Recently, indoor localization systems based on wireless sensor networks have received a great deal of attention because they help achieve high accuracy in position determination by using various algorithms. In order to minimize the error in the estimated azimuth that can occur owing to sensor drift and recursive calculation in these algorithms, we propose a novel relative azimuth estimation algorithm. The advantages of the proposed technique in an indoor environment are that an improved weight average filter is used to effectively reduce impulse noise from the raw data acquired from nodes with inherent errors and a rotational displacement algorithm is applied to obtain a precise relative azimuth without using additional sensors, which can be affected by electromagnetic noise. Results from simulations show that the proposed filter reduces the impulse noise, and the acquired estimation error does not accumulate with time by using proposed algorithm.