# Sample-Wise Aiding in GPS/INS Ultra-Tight Integration for High-Dynamic, High-Precision Tracking
## 4 Test Results and Discussion  
### Test Setups and Scenarios  
The scalar tracking based GPS/INS ultra-tight integration has been implemented in our software receiver. Both the traditional Doppler aiding and the sample-wise aiding with spline interpolation are incorporated into the receiver PLL and DLL (delay locked loop), and their tracking performance in high dynamic scenarios can be tested by using our digital IF GPS signal simulator. The accurate INS Doppler estimates needed in the tests can simply be obtained from the user trajectory provided by the simulator and the satellite ephemerides. Three factors have been considered in the design of dynamic scenarios for the tests: (1) to ensure that the receiver achieves steady state tracking before the aiding begins, no VAJ jumps are included in the trajectory, because carrier tracking loops are sensitive to dynamic jumps. For example, third-order loops are sensitive to jerk jumps; (2) the trajectory should be controlled within a limited spatial range; and (3) severe high-order dynamics should be included. As a result the following sinusoidal user trajectory in the height direction is constructed:  
\[h=h_{0}+D\left[1-\cos\left(\omega t\right)\right]\]  
where, \(h\) is the height of the receiver antenna phase center, \(h_{0}\) is the initial height, \(D\) is the amplitude of the sinusoidal trajectory, and \(\omega\) is its angular frequency. In the following tests, we chose \(\omega=1\) rad/s to simplify the control and calculation of dynamic parameters of different orders. For example, if \(D=500\) m, then the maximum velocity, acceleration, and jerk are \(500\) m/s, \(500\) m/s\({}^{2}\), and \(500\) m/s\({}^{3}\), respectively. With a satellite elevation angle of \(\alpha=28.67^{\circ}\), the LOS velocity is:  
\[V_{LOS}=\left(D\text{sin}\alpha\right)\omega\text{sin}\left(\omega t\right) \approx 239.88\text{ sin}\left(t\right) \tag{17}\]  
The receiver first tracks the high dynamic signals using a third-order PLL, and then changes to a second-order PLL aided by _a priori_ known carrier Doppler after decoding the navigation message. Meanwhile the reception time (in GPS time) of each individual sample point can be obtained by using the single-SV (satellite vehicle) timing method proposed in [30]. For high dynamic scenarios, the known user trajectory rather than a static user location is utilized in the timing process. In this way the time alignment necessary for the aiding can be achieved. \begin{table}
\begin{tabular}{c c} \hline
**Partitions of \(T_{a}\)** & **Features of Aiding Effect** \\ \hline \(T_{a}<T_{I}\left(\omega,R_{s}\right)\) & \(C_{a}\left(\omega T_{s}\right)\approx 0.5\,\omega T_{s}\), \(\omega T_{s}\) determined, independent of \(T_{a}\) and \\  & interpolation techniques \\ \(T_{m}\left(\omega,R_{s}\right)\leq T_{a}<T_{m}\left(\omega,R_{s}\right)\) & decreasing as either \(T_{a}\) or \(T_{s}\) decreases \\ \(T_{m}\left(\omega,R_{s}\right)\leq T_{a}<T_{u}\left(\omega\right)\) & \(\omega T_{a}\) determined, independent of \(T_{s}\), improved by advanced interpolation \\  & technique significantly (at kind of exponential rate) \\ \(T_{a}\geq T_{u}\left(\omega\right)\) & No much improvement even with smaller \(T_{s}\) and advanced interpolation \\ \hline \end{tabular}
\end{table} 
Table 1: Four regions of sample-wise aiding in terms of \(T_{a}\). The loop parameters recommended in Tables 5.6 in [2] are adopted in the tests. In addition, the PLL is configured with a loop bandwidth of 15 Hz and a loop update interval of 1 ms, while the DLL taking a 1 Hz bandwidth and a 20 ms loop update interval. For traditional aiding, the external Doppler data are injected to the PLL every 1 ms, and to the DLL every 20 ms whereas, for the sample-wise aiding, the receiver first interpolates the aiding data using cubic splines from 1000 Hz to the sampling rate, and then injects the interpolated carrier Doppler and code Doppler values into the carrier NCO and the code NCO, respectively.