The accuracy of the GNSS-based positioning depends on the quality of the carrier phase measurements, which is often influenced by cycle slips. This paper focuses on the solutions of cycle slips detection and repair with a light calculation burden, based on single-frequency carrier phase data, since the repair is supposed to be achieved in real time, and the carrier phase measurements provided by our indoor transmitters, i.e. the Repealites - a specific type of pseudolites, are currently only on L1. As a result, the carrier phase high-order difference approach is considered to be advantageous in this case, and hence the problem is transferred to be an issue of outlier detection. The mainstream methods for the outlier test are reviewed, including Chauvenet's criterion, Student's t-test, Grubbs' test, Dixon's test, etc. A set of compromise criteria with certain arbitrary parameters (thresholds) is proposed. The method is then evaluated with both simulated carrier phase sequences and real data taken indoors, in an urban canyon, and outdoors, from either the Repealites or the GPS satellites. Artificial cycle slips of various steps are added so as to diversify the testing cases. It is shown that the success rate and the robustness (to avoid the misjudgments) of the method highly depend on the thresholds in the judging criteria, as well as the movement pattern of the user receiver. A set of empirical thresholds are obtained with respect to each modality of the receiver, and a general configuration is proposed for a receiver under different movement modalities. A few directions of future works are also suggested