1. A position estimation device, comprising: a processor and associated program memory, the processor being programmed to execute: mathematical expression model processing that: i. obtains attitude information and positioning information indicating an attitude and a measured position of a mobile object from sensors; and ii. 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, 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; threshold calculation that calculates a threshold candidate value based upon the error having been calculated by the mathematical expression model processing, wherein the threshold candidate value represents a value of the condition quantity at which a plurality of mathematical expression models intersect; threshold value setting that updates the threshold value based upon the threshold candidate value; and mathematical expression model selection that selects 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 updated by the threshold value setting.