FAMCAR Approach for Efficient Multi-Carrier Ambiguity Estimation

The proposed addition of a third carrier for the modernized GPS as well as providing three and possibly four carriers for the planned Galileo system will boost the performance of carrier phase based positioning within the next decade. In principle, instantaneous (one-epoch) ambiguity resolution becomes feasible for a broad range of applications. Beyond the system level developments regarding the frequency allocation and signal structure the proposal of three and four carrier frequencies enables new approaches at the processing level. The Factorized Multi-Carrier Ambiguity Resolution (FAMCAR) algorithm introduces a number of new independent linear combinations of carrier-phase observations as well as of carrier-phase and pseudorange observations. The combinations include the minimum-error geometric carrier-phase combination, the minimum-error ionosphere combination, the new Quintessence combinations and the code-carrier combinations. From these individual estimates, the full floating solution for all carriers is derived. The paper will give a description of the approach and the statistical properties of these new linear combinations. Results of an experiment using FAMCAR for hardware-simulated data are presented in another paper. Existing standard techniques for multi-carrier ambiguity determination usually apply one big Kalman filter to estimate all unknowns (e.g. position, ambiguities, ionosphere and multipath). The factorization enables the stepwise modeling of each error component and leads therefore to a bank of significantly smaller filters. This approach results in significantly higher computational efficiency for the Kalman filter sets (i.e. float solution) und a better knowledge of error components for the individual measurements. In addition to enabling efficient processing of three and four carrier data the new approach is already applicable to a dual-frequency system. Furthermore the decreased computational load enables the use of smaller processor components and therefore provides a significant cost reduction.