Preprocessing, which effectively remove noise in the raw data acquired from nodes with inherent errors, is very important because it affects the accuracy of the relative azimuth. Generally, raw data acquired from the localization based on wireless communication includes noise due to clock drift and offset and especially propagation loss or distortion caused by obstacles in the non line of sight (NLOS) environment. A large number of methods used to reduce noise during preprocessing include a standard median filter, weighted median filter, center-weight median (CWM) filter, adaptive center weighted median (ACWM) filter, and modified adaptive center weighted median (MACWM) filter [14]-[16]. Although these filters use a threshold based on variance that provides reasonable noise removal performance to their systems, it is difficult to select the appropriate threshold value in the NLOS environment because the size of the impulse is changed in real-time. Therefore, this paper presents an improved weight average filter (IWAF) to improve these problems during preprocessing that can effectively remove impulse noise by applying each different weighting value, depending on the size of each impulse noise without threshold from the position data acquired from a mobile node and then calculating the average value. First, the IWAF is applied to reduce impulse noise in the acquired position data of mobile nodes following the procedure in Figure 1.

Figure 1: 
Block diagram of improved weight average filter

Generally, the population variance(σ²) is expressed as

where n is the number of raw data points, x_i is the i-th raw data point, and m is the average of the raw data points. The modified variation that represents the variation based on e-th raw data point is given by

where x_e represents the value of e-th raw data point, and the maximum value of σ²_e is limitless but a positive real number. As σ²_e becomes bigger, the standard deviation based on e-th raw data point becomes larger, and the noise characteristics of x_e appear strongly. This noise characteristic has the range of variation 0 to 1 and a weight given by

The size of W_e is expressed as a value between 0 and 1. The closer the value of W_e is to 0, the stronger its noise characteristic is. The closer the value of W_e is to 1, the weaker its noise characteristic is. The total sum(S) of W_e that gives each different weight to each raw data point is

Accordingly, to apply the different weights depending on the size of the noise to the raw data, the average (y_w) is

In Equation (5), y_w reduces the impulse noise, which is relatively large compared to the other noise source, because a larger impulse noise implies the use of a smaller weighting value.

The relative azimuth estimation method of the proposed algorithm is described as the stages (a)-(d) in Figure 2. When a user rotates a mobile node, as in Figure 2 (e), the node acquires an arbitrary arc point A_i(x,y), where i is the index number of the acquired arc point. S(x,y) is the starting point, E(x,y) is the ending point, H₁(x,y) is a point halfway between S(x,y) and E(x,y), which is expressed as

Figure 2: 
Sequence of proposed relative azimuth estimation

The equation of a straight line passing through S(x,y) and E(x,y) is

where α_n is y-intercept. The normal equation (y) passing through H₁(x,y) is

M(x,y) is the middle point that is the closest arc point A_i(x,y) from the normal. M(x,y) resulting from the substitution of A_ix into Equation (8) is selected as the following Figure 3 and Equation (9).

Figure 3: 
Acquisition of middle point (M(x,y))

H₂(x,y) is another point halfway between S(x,y) and M(x,y) using the same method in Equation (6). The equation of a straight line passing through S(x,y) and M(x,y) is

The normal equation (y) passing through H₂(x,y) is

C(x,y) is the center point obtained by Equation (8) and Equation (11), where C(x,y) is the center axis when a user rotates a mobile node. At the stage in Figure 2 (d), each side of the triangle with three points consisting of S(x,y), E(x,y), and C(x,y), are determined as follows

Furthermore, the interior angle(θ) between a and c is calculated by the second law of cosines.

Because θ is the revolved angle of mobile node by user, the direction of a user can be estimated from the relative azimuth by summing the previous azimuth with θ.

Simulations were carried out in order to verify the performance of the proposed algorithm. Figure 4 shows the performance of other filters compared to the proposed IWAF with a standard weight filter generally expressed as

Figure 4: 
Performance of proposed weight average filter.

Where x_k is the present weight average, α is a weight that has a value between 0 and 1, x_k-1 is the previous weight average, and x_k is a present average. When the x-axis value is about 10 in Figure 4, the raw data represents a form of an impulse, and as α changes, the characteristic of WF is also changes. Here, when α is large, a droop phenomenon occurs even if impulse is reduced because of the dependence on the previous raw data. This droop phenomenon is not suitable for preprocessing because it affects the impulse for a long time. On the other hand, the advantages of the proposed IWAF are that the droop phenomenon does not exist because the weight is not assigned according to the time, and the impulse noise decreases faster than the general weight filter because the weight is assigned depending on the size of impulse noise. Therefore, the IWAF is suitable for preprocessing to improve the performance of the proposed algorithm and can be applied widely in the field of signal processing using image, control, and sensor processing in which impulse noise exists.

Computer simulations are performed to evaluate the performance of the proposed relative azimuth estimation algorithm. The components and conditions for the simulation environment are the angular velocity (90 rad/s), the sampling rate (3 ms), the rate of the included impulse (1%), and the maximum size of the impulse (100 cm). Also, considering the length of the human arm and the development of the localization estimation, the radius and error of localization are set to 50 cm and 3 cm, respectively. The remaining elements were selected arbitrarily because they can vary depending on the installation environment and the characteristics of the system. Preprocessing is used in order to minimize the errors of localization acquired from a mobile node. In other words, if the error is 0 cm, the azimuth error for the proposed method is 0°. Figure 5 presents the performance of the cumulative average error when the experiments were repeated up to 100 times for the general WFs and the proposed IWAF. For the general WF used as a preprocessing step, the impulse noise is reduced more for α = 0.9 than α = 0.1 or α = 0.5, and the performance of the general WF (α = 0.9) represents an average error of 5.09°. Meanwhile, for the proposed IWAF, the average error is 2.5°. The performance improves by about a factor of two compared to the WF (α = 0.9) because the droop phenomenon does not exist, and the impulse noise is effectively reduced. Furthermore, it is confirmed that the relative azimuth estimation algorithm effectively obtains the azimuth in a localization system that contains an error. In an indoor navigation system, the proposed algorithm provides reliable orientation information to a user without using an azimuth sensor that is vulnerable to magnetic interference.

Figure 5: 
Cumulative average error when the experiments were repeated n times