1. A face tracking device for tracking an orientation of a person's face with using a cylindrical head model, the face tracking device being mounted to a vehicle, the face tracking device comprising: image memory; and a processor, the processor configured to continuously obtain a person's face image data from the image memory as a first image data; extract a facial area by extracting a second image data from the first image data, the second image data corresponding to a facial area of the person's face; determine an initial value determination by calculating an first fitting error value of the second image data by performing fitting process of the second image data with using an appearance model, and determining that the second image is usable as an initial value required for the cylindrical head model when all of the following conditions are satisfied: the first fitting error value is approximately smaller than a first predetermined error judgment value; a steering angle of the vehicle is approximately between −20 degree and +20 degree; a vehicle speed is approximately faster than 30 km/h; an acceleration of the vehicle is approximately larger than 0.03 G wherein a positive acceleration is provided by a case where the vehicle speed is being increased in the direction of vehicle movement; and a throttle angle of the vehicle is approximately larger than 13%; and track a facial orientation by obtaining the initial value determined to be usable by the initial value determination unit, processing the initial value by fitting calculation with using the cylindrical head model, calculating a second fitting error value from the initial value with using the cylindrical head model, and determining the orientation of a person's face when the second fitting error value is smaller than a second predetermined error judgment value.