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Compensation strategy for distributed tracking in wireless sensor networks with packet losses

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Abstract

Packet loss is inevitable in wireless sensor networks (WSNs). On the basis of the distributed Kalman filter (DKF) and consensus filter, we propose both biased and unbiased compensation strategies to improve tracking accuracy and reliability for WSNs’ packet dropout problem. In the biased compensation strategy, undelivered data from neighbours is compensated by the data of node itself; and in the unbiased compensation strategy, weights of all nodes are updated when packet dropout happens. With these two compensation strategies, DKF can be valid under both mild and poor connectivity conditions. Furthermore, sufficient condition is given to guarantee the convergence of estimation error system. Simulation results show that statistics average estimation errors of the biased and unbiased compensation strategies reduce 37.541 and 37.542 % of state estimation respectively compared to the DKF when the packet loss rate reaches 33.3 %, which demonstrates that the proposed algorithms perform better in filtering packet dropout than the DKF.

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Abbreviations

k :

Simulation iteration

A :

System matrix of moving target

x(k):

Target states

B :

Noise matrix

w(k):

Process noise (independent)

z i (k):

Observation of target from the ith sensor

H i :

Measurement matrix (reversible)

v i (k):

Measurement noise of the ith sensor (independent)

P i (k):

Priori estimation of gain matrix of the ith sensor

\(\hat{x}_{i} (k)\) :

State estimation of target from the ith sensor

\(\bar{x}_{i} (k)\) :

Mean state estimation of target from the ith sensor

N i (k):

The nodes that is connected to the Node i

J i (k):

The nodes which can deliver information to the Node i

u i (k):

Measurement aggregated by sensor data from the ith sensor

U i (k):

Covariance aggregated by covariance data from the ith sensor

y i (k):

Fused sensor data

S i (k):

Fused inverse-covariance matrices

ε:

Step-size

\(M_{i} (k)\) :

Defined as \((P_{i}^{ - 1} (k) + S_{i} (k))^{ - 1}\)

\(\hat{A} = \{ a_{ij} \}\) :

Adjacency matrix

L :

Laplacian matrix

\(\hat{P}_{ij}\) :

A matrix defined as \(\hat{P}_{ij} = I - \epsilon \cdot L_{ij}\)

γ ij k :

A binary variable to mark whether packet drop happens

e i (k):

Estimation error of the ith sensor

v(k):

Measurement noise vector in the k iteration

ρ(A) = α :

Spectral radius of system matrix of system matrix A

\(\hat{D}\) :

A matrix defined by \(\hat{D} = \hat{A} \cdot diag(H_{i}^{T} R_{i}^{ - 1} H_{i} )\)

\(\Xi\) :

A covariance matrix defined by lim k→∞ E(e(k) · e T(k))

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Acknowledgments

This work was supported by Key Project of Chinese National Programs for Fundamental Research and Development (973 program) under Grant (2012CB720003), the National Natural Science Foundation of China (Nos. 91016004, 61004023, 61127007, 61174069) and the International S&T Cooperation Program of China (No. 2013DEE13040).

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Authors and Affiliations

  1. School of Automation Science and Electrical Engineering, Beihang University, Beijing, 100191, People’s Republic of China

    Yan Wang, Chen Qian & Xiangyu Liu

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  1. Yan Wang
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  2. Chen Qian
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Correspondence to Yan Wang.

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Wang, Y., Qian, C. & Liu, X. Compensation strategy for distributed tracking in wireless sensor networks with packet losses. Wireless Netw 21, 1925–1934 (2015). https://doi.org/10.1007/s11276-014-0884-x

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