An object is to enable a state of a vehicle to be precisely estimated by a Kalman filter. A navigation system 1 includes an observation unit 21 that observes an observable concerning a variation of the vehicle, based on an output from a sensor, and an estimation unit 22 that estimates a state quantity indicating a state of the vehicle by a Kalman filter, and the estimation unit 22 calculates a prediction value of the state quantity of the vehicle, calculates an error covariance matrix of the prediction value, by the Kalman filter to which an error of the observable is inputted as an error of the state quantity which is in a relation of calculus with the observable, and calculates an estimation value of the state quantity of the vehicle and an error covariance matrix of the estimation value by the Kalman filter, based on the prediction value and the error covariance matrix of the prediction value which are calculated.