# Cloud-Based Single-Frequency Snapshot RTK Positioning
## 2 Methodology
### SRTK Performance
#### 2.4.2 Parameters of Interest  
The relationships between the parameters of interest are presented in Figure 5. The main purpose of this work is to explore the impact of the following 3 parameters on the SRTK performance: snapshot signal bandwidth, integration time, and baseline distance, which are shaded in red color in Figure 5.  
Starting from these 3 parameters, we can explore on the left and right directions to find their impacts on the SRTK fix rate and the snapshot data size, respectively.  
Looking leftwards, we can see first of all that the observables noise level of the rover is determined by the signal bandwidth and the integration time [2; 33; 34], while the baseline distance impacts the magnitude of the atmosphere delay variation between the rover and the base. The rover observable noise terms can be evaluated by their Cramer-Rao Bounds (CRBs), which are proportional to \(\propto\frac{1}{(C/N_{0})BT_{\text{int}}}\) and \(\propto\frac{1}{(C/N_{0})BT_{\text{int}}}\) for, respectively, the code delay and carrier phase observables [11; 35]. Here the \(T_{\text{int}}\), \(B\) and \(C/N_{0}\) variables denote the integration time, signal bandwidth and carrier-to-noise-density-ratio, respectively. It can be seen that both code delay and carrier phase errors decreases when the integration time \(T_{\text{int}}\) increases, while the bandwidth \(B\) only influences the code delay. The rover observable noise, together with other error terms such as reference receiver measurement noise and satellite position errors cause by timing inaccuracies are added up to form the DD measurement errors. Note that the atmosphere delay variations are also lumped into such errors since a simple DD measurement model is used in this research. The magnitude of the DD measurement errors directly decide the LRF value and the final fix rate. The RTK algorithm configuration also plays a role in the computation of fix rate but, since it is out of scope of this work, we applied the same configuration for all the experiments performed to disregard its impact.  
Looking rightwards, the bandwidth puts a constraint on the signal sampling rate in order to avoid the signal aliasing problems, that is, we must set the sampling rate no lower than the Nyquist rate, which is usually twice the bandwidth [36]. On the other hand, the integration time sets a minimum value of the total duration of the captured signal. These two parameters, together with the quantization factor, directly determine the snapshot data size with:  
\[S=2\cdot Q\times Fs\times T+A, \tag{18}\]  
where:  
* \(S\) is the size of the snapshot data, in bits;
* \(Q\) represtns the constant quantization parameter, in bits per sample;
* \(Fs\) stands for the sampling rate, in Hz;
* \(T\) is the total integration time, in \(s\);
* \(A\) stands for the size of additional data, in bits.  
The additional data size term \(A\) is usually very small (less than 1 kB) since only very limited amount of metadata is needed along side the snapshot signal data bits, such as  
Figure 5: Relationships between the parameters of interest.  
rover receiver ID. The multiplication by the constant 2 is due to the I and Q streams of the snapshot signal.  
As can be seen, changes to the 3 main parameters influence both the fix rate and the snapshot data size at the same time. The following experiments further explore the relationships between these parameters of interest.