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Abstract Indoor localization based on radio technology has been a long-standing issue for the past two decades. In this paper, we study the localization problem by using dual-tag range sensors. We show that the localization problem can be converted into a constrained optimization problem. Based on this, we then derive the constrained Cramer–Rao lower bound (CCRB) for the localization system to characterize the limiting localization accuracy of the system. Two types of estimators are used to solve the localization problem. The first is the maximum likelihood estimator (MLE). The second is the () optimization algorithm. It is shown that the positioning performance of the MLE is close to the CCRB, but its computational burden is very heavy, making it only suitable for solving 2D localization problems. The algorithm gives good positioning performance for both 2D and 3D localization problems by closely following the trend of the CCRB, with the gap being within 3 dB in signal-to-noise power ratio (SNR). The computation time needed by the algorithm for both 2D and 3D localization problems is on the order of seconds. The dual-tag sensor approach is compared to the synthetic aperture radar (SAR) approach. It is shown that the SAR approach yields very good localization accuracies only for 2D localization problems and when SNR is high, but it does not work either for 3D localization problems or for 2D problems with low SNR.
Zheng et al. (Wed,) studied this question.