Initial bias is a random parameter in micro-electro-mechanical rate gyroscopes that changes with each turn on and turn off. The bias can be estimated by averaging in static condition or by extended Kalman filter in other conditions. In addition, this parameter is affected by temperature or linear acceleration. Curve fitting on the bias variation of micro-electro-mechanical rate gyroscopes due to thermal effects is a usual method for thermal compensation of these sensors. However, these approximate curves cannot completely compensate the effect of the thermal bias in long-time applications. In this study, it is tried to improve the calculating accuracy by a combination of extended Kalman filter and the results of these curves and using advantages of both methods. Also bias estimation is improved using the switching algorithm in accelerated motions by avoiding improper data in the estimation process. Experimental tests show the effectiveness of this method especially in long-time accelerated motions.