.051	−0.117	0.007	−0.046	−0.068
22 h	−0.024	−0.075	−0.038	0.015	−0.074	−0.11	0.008	−0.009	−0.065
24 h	−0.024	−0.079	−0.04	0.011	−0.089	−0.093	0.006	−0.015	−0.058

Tested stations’ geographic coordinates

KSA-CORS station	Latitude (deg. min. sec)	Longitude (deg. min. sec)	Ellipsoidal height (m)
NB03	N 32° 08′ 18.30054″	E 39° 11′ 53.66771″	960.417
RY99	N 24° 40′ 26.82870″	E 46° 41′ 39.29147″	644.579
NJ04	N 17° 28′ 28.02108″	E 47° 05′ 14.51550″	716.362

Static-PPP accuracy variation with observation duration from single-frequency observations (quiet ionosphere) (GPS day 21,390) (station NJ04)

Duration of observations	GLONASS			GPS			Mixed GPS/GLONASS
	Lat. (m)	Long. (m)	Ellip. height (m)	Lat. (m)	Long. (m)	Ellip. height (m)	Lat. (m)	Long. (m)	Ellip. height (m)
15 min	3.987	6.421	9.192	1.050	1.404	2.388	0.977	1.375	2.221
30 min	2.378	4.863	4.491	0.808	1.404	1.304	0.744	1.375	1.315
1 h	1.001	3.324	1.938	0.564	1.404	0.968	0.513	1.375	0.933
2 h	0.355	1.952	0.978	0.298	1.097	0.858	0.220	0.811	0.580
4 h	0.278	1.203	0.755	0.138	0.488	0.389	0.121	0.442	0.337
6 h	0.215	0.827	0.522	0.133	0.429	0.359	0.113	0.383	0.296
8 h	0.182	0.511	0.479	0.105	0.331	0.286	0.089	0.259	0.245
10 h	0.175	0.478	0.452	0.109	0.302	0.303	0.090	0.242	0.249
12 h	0.169	0.533	0.455	0.104	0.285	0.293	0.083	0.230	0.231
14 h	0.163	0.448	0.446	0.094	0.253	0.258	0.075	0.198	0.210
16 h	0.173	0.415	0.475	0.080	0.232	0.228	0.068	0.180	0.191
18 h	0.155	0.400	0.424	0.074	0.218	0.212	0.062	0.170	0.174
20 h	0.142	0.395	0.401	0.069	0.202	0.194	0.057	0.161	0.160
22 h	0.133	0.349	0.373	0.065	0.180	0.181	0.053	0.143	0.149
24 h	0.123	0.290	0.347	0.060	0.160	0.169	0.049	0.124	0.139

Static-PPP accuracy variation with observation duration from single-frequency observations (quiet ionosphere) (GPS day 21,390) (station NB03)

Duration of observations	GLONASS			GPS			Mixed GPS/GLONASS
	Lat. (m)	Long. (m)	Ellip. height (m)	Lat. (m)	Long. (m)	Ellip. height (m)	Lat. (m)	Long. (m)	Ellip. height (m)
15 min	3.789	4.922	7.551	1.313	1.437	2.061	1.190	1.371	2.017
30 min	2.502	4.720	4.432	0.856	1.437	1.241	0.785	1.371	1.278
1 h	1.217	3.338	1.859	0.528	1.437	0.736	0.508	1.371	0.843
2 h	0.489	2.035	0.870	0.345	1.366	0.704	0.224	0.812	0.453
4 h	0.251	1.032	0.516	0.142	0.481	0.292	0.121	0.424	0.250
6 h	0.207	0.650	0.424	0.102	0.296	0.234	0.091	0.269	0.204
8 h	0.174	0.333	0.395	0.089	0.243	0.210	0.079	0.196	0.185
10 h	0.167	0.316	0.362	0.104	0.238	0.234	0.089	0.191	0.198
12 h	0.148	0.310	0.332	0.099	0.222	0.220	0.083	0.181	0.184
14 h	0.133	0.262	0.304	0.086	0.201	0.193	0.073	0.160	0.164
16 h	0.129	0.236	0.293	0.072	0.186	0.168	0.064	0.146	0.146
18 h	0.110	0.217	0.264	0.064	0.165	0.151	0.056	0.132	0.132
20 h	0.091	0.209	0.233	0.059	0.149	0.139	0.050	0.122	0.121
22 h	0.085	0.189	0.220	0.057	0.132	0.132	0.047	0.109	0.114
24 h	0.083	0.171	0.213	0.053	0.121	0.123	0.045	0.099	0.107

Static-PPP accuracy variation comparing true coordinates for different observation duration from single-frequency mixed GPS/GLONASS observations (quiet ionosphere) (GPS day 21,390) for the three tested stations

