# Initial Assessment of the LEO Based Navigation Signal Augmentation System from Luojia-1A Satellite
## 4 In-Orbit Performance Evaluation Results
### Handling Error Sources of the Ranging Measurements  
There are a few LEO navigation constellations, such as the U.S. Transit system [64] and the Russian Parus system [65]. All of them are Doppler based positioning systems, so the error sources are simpler than the range based navigation system. On the other hand, the error sources for the LEO based ranging measurement are not exactly the same as the medium/geo-synchronized earth orbit navigation satellites. With the Luojia-1A pseudorange measurements and carrier phase measurements, their error sources are classified into three types: satellite specific, the propagation path specific and the receiver specific [66]. The satellite specific error includes the orbit error, the satellite clock error, the relativistic effect, the satellite hardware delay bias, the satellite antenna phase center offset (PCO), phase center variation (PCV), solar radiation error, albedo error, attitude error and phase windup error, etc. The propagation path specified error source includes the troposphere delay, the ionosphere delay, and the multipath error. The receiver specific error includes the receiving antenna PCO, PCV, the receiver clock bias and the receiver hardware biases. The uniqueness of the LEO error sources characteristics lies in the following aspects:  
1. The satellite hardware delay bias. Since the time system of the Luojia-1A satellite is aligned to the GPS time. The onboard GNSS receiver can only provide the time of receiving, rather than transmitting. The time consumption of baseband processing, position/velocity/timing computation, the ranging signal generation and the circuit delays all contribute to the hardware delays. Although some of the delays are compensated based on laboratory calibration, it still varies due to the complex space environment and temperature variation. Therefore, how to calibrate the hardware biases of the transmitter is challenging. 2. The relativistic effect. Due to low orbit height, the relativistic effect calculation method for the medium earth orbiters and GEOs is not directly applicable to the LEOs since the Earth cannot be treated as a mass point in this case. For the LEO, the J2 term of the gravity field has to be considered during the relativistic correction calculation [67; 68]. The average term of relativistic effect is not compensated in the ground test, so a new relativistic model should be developed for LEO navigation augmentation satellites. Figure 11: The observation noise structure of Luojia-1A pseudorange and carrier phase measurement evaluated via the geometry-free combination. The satellite phase center offset. For the GNSS satellites, the PCO refers to the phase center offset with respect to the mass center. For Luojia-1A satellite, it refers to the offset between the \(-\)z receiving antenna and the transmitting antenna installed on the +z side. The offset for Luojia-1A is a few decimeters. The transmitting beam angle of Luojia-1A satellite is also not the same as the GNSS. For the MEOs, the beam width is \(14.6^{\circ}\) to cover the earth [69]. While the beam width has to be up to \(60^{\circ}\) for Luojia-1A satellite to achieves maximum service coverage. Hence the satellite PCV also has different characteristics. 4. The ionosphere delay of the ranging signals. Luojia-1A satellite is moving in the F2 layer of the ionosphere, while most GNSS satellites are located above the ionosphere. Hence the empirical ionosphere delay model based on GPS observations, such as the Klobuchar model may not work well for the Luojia-1A ranging signals. Since there is only one such type LEO satellite in current operation, it is not possible to model all the errors considering some of them are not separable. For example, the satellite clock error and the receiver clock bias are not separable for only one satellite scenario, but this problem can be dealt with the datum transformation method. With properly defined clock datum, the receiver clock bias estimation is still possible.