1. A position estimation device, comprising: a mathematical expression model processing unit that obtains attitude information and positioning information indicating an attitude and a measured position of a mobile object from sensors and calculates a position of the mobile object, a condition quantity indicating a moving condition of the mobile object and an error in the condition quantity through filtering processing executed by using a probability model based upon the attitude information and the positioning information having been obtained and a specific mathematical expression model among a plurality of mathematical expression models expressing behavior of the mobile object, which are acquired in advance; a threshold calculation unit that calculates a threshold candidate value for a threshold value to be used as a criterion when selecting the specific mathematical expression model, by using the error having been calculated by the mathematical expression model processing unit; a threshold value determining unit that determines the threshold value based upon the threshold candidate value; and a mathematical expression model selection unit that selects the specific mathematical expression model based upon the threshold value determined by the threshold value determining unit.