Abstract
The subject of localization has received great deal attention in the past decades. Although it is perhaps a well-studied problem, there is still room for improvement. Traditional localization methods usually assume the number of sensors is sufficient for providing desired performance. However, this assumption is not always satisfied in practice. This paper studies the time of arrival (TOA)-based source positioning in the presence of sensor position errors. An error refined solution is developed for reducing the mean-squared-error (MSE) and bias in small sensor network (the number of sensors is fewer) when the noise or error level is relatively large. The MSE performance is analyzed theoretically and validated by simulations. Analytical and numerical results show the proposed method attains the Cramér-Rao lower bound (CRLB). It outperforms the existing closed-form methods with slightly raising computation complexity, especially in the larger noise/error case.
Highlights
Location determination is one of the classical research fields in signal processing
The 2-stage WLS (2WLS), improved projection method (IPM) and the proposed algorithm have comparable MSE and bias if σr2 6 10−2 m2, while the multidimensional scaling (MDS) is more robust than 2WLS, IPM and even the proposed in relatively larger error region, the sensor position errors are not taken into account
The MDS is more robust than 2WLS, IPM and even the proposed in relatively larger error region, the sensor position errors are not taken into account
Summary
Location determination is one of the classical research fields in signal processing. With the rise of the fifth-generation communication system (5G), Internet of things, automatic pilot and unmanned aerial vehicle, localization continues to receive great attention [1,2,3,4]. Converting the sensor position errors and measurement noise together as equivalent measurement noise, the TOA-based source location estimation is formulated as a weighted optimization problem with constraint. The weighted spherical-interpolation is derived, which solves the source position and redundant variable successively; An approximate expression of the theoretical covariance analysis is presented for the weighted spherical-interpolation; Eliminating the redundant variable, a refinement for the solution is proposed to improve the MSE and bias further; The simulation shows the proposed method performs better than the state-of-the-art methods when using fewer sensors. The novelties of this paper are: Introducing a weighting matrix for spherical-interpolation resulting in the weighted spherical-interpolation; Analyzing the covariance in the small noise region; Refining the solution to improve the MSE and lower the bias further when using only 4 sensors. XT and X−1 are the transpose and inverse of X. x(i : j) denotes a subvector constructed by the i-th to j-th elements. is the Hadamard product. sgn is the the signum operation
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