algorithm for UWB wireless sensor network employing modified propagator method for multipath time delay estimation and 3D. Chan algorithm for determining ...
2013 IEEE International Conference on Consumer Electronics (ICCE)
Fast Three-Dimensional Node Localization in UWB Wireless Sensor Network Using Propagator Method Digest of Technical Papers Hong JIANG, Member, IEEE , Yu ZHANG, Haijing CUI, and Chang LIU
Abstract—This paper presents a fast 3D node localization algorithm for UWB wireless sensor network employing modified propagator method for multipath time delay estimation and 3D Chan algorithm for determining the position of sensor nodes. It enhances the estimation accuracy while requires neither spectral peak searching nor covariance matrix estimation.
II. SIGNAL MODEL Assume that a UWB pulse is transmitted from an unknown node to an anchor node by L paths. In the q-th snapshot, q = 1," , Q , the received signal can be expressed as
I. INTRODUCTION Ranging and localization of unknown sensor nodes in wireless sensor networks (WSN) [1]-[3] have drawn considerable attention in environmental monitoring, health tracking, smart home, M2M, etc. So far, most localization algorithms in WSN are only applicable for two-dimensional (2D) networks, However, in many actual environment, nodes are placed in three-dimensional (3D) terrains, such as workshops, forests, oceans, etc. Although some 3D localization algorithms have been proposed [4],[5], many aspects should be improved in accurate localization, small computational amount, robustness in multipath, energy saving, fast executing, etc. Since the energy and the processing power carried by sensor nodes are limited, the research on effective methods for 3D node positioning is of great significance. This paper investigates 3D localization problem for ultra wideband (UWB)-based WSN using multipath time-delay measurement. Time-delay estimation problem has been studied with a variety of super-resolution techniques, such as Matrix Pencil, MUSIC, TLS-ESPRIT. Compared with correlator methods, they can increase time-resolution even if time delay is smaller than a pulse width. Unfortunately, these techniques increase the complexity of WSN implementation. The propagator method (PM), developed in [6], is a subspace method for direction-of-arrival (DOA) estimation. It can avoid the estimation and eigen-decomposition of the covariance matrix of the received signals which is the main computational burden in traditional subspace methods. However, spectral peak searching through all the space is needed in PM method, which increases computational complexity. Under the principle of low cost, low complexity and low power consumption of node equipment, considering multipath effect, we put forward a fast range-based node localization method for UWB wireless sensor networks in this paper. We develop a modified propagator method (MPM) for time-of-arrival (TOA) estimation in frequency domain, which enhances the estimation accuracy and requires neither spectral searching nor covariance matrix estimation. The computational load is lower than traditional subspace methods. Furthermore, 3D Chan algorithm combined with multilateral localization instead of trilateral localization is developed in the paper to accurately determine the physical coordinates of a group of sensor nodes.
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L
L
l=1
l=1
y(q) ( t ) = ∑βl(q) p( t −τTOA −Δτl ) + w(q) ( t ) =∑βl(q) p( t −τl ) + w(q) ( t ) (1) where p( t ) is UWB waveform.
τ TOA denotes the TOA of the
unknown node, Δτ l and βl represent the relative delay and time-varying complex fading amplitude of the l-th path, respectively. Δτ1 =0 . τl = τ TOA +Δτl denote the propagation (q)
time of the l-th path. w(q) ( t ) is noise. The discrete frequencydomain representation of the identified channel is written as L
H ( q ) ( k ) = ∑ βl ( q ) e
−j
2π kτ l KT
l =1
−j
for k = 0,1,", K −1. zl = e
L
+ V ( q ) ( k ) = ∑ βl ( q ) zlk + V ( q ) ( k )
(2)
l =1
2πτl KT
contains the estimated parameter
τ l . Collecting the data of Q snapshots from (2) yields H = Z(τ )B + V
(3)
where B ∈ ^ L×Q , H ∈ ^ K ×Q , V ∈ ^ K ×Q , and Z(τ ) ∈ ^ K ×L . The problem interest is to estimate parameter
τl
based on (3).
