Integrity Analysis of Cascaded Integer Resolution with Decorrelation Transformations

A method for the resolution of the integer ambiguities of double difference carrier phase measurements is studied with respect to its integrity. The method is an enhancement of the Three-Carrier Ambiguity Resolution (TCAR) method introduced by Forssell, Neira and Harris in [1] and the Cascade Integer Resolution (CIR) considered by Jung, Enge and Pervan. The proposed method is based on a full-geometry approach, i.e. the code and phase measurements of all satellites are considered as a set. Decorrelation and rounding steps of the LAMBDA method are performed successively on the Galileo Super Wide Lane (SWL) and Widelane (WL) carrier combinations and the E5a carrier. The probability of wrong fixing for the WL combination L1-E5a is greatly reduced by the a-priori knowledge of the SWL ambiguity. An optimized choice of WL combination(−4.121φL1+39.831φE5b−34.800φE5a) further improves the result by several orders of magnitude without much affecting the ionospheric delay. The probability distribution of the baseline error is estimated using an importance sampling approach. This probability distribution leads to a Galileo like implicit definition of Horizontal and Vertical Protection Levels (XPL) for carrier phase measurements. The new definition can be used to detect a wrong fixing at one level, e.g. X=WL, whenever the protection level at the previous level, SWL in the current example, is smaller than the smallest baseline error due to a wrong fixing at the X level.