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This paper presents robust positioning methods that use range measurements to estimate location parameters. The existing maximum correntropy criterion-based localization algorithm uses only the <inline-formula> <tex-math notation="LaTeX">$l_{2}$ </tex-math></inline-formula> norm minimization. Therefore, the localization performance may not be satisfying because the <inline-formula> <tex-math notation="LaTeX">$l_{2}$ </tex-math></inline-formula> norm minimization is vulnerable to the large error. Therefore, we propose the convex combination of <inline-formula> <tex-math notation="LaTeX">$l_{1}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$l_{2}$ </tex-math></inline-formula> norm because the <inline-formula> <tex-math notation="LaTeX">$l_{1}$ </tex-math></inline-formula> norm minimization is effective in the large noise condition. The mixed-norm maximum Versoria criterion-based unscented Kalman filter, mixed-norm least lncosh unscented Kalman filter, mixed-norm maximum Versoria criterion iterative reweighted least-squares, mixed-norm least lncosh iterative reweighted least squares and closed-form localization approaches are proposed for mixed line-of-sight/ non-line-of-sight environments. The proposed mixed-norm unscented Kalman filter-based algorithms are more superior to the other methods as the line-of-sight noise level increases by the use of the convex combination of <inline-formula> <tex-math notation="LaTeX">$l_{1}$ </tex-math></inline-formula> norm and <inline-formula> <tex-math notation="LaTeX">$l_{2}$ </tex-math></inline-formula> norm. The iterative reweighted least sqaures-based methods employ a weight matrix. The closed-form weighted least squares algorithm has an advantage that its computational complexity is lower than that of other methods. Simulation and experiments illustrate the localization accuracies of the proposed unscented Kalman filter-based methods are found to be superior to those of the other algorithms under large noise level conditions.

Robust Localization Based on Mixed-Norm Minimization Criterion