III. THE ALGORITHMS A. Multipath Delay Estimation Algorithm Using Modified Propagator Method (MPM) The steps of MPM algorithm are as follows: i) Divide H into H1 and H 2 consisting of the first and last K − 1 rows of H , respectively. ii) Compose H1 and H 2 to form a 2( K − 1) × Q matrix T
X= ⎡⎣H1TH2T ⎤⎦ . Partition X into two matrices X1 and X2 , such that ⎡X1 ⎤ }L . X=⎢ ⎥ ⎣X2 ⎦ }2(K −1) − L
iii) Solve P H by PH = X2X1H ( X1X1H ) , where P H is a propagator −1
⎡ IL ⎤ operator. Let P = ⎢ H ⎥ , evenly divide P into two ( K − 1) × L ⎣P ⎦ −1 P 1 H . matrices P1 and P 2 , and solve Ψ = P 2 P 1 H P 1
(
)
iv) Obtain the eigen-value matrix Φ of Ψ . Therefore, KT angle ( λl ) , where λl is the eigen value of Ψ , l = 1,", L . τˆl = 2π
627
B. 3D CHAN Algorithm and Multilateral Computation for 3D Node Localization According to the results of MPM-based multipath delay estimation, the TOAs and distances from a node to multiple anchor nodes can be determined. Here, Chan algorithm [7] is extended to 3D, the nonlinear equations are accurately solved to obtain 3D positions of unknown nodes. The geometry relationship of cross points of spheres using five anchor nodes and the localization process are shown in fig.1.(a)(b).
anchor node unknown node estimation of unknown node 1
z(m)
0.5
0
-0.5
-1 1
an unknown node (x,y,z)
0.5
y(m)
τTOA2
τTDOA1
τTOA3
τTDOA2
τTOA4
τTDOA3
τTOA5
τTDOA4
Position computation of unknown node (xˆ , yˆ , zˆ )
MPM-based TOA
TDOA
x(m)
4
3D Chan algorithm
Matrix Pencil algorithm 3.5
Proposed MPM algorithm
3D position error (cm)
3
A. MPM-based multipath delay estimation results Fig. 2 shows the transmitted UWB signal and the received 5-path superposition signal.
2.5
2
1.5
1
0.5
1.2 Transmitted Signal Received Multipath Signal
5
5.5
6 6.5 7 Number of anchor nodes
7.5
8
Fig. 4. Effect of the number of anchor nodes
The simulations shows better performance of the proposed MPM algorithm compared with Matrix Pencil algorithm. In addition, the performance is promoted by increasing the number of anchor nodes. Our method greatly enhances the accuracy and reduces the computational complexity.
0.8 TOA Amplitude
-0.5 -1
C. Accuracy of the Proposed Algorithm In fig.4, SNR=10 dB, the number of anchor nodes varies from 5 to 8. We generate randomly 100 unknown nodes and localize them using traditional Matrix Pencil-based estimation algorithm and the proposed MPM algorithm.
IV. SIMULATIONS
0.6
0.4
0.2
ACKNOWLEDGMENT
0
-0.2
-0.5
Fig. 3. 3D Node Localization (100 unknown nodes, 7 anchor nodes)
(a) 3D localization geometric relationship (b) Localization process Fig.1. Node localization based on TOA and 3D Chan algorithm
1
0 -1
(X1,Y1,Z1) (X2,Y2,Z2) (X3,Y3,Z3) (X4,Y4,Z4) (X5,Y5,Z5)
τTOA1
1 0.5
0
anchor nodes
0
0.2
0.4
0.6
0.8 1 Time (ns)
1.2
1.4
1.6
1.8
The research is supported by Chinese National Natural Science Fund (61071140), as well as Jilin Provincial Natural Science Foundations of China (201215014).
2
Fig. 2. Transmitted signal and received multipath signal of UWB.
Table.1 shows the estimation results of 5-path time delays using the proposed MPM algorithm. SNR=10dB. Q=100. K=1000. T=0.02ns. L=5. The simulations confirm good resolution of the proposed algorithm in multipath.
REFERENCES [1] [2]
Table.1 MPM-based delay estimation results when SNR=10dB τˆ l
True value (ns)
Estimation value (ns)
[3]
Path 1 Path 2 Path 3 Path 4 Path 5
1.60 1.65 1.70 1.75 1.80
1.576 1.629 1.680 1.731 1.784
[4] [5]
B. Position Computation Results using 3D Chan Algorithm In fig. 3, we randomly generate 100 unknown nodes in a 2m × 2m × 2m space, and locate them using 3D Chan algorithm. It shows that the coordinates of these nodes can be estimated with high accuracy even with low density of anchor nodes.
[6] [7]
628
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