High Integrity Carrier Phase Based Relative Positioning for Precision Landing using a Robust Nonlinear Filter

Kurzfassung

In this work a GNSS navigation filter is developed and procedures are derived in order to provide integrity of the navigation solution. The position solution has to meet high accuracy demands, for example those of zero-visibility precision approach. Therefore, low-noise carrier phase measurements are processed in addition to the GNSS pseudorange measurements. It is essential to resolve the ambiguities of the carrier phase measurements quickly and reliably in order to support high-accuracy real-time kinematic (RTK) positioning. Ambiguity resolution relies in this work on a geometry-based model. It is expected for the near future that the satellite geometry and the signal quality will improve, since GPS is planned to be modernized and GALILEO will be operational. Both factors are relevant for making progress in the domain of RTK carrier phase-based relative positioning. This study is restricted to the use of dualfrequency measurements in order to ensure compatibility with the requirements of civil aviation with respect to the Aeronautical Radio-Navigation Service (ARNS) bands. GPS’s L1 and L5 signals or GALILEO’s E1 and E5a signals are considered as measurement input to the filter. The user position and velocity vector, the ambiguities of the phase measurements and ionospheric terms are estimated by the filter. The performance of three different ionosphere models has been investigated. Although the estimation of ionospheric range errors is improved by processing measurements on two different frequencies, the results are only very good in absence of unmodeled biases. For example, if multiple measurements are biased by multipath it might happen that these un-modeled biases intrude into the ionosphere state estimation. The unknown states are only estimated reliably by the Extended Kalman Filter (EKF) if all un-modeled error sources were white Gaussian noise. Both multipath errors and residual tropospheric range errors after double-differencing are neglected in this filter approach. Alternatively to estimating the residual ionospheric errors it has also been considered to utilize ionosphere-free linear combinations. The user velocity vector is derived from instantaneous Doppler shift measurements. All measurements which are processed by the filter are double-differenced in order to keep the number of parameters to be estimated as small as possible. The disadvantage of doubledifferencing is that the measurement noise is amplified. By implementing the standard equations of the EKF numeric stability cannot be assured. Numerical problems were avoided by choosing the Bierman-Thornton UD filter implementation for the problem at hand. Though, it is already sufficient to make the standard EKF equations more robust by implementing the Joseph form for the update of the covariance matrix of state estimation uncertainty. After introducing this measures in order to improve numeric robustness of the filter in presence of computer round-off errors, no further numerical problems where observed any longer in the succeeding simulation runs. Because of the usage of an EKF it is difficult to derive the integrity risk analytically. The results depend on filter initialization and the concrete data sequence. However, a linear Kalman filter produces optimal state estimates by minimizing the sum of the mean-square errors. The integrity risk can be estimated for the nonlinear navigation filter solution by making some restrictive assumptions. Nevertheless, the effective integrity risk has to be determined by excessive simulations. Autonomous Filter-based fault Detection, Identification and model Adaptation (AFDIA) is proposed in order to detect model invalidations and to compensate them. So far only single-channel biases can be detected and corrected, although the extension to multiple biases is possible, but complex. In the navigation algorithm tests all simulated cycle slips and code outliers were detected successfully and the model was adapted properly afterwards. Protection levels are computed for both the user position estimates and the user velocity estimates. The derivation of the protection levels for the filter-based approach is restricted to two mutually exclusive hypotheses: normal operation of the filter in absence of biases and the fault mode if there is one bias in the measurement data. The non-Gaussian tails of the error distributions are accounted for by introducing inflation factors in the computation of the protection levels. This procedure is referred to as sigma-overbounding. The performance of the navigation filter and the plausibility of the protection levels have been verified by Monte-Carlo simulations. In addition, real-signal tests of a precision approach have been carried out with a hardware simulator and a GALILEO receiver. The accuracy of the position estimates and the magnitude of the protection levels strongly depend on the availability of a carrier phase ambiguity-fixed solution. The float solution is already very accurate after the first hundred observation epochs because of the filter-based approach. In the Monte-Carlo simulations the carrier phase ambiguities could be typically fixed at a baseline length of 20 km between the user receiver and the reference receiver. The probability of wrong ambiguity fixing has been set to 1·10^-9. Successful carrier phase ambiguity resolution is demonstrated in the real-signal tests for a baseline length of 54 km, where the navigation filter has been started when the airplane was about 75 km away from the airport. The results of the real-signal tests are very good because of the availability of low-noise E5a pseudorange measurements. Furthermore, only ionospheric delays have been simulated with the hardware simulator. Tropospheric delays and multipath were neglected. The Vertical Protection Level (VPL) of the carrier phase ambiguity fixed position solution is below 20 cm under the condition of good satellite geometry. The associated integrity risk is assumed to be at the order of 3·10^-9. If there are only few visible satellites, the VPL may be as large as 2 m although the ambiguities have already been fixed correctly. There is a great difference between the fault-mode protection level and the fault-free protection level. With respect to bad satellite geometry, the fault-mode protection level clearly dominates the overall protection level. The performance results of the navigation filter are very promising with respect to the position accuracy and the magnitude of the protection levels which can be achieved. Since the actual integrity risk has to be assessed by simulations, it is rather difficult to proof that the integrity risk is indeed in the range of 10^-9, which is required for zero-visibility precision approach in civil aviation. The application of the navigation filter in domains where even higher position accuracy than in civil aviation is required, but where the specified integrity risk can still be verified by simulations, seems to be more likely. Several airport-related applications can be listed, for example automated cargo traffic, taxiing and coasting, but also precision approach in the military domain.