An investigation has been made on the models and characteristics of triple-frequency carrier-phase linear combinations for the Bei Dou Navigation Satellite System(BDS). Based on the three frequencies of the BDS, three categories of combinations are developed: ionosphere-free combinations(i.e., those that eliminate the ionospheric effect), minimum-noise combinations(those that mitigate the effects of thermal noise and multiple paths), and troposphere-free combinations(those that mitigate tropospheric effects). Both the ionosphere-free and troposphere-free combinations can be expressed as planes, whereas the minimum-noise combinations can be expressed as a line. The relationships between these three categories of linear combinations are investigated from the perspective of geometry. The angle between the troposphere-free plane and ionosphere-free plane is small, while the angles between the troposphere-free plane and the minimum-noise line, and between the ionosphere-free plane and the minimum-noise line, are large. Specifically, the troposphere-free plane is orthogonal to the minimum-noise line. By introducing the concepts of lane number and integer ionosphere number, the characteristics of the long-wavelength integer combinations and ionosphere-free integer combinations are investigated. The analysis indicates that the longest wavelength that can be formed for integer combinations is 146.53 m, and the ionosphere-free integer combinations all have large noise amplification factors. The ionosphere-free integer combination with minimum noise amplification factor is(0, 62, 59). According to the lane number, integer ionosphere number, and noise amplification factor, optimal integer combinations with different characteristics are presented. For general short baselines and long baselines, three independent integer combinations are suggested.
