In this study, we present an algorithm for indoor robot position estimation. Estimating the position of an indoor robot using a fixed imaging device obviates the need for complex sensors or hardware, enabling easy estimation of absolute position through marker recognition. However, location estimation becomes impossible when the device moves away from the surrounding obstacles or the screen, presenting a significant drawback. To solve this problem, we propose an algorithm that improves the precision of robot indoor location estimation using a Gaussian Mixture Model(GMM) and a Kalman filter estimation model. We conducted an actual robot operation experiment and confirmed accurate position estimation, even when the robot was out of the image.