6. A computer implemented position estimation method according to claim 5 , wherein: restrictions imposed with regard to a valid range, within which each of the plurality of mathematical expression models expressing the behavior is applicable to the behavior, are defined based upon information that can be collected through observation made from outside or based upon the position, the condition quantity and the error having been calculated; the threshold value is determined based upon values representing extents of the error calculated each in correspondence to one of the plurality of mathematical expression models; and the specific mathematical expression model is selected in correspondence to the restrictions.
5. A computer implemented position estimation method, comprising: obtaining attitude information and positioning information indicating an attitude and a measured position of a mobile object from sensors; calculating 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, the positioning information, and a specific mathematical expression model among a plurality of mathematical expression models expressing behavior of the mobile object, which are acquired in advance, the specific mathematical expression model being selected based upon a threshold value; calculating a threshold candidate value based upon the error having been calculated, wherein the threshold candidate value represents a value of the condition quantity at which a plurality of mathematical expression models intersect; updating the threshold value based upon the threshold candidate value: and selecting the specific mathematical expression model to be used in a next stage of mathematical expression model processing from among the plurality of mathematical expression models, based upon the threshold value having been updated.