GNSS Integer Ambiguity Estimation and Evaluation: LAMBDA and Ps-LAMBDA

Successful integer carrier-phase ambiguity resolution is crucial for high precision GNSS applications. It includes both integer estimation and evaluation. For integer estimation, the LAMBDA method has been applied in a wide variety of GNSS applications. However, before conducting ambiguity resolution, one needs to infer how reliable the fixed solution is expected to be, as incorrect fixed ambiguity solutions often lead to unacceptable positioning errors. In this paper, two Matlab software tools are introduced for the evaluation and integer estimation: Ps-LAMBDA and an updated version of LAMBDA. Evaluation of the integer solution is based on the ambiguity success rate. Since the success rate is generally difficult to compute, some easy-to-use approximations and bounds are provided by the Ps-LAMBDA software. This success rate tool is valuable not only for inferring whether to fix the ambiguities but also for design and research purposes. For the integer estimation, the new version LAMBDA software provides more options of integer estimation and integer search, including the search-and-shrink strategy. In addition, the ratio test is incorporated to validate the significance of the fixed solution. Using these two software tools together allows for the combined execution of integer estimation and evaluation, thus benefiting multi-frequency, multi-GNSS applications.