HYBRID TDOA/AOA METHOD FOR INDOOR POSITIONING SYSTEMS

Transcription

1 HYBRID TDOA/AOA ETHOD FOR INDOOR POSITIONING SYSTES Chunhua Yang* +, Yi Huang* and Xu Zhu* *Department of Electrical Engineering and Electronics, the University of Liverpool, Liverpool, L69 3GJ, UK + Guidance onitoring Ltd., Leicester, LE19 1RP, UK {cyang, yi.huang, xuzhu}@liv.ac.uk Keywords: Indoor positioning, TDOA, AOA, and Leastsquare. Abstract We propose a hybrid time difference of arrival (TDOA) / angle of arrival (AOA) method for indoor positioning systems. The combined AOA includes both the azimuth AOA (A-AOA) and elevation AOA (E-AOA). Thus, this method makes full use of the AOA information to minimize the errors due to estimation of multipath parameters and gives the position of the estimated mobile terminals by simultaneously resolving a set of linearised location equations. Simulation results show that the hybrid method can improve the positioning accuracy significantly. 1 Introduction Recently, more and more attention from both academia and industry has been paid to indoor radio wave positioning and tracking systems. The rapid development of mobile devices leads to a higher demand for the so-called location based services (LBSs) [1]. LBSs depend heavily on the underlying positioning systems that determine the current location of the user. The Global Positioning System (GPS) is a dedicated positioning system which calculates the position of the user with an accuracy of several meters. However, GPS highly depends on the line-ofsight (LOS) path to the satellites, and therefore it is not suitable for indoor positioning. A different approach is the localisation of a user via his/her mobile phone in the cellular communications network, which is mainly based on the currently used base stations (BSs). However, this approach has an accuracy of up to tens of meters, which is not enough for indoor applications. The ultra wideband (UWB) technology is suitable for indoor positioning applications []. It offers the advantages of high positioning accuracy, economy, mobility and a good coverage for multipath environment. It has the potential to be integrated with the widely used GPS system. There are several other positioning systems for indoor positioning purpose such as Infrared, Ultrasound, or radio frequency identification (RFID) etc. All of these systems require installations in the building and special devices wore by the users. To the best of our knowledge, there are generally seven positioning methods: Taylor series expansion [3], Chan s method [4], Fang s method [5], Spherical intersection (SX) method [6], Spherical interpolation (SI) method [7], Divide and Conquer (DAC) method [8] and hybrid time difference of arrival (TDOA) / angle of arrival (AOA) method [9]. They are all based on ranging measurement while the hybrid one combines both ranging and bearing measurements. The hybrid method is essentially a combination of both angulation and lateration which are used to increase the positioning accuracy compared to just using one associated positioning metric. In this paper, a three-dimensional (3D) hybrid TDOA/AOA positioning method is proposed, which uses the azimuth AOA (A-AOA), elevation AOA (E-AOA) and the TDOA information. Therefore, this method is referred to as TDOA/AE-AOA. Using the same rule, another hybrid TDOA/AOA method [9] is referred to as TDOA/A-AOA. The effects of AOA noise/errors and TDOA noises/errors are also investigated. The accuracy of AOA data is critical for the hybrid TDOA/AOA method. Fortunately, the AOA data can be measured with a high accuracy since there is usually a maximum AOA measurement error extension of several degrees for indoor UWB propagation. These two AOA values are needed for independent equations. The performance is compared with three other positioning methods published in the public domain and good results are obtained. Simulation results show that an AOA value is equivalent to a high accuracy TDOA value. For example, AOA noise with a standard deviation (STD) of 0.7 degree in linearised equation corresponds to be in the order of millimetre of ranging noise. Two BSs can provide one TDOA value, two A-AOA values and two E-AOA values. So this scenario corresponds to more than three TDOA values and can be used to provide a D and even 3D indoor positioning. However, in practice we need at least four or five BSs to reach a reasonable positioning accuracy. The rest of this paper is organised as follows. In Section, we establish the formulation for the proposed hybrid positioning method. The performance of the hybrid method is evaluated via computer simulation in Section 3. Conclusions are drawn in Section 4.

