Simulations are performed to show the effectiveness of the proposed VBS scheme. The noise models and the simulation parameters are illustrated in the chapter 9.2.1. The performance comparison between the proposed VBS algorithm with the other existing location estimation schemes, i.e. straight Line of Position (LOP) and the two-step LS methods, are conducted in the chapter 9.2.2.
9.2.1 Noise Models and Simulation Parameters
In the simulations, the noise model for the TOA measurements is the same as the one in chapter 9.1. On the other hand, the home BS, i.e. BS1, is located at (0, 0) in meters; while the positions of the other two BSs, BS2 and BS3, are located at (1000, 1000√
3) and (-1000, 1000√
3) in meters. The true position of the MS is assumed to be at (200, 200) in meters.
VBS(1) VBS(3) VBS(6)
Figure 9.4: The Three Cases for the VBS Scheme with Different Placements of the Virtual BSs (The Black Dots (•) are the Locations of the Virtual BSs; The Solid Triangle Represents the Area Enclosed by the BS1BS2BS3)
The performance evaluation is conducted under the following three different cases as shown in Fig. 9.4:
1. VBS(1): A single virtual BS is assigned inside of the triangular area, i.e. (xv, yv) = ((x1+ x2+ x3)/3, (y1+ y2+ y3)/3).
2. VBS(3): Three virtual BSs are located outside of the triangular region, i.e. (xv1, yv1) = (0, 2000/√
3), (xv2, yv2) = (1000, −1000/√
3), and (xv3, yv3) = (2000, 2000/√ 3).
3. VBS(6): Six virtual BSs are located outside of the triangular region, i.e. (xv1, yv1) = (0, 2000/√
3), (xv2, yv2) = (1000, −1000/√
3), (xv3, yv3) = (2000, 2000/√
3), (xv4, yv4) = (−1000, −1000/√
3), (xv5, yv5) = (3000, −1000/√
3), and (xv6, yv6) = (1000, 5000/√ 3).
9.2.2 Simulation Results
Fig. 9.5 shows the performance comparison between the proposed VBS algorithm (including the VBS(1), VBS(3), and VBS(6)), the conventional two-step LS algorithm, and the LOP scheme. The mean value of the NLOS noises are assumed as τm = 0.3 µs for all cases. It can be seen that the VBS scheme with six virtual BSs situated outside of the triangular region outperforms the other schemes. The VBS(6) case surpasses the conventional two-step LS method with around 110 m of RMS error under 67% of average position errors. It can also be seen that the VBS(3) case also provides feasible performance comparing with the
0 100 200 300 400 500 600 700 800 900 0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Average Position Error <= Abscissa
RMS Error (m)
VBS(1) VBS(3) VBS(6) 2−step LS LOP
Figure 9.5: Performance Comparison between the Location Estimation Schemes under NLOS Environments (with Median Value of the NLOS Noises: τm =0.3 µs)
VBS(1), the LOP, and the two-step LS methods. As predictable, the VBS(1) case does not provide satisfactory performance since the corresponding virtual BS is located inside of the triangular area. The results are consistent with the observation obtained from the GDOP effect. Fig. 9.6 illustrates the RMS errors under different NLOS noises (with 50% of average position errors). It can be observed that the VBS(6) case can effectively mitigates the RMS errors, especially under the environment with excessive NLOS noises. It is noted that the VBS scheme with cases that includes more than six virtual BSs have also been conducted via simulations. However, not much improvement on the RMS error has been achieved with different placements of the additional virtual BSs. The case with the VBS(6) layout (as shown in the right schematic diagram of Fig. 9.4) can be sufficient in improving the RMS errors for location estimation of the MS.
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0
50 100 150 200 250 300 350
Median Value of the NLOS Noises
RMS Errors (m)
VBS(1) VBS(3) VBS(6) 2−step LS LOP
Figure 9.6: Performance comparison between the Location Estimation Schemes under Differ-ent NLOS environmDiffer-ents (with 50% of Average Position Errors)
Chapter 10
Conclusion
In part I of this thesis, a hybrid location estimation and tracking system is proposed. The system is capable of estimating the three dimensional position and velocity of the mobile de-vices. It is shown in the simulation results that the proposed hybrid scheme provides consis-tent location estimation accuracy under different environments. Additionally, the Geometry-constrained Location Estimation (GLE) and location algorithm with Virtual Base Stations (VBS) are presented in part II of this thesis. Both algorithms enhances the conventional two-step LS algorithm by imposing additional geometric constraints within its formulation. By using the GLE and VBS methods, the computational efficiency acquired from the two-step LS method is preserved. GLE obtains higher location estimation accuracy for the MS, especially under NLOS environments. Moreover, estimation accuracy can further be improved by the proposed VBS method, especially the environments with both the NLOS noises and the poor GDOP circumstance. It is shown in the simulation results that the proposed GLE and VBS algorithms provide better position location estimate comparing with other existing methods.
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