A position estimation apparatus, a position estimation method, and a program that can estimate a position of a tracker with high accuracy while the power consumption is reduced is provided. An estimation result storage section (50) stores a result of estimation of a position of a tracker (12). An acceleration data acquisition section (52) repeatedly acquires acceleration data indicative of an acceleration of the tracker (12) from a sensor that detects an acceleration of the tracker (12). An estimation result updating section (56) updates the result of estimation on the basis of the result of estimation of a position of the tracker stored in the estimation result storage section (50) and the acquired latest acceleration data. A velocity information acquisition section (54) acquires information of the velocity of the tracker (12). The estimation result updating section (56) updates, when the velocity information is acquired by the velocity information acquisition section (54), the estimation result of a position of the tracker (12) stored in the estimation result storage section (50) on the basis of the velocity information and the acquired latest acceleration data.