## 6 Conclusions  
In this study, we presented a novel submillimeter-level accuracy K-band microwave ranging (MWR) payload, used for the on-orbit demonstration of precise ranging technology for a future HEO \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multirow{2}{*}{**Unit**} & \multicolumn{3}{c}{**KF-Beilou/SBR\({}^{*}\)**} & \multicolumn{3}{c}{**AF-Beilou/SBR\({}^{*}\)**} & \multicolumn{3}{c}{**AF-MWR**} \\ \cline{3-8}  & & & **Perigee** & **Apogee** & **Perigee** & **Apogee** & **Perigee** & **Apogee** \\ \hline \multirow{2}{*}{range} & \multirow{2}{*}{\(\upmu\)m} & ME\({}^{*}\) & \(7.8\times 10^{5}\) & \(8.65\times 10^{4}\) & \(9.12\times 10^{4}\) & \(1.05\times 10^{4}\) & / & \(3.5\times 10^{1}\) \\  & & RMS & \(3.02\times 10^{5}\) & \(5.65\times 10^{4}\) & \(3.64\times 10^{4}\) & \(8.27\times 10^{3}\) & / & 9.50 \\ \hline \multirow{2}{*}{range rate} & \multirow{2}{*}{\(\upmu\)m/s} & ME & \(1\times 10^{3}\) & \(3\times 10^{1}\) & \(9\times 10^{1}\) & \(1.5\times 10^{1}\) & / & 8.5 \\  & & RMS & \(5.91\times 10^{2}\) & \(2.54\times 10^{1}\) & \(4.51\times 10^{1}\) & 9.8 & / & 2.6 \\ \hline \multirow{2}{*}{elevation angle} & \multirow{2}{*}{deg} & ME & \(5\times 10^{-2}\) & \(5\times 10^{-2}\) & \(4\times 10^{-3}\) & \(3\times 10^{-3}\) & / & \(1.4\times 10^{-3}\) \\  & & RMS & \(4.21\times 10^{-2}\) & \(3.4\times 10^{-2}\) & \(3.1\times 10^{-3}\) & \(2.2\times 10^{-3}\) & / & \(9\times 10^{-4}\) \\ \hline \multirow{2}{*}{elevation rate} & \multirow{2}{*}{deg/s} & ME & \(1.9\times 10^{-3}\) & \(1.7\times 10^{-3}\) & \(9.2\times 10^{-4}\) & \(7\times 10^{-4}\) & / & \(1.2\times 10^{-4}\) \\  & & RMS & \(1.8\times 10^{-3}\) & \(1.54\times 10^{-3}\) & \(8.14\times 10^{-4}\) & \(5.22\times 10^{-4}\) & / & \(5.24\times 10^{-5}\) \\ \hline \multirow{2}{*}{azimuth angle} & \multirow{2}{*}{deg} & ME & \(8\times 10^{-2}\) & \(7\times 10^{-2}\) & \(4\times 10^{-3}\) & \(4\times 10^{-3}\) & / & \(1.5\times 10^{-3}\) \\  & & RMS & \(6.1\times 10^{-2}\) & \(4.8\times 10^{-2}\) & \(3.02\times 10^{-3}\) & \(2.6\times 10^{-3}\) & / & \(1.1\times 10^{-3}\) \\ \hline \multirow{2}{*}{azimuth rate} & \multirow{2}{*}{deg/s} & ME & \(1.9\times 10^{-3}\) & \(1.9\times 10^{-3}\) & \(8.6\times 10^{-4}\) & \(8\times 10^{-4}\) & / & \(1.3\times 10^{-4}\) \\  & & RMS & \(1.62\times 10^{-3}\) & \(1.59\times 10^{-3}\) & \(7.03\times 10^{-4}\) & \(6.21\times 10^{-4}\) & / & \(8.16\times 10^{-5}\) \\ \hline \hline \end{tabular}  
* Note: KF: typical Kalman filter; AF: adaptive filter; ME: maximum error.  
\end{table} 
Table 4: Relative navigation estimation error during simulation. Figure 13: Relative range rate estimation errors from different payloads and filters (refer to Figure 12 for the denotation of color lines). SFF mission, which we have named the highly elliptical formation flying demonstration (HEFFD) mission. The MWR uses DOWR microwave phase accumulation, and details on the development of MWR are introduced, including a K/Ka-band dual-frequency corrugated horn antenna, frequency reference unit, microwave channel, and signal processing platform. Relative orbit models with perturbations and an improved adaptive filter algorithm that incorporates process noise uncertainty are presented, and are used for the SFF relative navigation system design. The MWR equipment was tested in two stages: an assessment of the ranging accuracy, and an HIL simulation within the SFF GNC system. First, the MWR payload was fixed in a high-precision 6-DOF moving platform and extensively tested under a relative velocity of 5 \(\upmu\)m/s. The ranging errors were less than 40 \(\upmu\)m and the range rate errors were 1.6 \(\upmu\)m/s. Second, a complex HIL simulation system was constructed which incorporated an optical sensor, a BeiDou dual-frequency receiver, and SBR equipment, aiming to evaluate real relative navigation filter performance during the HEFFD mission.