2 Formulation In this section, the A-AOA and E-AOA noise equations are derived based on their geometrical relationships and are combined into the linearised least-square equations, respectively..1 AOA noise introduction Figure 1 depicts the A-AOA noise equation while Figure is for E-AOA noise equation. Base on the geometrical relationship of Figure 1, there is x + y sin nϕ = xsinϕ ycosϕ (1) and from Figure, there is where, y P1 r n = z x + y () O (BS1) sin sin cos n φ φ V1 r = x + y + z U P Figure 1: Azimuth angle noise introduction z U1 V1 G O (BS1) U n G P Figure : Elevation angle noise introduction 1/ (x + y ) sin n φ V (S) U1 P1 x V (S) r sinn 1/ (x + y ) Also, from Figure 1 it is obvious that x y x y cosϕ sinϕ (3) To include both x and y variables, it could be set that x y x y α ( 1 α), cosϕ sinϕ 0 α 1 (4) A choice is to set that α = cos ϕ (5) So, x y xcosϕ y + = + sinϕ (6) By doing so, possible singularity issues in equation (4) could be avoided. Thus, equation () is in its linear form. rsin n = xcosϕ cos ysinϕcos + zsin (7) It is assumed that n ϕ and n are both very small so that the angle values both approximate their corresponding sine function values. Finally, equation (1) and () are in the following forms: n x + y = xsin ycos (8) ϕ ϕ ϕ nr = xcosϕ cos ysinϕcos + zsin (9). Least-square algorithm According to the proposed hybrid method, the equation (11) in reference [4] should now be changed as follows: where ψ = h G z (10) 0 a a r,1 K + K 1 r3,1 K3+ K1 r,1 K + K1 x1sinϕ1+ y1cosϕ1 1 xsinϕ + ycosϕ h = xsinϕ + ycosϕ x1cos1cosϕ1+ y1cos1sinϕ1 z1sin1 xcoscosϕ + ycossinϕ zsin xcoscosϕ + ycossinϕ zsin

3 x,1 y,1 z,1 r,1 x3,1 y3,1 z3,1 r 3,1 x,1 y,1 z,1 r,1 sinϕ1 cosϕ1 0 d 1 sinϕ cosϕ 0 d Ga = sinϕ cosϕ 0 d cos1cosϕ1 cos1sinϕ1 sin1 r1 coscosϕ cossinϕ sin r coscosϕ cossinϕ sin r Figure 3: 3D simulation environment and d = x + y Then use the approach described in reference [4] to solve the problem. 3 Simulation results The 3D simulation environment is demonstrated in Figure 3, where the circle point is the estimated mobile station (S) located at (8,, ) and the cross points represent five BSs located at (-5, 8, ), (0, 0, 3), (4, 6, 3), (-, 4, 0) and (7, 3, 1) respectively. 3.1 TDOA noise analysis According to reference [10][11], it is reasonable to set AOA noise STD to be 0.7 degree. Figure 4 and Figure 5 present a 3D performance comparison of several positioning methods when Guassian TDOA noise STDs vary. Figure 6 shows the performance of TDOA/AE-AOA method with different numbers of BSs when TDOA noise varies. Figure 7 presents the performance comparison with Cramer Rao Lower Bound (CRLB). All AOA noise STDs are set to be 0.7 degree. From Figure 4 and Figure 5, it is observed that our proposed hybrid method performs better based on our positioning parameters set. According to Figure 6, it is feasible for BSs to provide a reasonable performance. It is seen from Figure 7 that the proposed hybrid method performs closely to the theoretically best positioning accuracy. Figure 4: Performance comparison of TDOA/AE-AOA with Taylor s method [3] and Chan s method [4] Figure 5: Performance comparison of TDOA/AE-AOA with TDOA/A-AOA method [9]

4 Figure 6: Performance of TDOA/AE-AOA with different numbers of BSs Figure 8: TDOA/AE-AOA performance comparison while both A-AOA and E-AOA noises varying Figure 7: Performance comparison of TDOA/AE-AOA with CRLB Figure 9: TDOA/AE-AOA performance comparison with CRLB 3. AOA noise analysis Figure 8 shows TDOA/AE-AOA performance comparison while E-AOA noise varying from 0.5 degree to.3 degree stepped by 0. degree and A-AOA noise from 0.5 degree to 1.3 degree also stepped by 0. degree. Figure 9 illustrates a 3D performance comparison between TDOA/AE-AOA and CRLB when E-AOA noise STDs vary. The number of BSs involved is 5 and TDOA STD is set to be micron. All other AOA noise STDs are set to be 0.7 degree. It can be observed in these two figures that the performance decreases with the increasing of either A-AOA or E-AOA noise and that our proposed hybrid method performs well close to the theoretically best positioning accuracy values. 4 Conclusion A novel hybrid TDOA/AOA method has been proposed, which has a better positioning performance than other methods and is not sensitive to TDOA noise. When the number of available BSs is very small, our proposed hybrid TDOA/AOA method can significantly improve the positioning accuracy, especially making the positioning feasible with only BSs.

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