Two geometric-free phase combinations and one geometric-free pseudo-range phase combination are constructed to form three linearly independent cycle slip detection quantities, which can effectively detect cycle slips as small as one cycle. To solve the problem of ill-conditioned equations in this detection combination, a real-time method for repairing BeiDou navigation satellite system(BDS)triple-frequency cycle slip based on extended ridge estimation is proposed. Firstly, the searching region R
of ridge parameters is determined using statistical-validation-optimization method. Then, the k
value of ridge parameters is searched in R
based on the principle of minimizing the sum of squared residual errors. Finally, the ridge estimated real value is rounded to obtain the integer cycle slip, and the sum of two residual squares after the repair in the epoch is used as the cycle slip repair reliability test index. The algorithm is verified with the measured BeiDou triple-frequency data, and the results show that the algorithm can realize real-time detection and repair of the triple-frequency cycle slip in BDS-2 and BDS-3 observations, with high processing efficiency, applicability and reliability.