Duration of observations	Station (NB03)			Station (RY99)			Station (NJ04)
	Lat. (m)	Long. (m)	Ellip. height (m)	Lat. (m)	Long. (m)	Ellip. height (m)	Lat. (m)	Long. (m)	Ellip. height (m)
15 min	−0.052	−0.329	−0.06	−0.132	0.001	−0.19	−0.266	−0.404	−0.149
30 min	−0.064	−0.338	−0.006	−0.008	−0.136	−0.327	−0.129	−0.394	−0.107
1 h	−0.059	−0.232	−0.15	−0.045	−0.008	−0.261	−0.107	−0.017	0.045
2 h	−0.013	−0.179	−0.051	0.001	−0.13	−0.14	−0.032	−0.096	−0.058
4 h	−0.005	−0.063	−0.02	0.014	−0.036	−0.07	−0.005	−0.016	−0.002
6 h	−0.004	−0.033	−0.025	0.005	−0.023	−0.059	−0.008	−0.034	−0.032
8 h	−0.007	−0.028	−0.037	0	−0.021	−0.066	−0.004	−0.026	−0.012
10 h	−0.009	−0.035	−0.051	−0.004	−0.023	−0.076	−0.005	−0.034	−0.007
12 h	−0.012	−0.036	−0.053	−0.007	−0.02	−0.07	−0.003	−0.042	0.002
14 h	−0.015	−0.034	−0.048	−0.01	−0.013	−0.072	−0.003	−0.048	0.003
16 h	−0.014	−0.029	−0.045	−0.008	−0.012	−0.074	−0.003	−0.045	0.006
18 h	−0.016	−0.017	−0.04	−0.009	−0.003	−0.072	−0.003	−0.036	0.006
20 h	−0.016	−0.014	−0.035	−0.007	−0.015	−0.065	0	−0.032	0.007
22 h	−0.016	−0.011	−0.036	−0.008	−0.014	−0.07	0.002	−0.02	0.006
24 h	−0.015	−0.01	−0.038	−0.006	−0.014	−0.069	0.001	−0.016	0.004

Static-PPP accuracy variation with observation duration from single-frequency observations (quiet ionosphere) (GPS day 21,390) (station RY99)

Duration of observations	GLONASS			GPS			Mixed GPS/GLONASS
	Lat. (m)	Long. (m)	Ellip. height (m)	Lat. (m)	Long. (m)	Ellip. height (m)	Lat. (m)	Long. (m)	Ellip. height (m)
	15 min	4.171	6.356	8.762	1.151	1.399	2.112	1.070	1.377	2.052
	30 min	2.339	4.984	4.448	0.855	1.399	1.254	0.779	1.377	1.317
	1 h	0.984	3.294	1.895	0.478	1.399	0.801	0.472	1.377	0.870
	2 h	0.372	2.037	0.921	0.344	1.399	0.943	0.225	0.899	0.577
	4 h	0.258	1.117	0.662	0.144	0.492	0.379	0.124	0.439	0.323
	6 h	0.232	0.785	0.559	0.110	0.334	0.285	0.098	0.307	0.252
	8 h	0.200	0.498	0.518	0.123	0.351	0.317	0.100	0.257	0.265
10 h	0.247	0.590	0.622	0.175	0.435	0.443	0.135	0.317	0.345
12 h	0.224	0.596	0.577	0.166	0.391	0.417	0.125	0.297	0.320
14 h	0.212	0.491	0.558	0.142	0.343	0.352	0.108	0.247	0.279
16 h	0.217	0.446	0.570	0.118	0.311	0.302	0.095	0.221	0.247
18 h	0.186	0.424	0.500	0.104	0.288	0.271	0.082	0.204	0.216
20 h	0.160	0.394	0.447	0.095	0.266	0.245	0.072	0.188	0.193
22 h	0.151	0.347	0.423	0.088	0.237	0.227	0.067	0.165	0.179
24 h	0.142	0.302	0.397	0.081	0.213	0.211	0.062	0.146	0.167

Average number of visible satellites and average PDOP values for tested stations on tested days; GPS days 21,390 and 21,820

Date	Station	System	Average no. visible satellites	Average PDOP
(03-01-2021) (quiet ionosphere)	NB03	GPS	8	1.888
		GLONASS	6	2.765
		GPS/GLONASS	15	1.388
	RY99	GPS	8	1.970
		GLONASS	6	5.003
		GPS/GLONASS	15	1.432
	NJ04	GPS	9	1.957
		GLONASS	6	2.721
		GPS/GLONASS	15	1.415
(31-10-2021) (active ionosphere)	NB03	GPS	8	2.002
		GLONASS	6	3.527
		GPS/GLONASS	15	1.439
	RY99	GPS	8	1.947
		GLONASS	6	4.250
		GPS/GLONASS	15	1.436
	NJ04	GPS	9	1.921
		GLONASS	6	4.123
		GPS/GLONASS	15	1.418