## 5 Experiment Design and Test Results
### Positioning Solution  
The final weekly empirical stochastic model was evaluated based on solution results of the positioning model presented in Section 4. Positioning was performed for short baseline WUT1-WUT2 using 24-h data on a DOY 180, year 2018 which did not coincide with the data used to estimate the stochastic model. Raw 1 Hz code and carrier-phase measurement data was recorded using Septentrio PolaRx5 receivers connected to a Leica Choke-Ring AT504 antenna at WUT1 and a Septentrio PolaNt ChokeRing B3/E6 at WUT2. The ionosphere- and troposphere-fixed model, which assume that both delays are negligible for such a short baseline, was derived in a kinematic mode with an interval of 1 s, so 86,400 solutions were obtained in total. Although the short baseline observations are burdened with the multipath, which is not included in the positioning model, such a selection of test data allows estimating the effectiveness of the developed empirical stochastic model in real conditions that are never free from this phenomenon. The modified Kalman Filter was used to determine the receiver position as well as float carrier-phase ambiguity. The parameters for tuning KF were set as follows: the variance of process noise was set to 1 m\({}^{2}\)/s for position components, nine cycle\({}^{2}\)/s for carrier-phase ambiguity as an initial value and 10\({}^{-6}\) cycle\({}^{2}\)/s for subsequent epochs. The tuning parameters were adopted based on preliminary tests, assuming: kinematic solution for a receiver with the very low dynamics, large initial value of ambiguity process noise and a very low value for subsequent epochs [93; 94]. The AR was performed applying the LAMBDA method [95]; the correctness of AR was verified in comparison with the true values computed based on the known coordinates of the WUT1 and WUT2 stations (called empirical success rate probability) as well as using a validation test based on theoretical probability of a success rate (its lower bound approximation) with a threshold not exceeding 0.99 [96]. The positioning model solution was performed in continuous mode, and the KF was reset to initial tuning parameters for ambiguity when cycle slips occurred or for all parameters when a number of estimated carrier-phase ambiguities dropped below six. The impact of the developed empirical stochastic model on the positioning model solution was verified by comparing the results of the AR and the position estimation for several data processing scenarios: (a) the empirical model (denoted as \"C/N\({}_{0}\)\" model in Tables 4-8) vs. standard satellite elevation-dependent variance model (denoted as \"Elev.\") for which the parameters \(\sigma_{L}=0.003\) m +0.002 m/sin \(e\) for carrier phase measurement and \(\sigma_{C}=100\cdot\sigma_{L}\) for code measurement were adopted uniformly for all GNSS systems and signals; (b) the impact of using only variance parameters in both tested stochastic models vs. including also the determined time- and cross-correlation parameters; (c) the empirical models distinguishing between satellites blocks (denoted as \"C/N\({}_{0}\)(b)\") vs. the unified model for all observations of a given signal; (d) using different combinations of GNSS measurements--single system GPS and GLONASS, dual system solution GPS + Galileo, GPS + BeiDou as well as Multi-GNSS approach using all systems. In all tested solutions, the observation cut-off mask was set to 5\({}^{\circ}\) in case of using elevation-dependent stochastic  
Figure 23: Empirical carrier-phase tracking errors for GNSS signals for a receiver Septentrio PolaRx5. model, and the 5 th percentile of C/N\({}_{0}\) in case of the empirical model, which corresponded to a very similar number of observations in both cases. Table 4 presents the model solution results for tested scenarios for GPS observations. The AR outcomes are presented as the empirical success rate probability (expressed in percent) with the number of epochs (in parentheses) for which an incorrect AR was obtained.