8.4.2. Localisation Performance

The localisation performance of the proposed system was compared with two other studies that proposed different models for angle estimation and BSE compensation, including the work presented in [17], referred to as MODEL I, and in [20], referred to as MODEL II. To compare the relative accuracy of the proposed system with these studies, we mainly implemented the angle estimation and compensation models as proposed by the researchers, and then applied the fingerprinting localisation method. For example, the use of multiple wearable devices and Semcad simulation parts were omitted for MODEL I, and Kalman filter and path loss model implementation were overlooked for MODEL II. Moreover, identical preprocessing of the raw data was considered, and the same weight calculation method was applied for all the cases with a value of 3 for *k*, both in the K-NN and WK-NN algorithms.

Figure 18 presents the routes for the experimented path estimated by the different systems using the classical K-NN algorithm. As shown in the figure, the performance of the systems with BSE compensation (WBSEC) on indoor localisation is apparent and the estimated route of the systems without BSE compensation (WOBSEC) produced the worst path. Among the other results, MODEL II generated a better path compared to MODEL I, because in MODEL I the authors only considered two groups for orientation angle (over/underestimation) when applying their compensation model. MODEL II considered three groups (front, back, side) and there was no consideration of the volume of body parts that creates the NLOS scenarios. However, this work considered three groups as well as the consideration of body volume when calculating the compensation value, and hence produced the best path.

**Figure 18.** Routes estimated by different systems using the K-NN method: (**a**) Without BSEC; (**b**) Model I; (**c**) Model II and (**d**) With BSEC.

The details of the positioning performance are presented in Figure 19 and Table 2 for the K-NN algorithm. The boxplot indicates the summary of some error statistics including the maximum, minimum, 25th, 75th, mean, and median errors for each system. As presented in Figure 19 and Table 2, the proposed system significantly outperformed the other systems for all types of statistics. The proposed system demonstrated the best performance with a mean error of 1.62 m and median error of 1.46 m, followed by MODEL II (mean error 2.17 m and median error 2.38 m). The mean and median errors of MODEL I were 2.39 m and 1.75 m, respectively. The system without any BSE compensation achieved a mean error of 3.17 m and a median error of 2.68 m.

**Figure 19.** Localisation performance of the proposed system compared with other systems using the K-NN method.


**Table 2.** Localisation accuracy comparison for different systems with K-NN method.

Figure 20 illustrates the accumulative distribution function of the estimated localisation errors of the different systems for the K-NN algorithm. This plot also shows the superiority of the proposed system compared to the others. More specifically, the introduced system can achieve a performance that produces localisation errors less than 2.5 m for 80% of cases, while it is around 60% for MODEL II and around 70% for MODEL I. The result that was produced without compensating the BSE outputted the worst, since the body effect errors are not considered when comparing a query fingerprint with the radio map.

**Figure 20.** Accumulative distribution of positioning error of the proposed system compared with other systems using the K-NN method.

The superiority of the proposed system is further increased by applying the WK-NN algorithm when comparing a query fingerprint with the radio map. The performance is improved by including the spatial prominence of the neighbouring RPs in terms of weight factor. Figures 21 and 22, and Table 3 compare the performance of the different systems using the WK-NN algorithm. As can be seen, the WK-NN algorithm with the proposed weighting method improves the localisation accuracy for all the considered systems. The developed system yields a mean error of 1.01 m and median error of 0.74 m, while they are 1.56 m and 1.19 m for MODEL II, and 2.74 m and 2.23 m for MODEL I. The system without any BSE compensation can attain a mean error of 2.99 m and a median error of 2.98 m using the WK-NN algorithms. Moreover, as presented in Figure 22, the WK-NN algorithm produces localisation errors less than 1.5 m for 80% of cases for the proposed system, while it is around 60%, 25%, and 15% for MODEL II, MODEL I, and without applying any compensation, respectively. Overall, the proposed BSE compensation model along with the landmark-assisted WK-NN method is able to achieve sub-metre median localisation accuracy that outperforms some recent related methods.

**Figure 21.** Localisation performance of the proposed system compared with other systems using the WK-NN method.

**Figure 22.** Accumulative distribution of positioning error of the proposed system compared with other systems using the WK-NN method.

**Table 3.** Localisation accuracy comparison for different systems with the proposed WK-NN method.

