## 3 Tracking Measurement Overview
### TDRS Measurements
#### 3.2.2 BRTS Measurements  
The BRTS system is designed to provide highly accurate range and Doppler measurements necessary for determining the TDRS spacecraft's orbit. The BRTS consists of ground-based transponders that are treated as if they were TDRS user spacecraft. Since their positions are precisely known, by tracking the BRTS transponders the trajectory of the TDRS can be determined with great accuracy.  
Figure 3 illustrates the tracking configuration of the BRTS measurements. The BRTS employs radio signals to measure the distance between two points, and in this setup, the signals in the same round-trip link are generated by the same atomic ground clock. This coherence in signal generation eliminates the effects of clock phenomenology and relativity, ensuring that the measurements obtained are accurate and reliable. As such, the four-legged range and five-legged Doppler measurements are two-way coherent measurements.  
The measurement of the range utilizing four-legged methodology entails measuring the duration of propagation for a radio signal traveling from a transmitter (Node #1) to a receiver (Node #5); see Figure 3. Specifically, the process involves the emission of a signal from the ground station (Node #1) to the TDRS satellite (Node #2), which is subsequently retransmitted by the satellite's transponder to the BRTS transponder (Node #3). After receiving the signal, the BRTS transponder sends it back to the TDRS (Node #4), which ultimately forwards it to the ground station (Node #5).  
The Doppler measurement, on the other hand, employs a five-legged methodology to account for the frequency drift of a signal as a consequence of the relative motion between the transmitters and receivers. The BRTS Doppler measurement method is established by creating two signal pathways. The first signal path starts from the ground station (Node #1) and is transmitted to the TDRS satellite (Node #2). It is then received by the satellite and retransmitted by its transponder to the BRTS transponder (Node #3). The BRTS transponder  
Figure 3: The Bilateration Ranging Transponder System (BRTS) range and Doppler tracking configurations. Node #2 and Node #4 represent the position of the TDRS satellite in space at different times. Node #1, Node #5, and Node #6 are identical ground stations used for transmitting and receiving signals in relation to the TDRS satellite. Antennas shown in green (Node #3) represent the BRTS transponders on the ground.  
subsequently retransmits the signal to the TDRS satellite (Node #4). At Node #4, the signal is combined with the second signal path employing a signal mixer. The mixed signal is transmitted to the receiving ground station at Node #5. The second signal is initiated from the same ground station at Node #1 but at a different transmission time (Node #6). This signal is transmitted to the TDRS satellite at Node #4, mixed with the first path's signal at Node #4, and then sent back to the ground station at Node #5.  
In comparison to TT&C measurements, BRTS measurements are considerably more complicated. Typically, multiple ground transponders are used to obtain these measurements, with each transponder positioned at a different relative geometry. Such multi-geometry configuration offers potential benefits in terms of more accurate orbit determination compared to single-site TT&C measurements. The BRTS tracking events generally occur every four hours and measures range with an accuracy of 5 to 10 m, while Doppler measurements are precise up to 0.02 Hz (a typical residual range of FDF's operational solutions).