The traditional linear phase Finite Impulse Response (FIR) filter had the disadvantages of large computation complexity and long time delay in mechanically dithered Ring Laser Gyro (RLG) Position and Orientation System(POS) noise attenuation. In this paper, a noise attenuation method based on linear phase Infinite Impulse Response (IIR) filter was proposed. In time-domain, a linear phase IIR lowpass filter was obtained by approaching a linear phase FIR lowpass filter through Kalman filter parameter estimating. In frequency-domain, the target function of the IIR lowpass filter was established and it was optimized by Quasi-Newton method. The time delay of the IIR filter was decreased. To further reduce computation complexity, a new low order IIR bandstop filter was designed. The experimental results show that the linear phase IIR filter designed by this method decreases the computation complexity by more than 40% and reduces the time delay from 10.125 ms to 4.83 ms with guaranteeing the noise attenuation performance, compared with the traditional FIR lowpass filter.