Orbit Determination Using TDMA Radio Navigation Data with Implicit Measurement Times

An orbit determination Kalman filter has been developed that uses two types of measurements of time division multiple access (TDMA) L-Band signals from satellites in low Earth orbit, a carrier phase measurement and a biased pseudorange measurement. This algorithm will enable precise orbit determination of satellites broadcasting TDMA signals not originally intended for navigation. The TDMA structure of the carrier phase data introduces carrier phase ambiguities, which can be partially removed via preprocessing based on rough orbit estimates. It is often impossible to remove a residual integer-valued Doppler shift measured in cycles per data burst. The orbit determination square-root information Kalman filter (SRIF) is a mixed real/integer extended Kalman filter which deals explicitly with the integer Doppler shift ambiguities of its partially corrected carrier phase measurements. It isolates the integer unknowns from the real-valued unknowns, and solves for its integer-valued estimates using an integer linear least-squares solver. The carrier phase and pseudorange measurements are available at known measurement times at ground-based receivers, but they provide information about the satellite’s orbital state at an unknown signal transmission time. An additional feature of the Kalman filter is its explicit treatment of the uncertain range delay. This is accomplished by applying a new technique that includes Chebyshev polynomial models of random process noise, dense output state interpolation that is consistent with numerical integration of the state differential equation, iterative solution for signal transmission times, and consistent propagation of all of these effects through the SRIF. The effectiveness of this new Kalman filter has been evaluated using truth-model data. The truth model simulation tests evaluate the filter results against known “truth” states and known “truth” Doppler shift ambiguities. The simulation results predict that the Kalman filter will achieve RMS position errors of about XX meters magnitude using only five ground stations located in the contiguous United States.