Fundamentals of statistical signal processing: estimation theory
Fundamentals of statistical signal processing: estimation theory
A constrained least squares approach to mobile positioning: algorithms and optimality
EURASIP Journal on Applied Signal Processing
Numerical Mathematics and Computing
Numerical Mathematics and Computing
Optimality analysis of sensor-target localization geometries
Automatica (Journal of IFAC)
A simple and efficient estimator for hyperbolic location
IEEE Transactions on Signal Processing
Exact equivalence of the Steiglitz-McBride iteration and IQML
IEEE Transactions on Signal Processing
Closed-Form Formulae for Time-Difference-of-Arrival Estimation
IEEE Transactions on Signal Processing
Optimal sensor placement and motion coordination for target tracking
Automatica (Journal of IFAC)
Accurate sequential self-localization of sensor nodes in closed-form
Signal Processing
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The linear least squares (LLS) technique is widely used in time-difference-of-arrival based positioning because of its computational efficiency. Two-step weighted least squares (2WLS) and constrained weighted least squares (CWLS) algorithms are two common LLS schemes where an additional variable is introduced to obtain linear equations. However, they both have the same measurement matrix that becomes ill-conditioned when the sensor geometry is a uniform circular array and the source is close to the array center. In this paper, a new CWLS estimator is proposed to circumvent this problem. The main strategy is to separate the source coordinates and the additional variable to different sides of the linear equations where the latter is first solved via a quadratic equation. In doing so, the matrix to be inverted has a smaller condition number than that of the conventional LLS approach. The performance of the proposed method is analyzed in the presence of zero-mean white Gaussian disturbances. Numerical examples are also included to evaluate its localization accuracy by comparing with the existing 2WLS and CWLS algorithms as well as the Cramer-Rao lower bound.