Biased Constrained Hybrid Kalman Filter for Range-Based Indoor Localization

The range-based localization method is widely used in wireless sensor localization systems. Many existing localization algorithms are unbiased estimators. However, the estimation performance presents biased features in the real localization systems. On the other hand, many biased location estimators show some essential advantages over unbiased estimators, e.g., robust to the noise, more accurate estimation, and low complexity. In this paper, we deeply investigate the performance of biased estimator, min-max, to achieve a new accuracy limit, and propose a hybrid Kalman filtering algorithm, which recursively locates the target based on biased feature. The first contribution is that we formulate the biased Cramér-Rao lower bound of the min-max algorithm to indicate that the biased localization algorithm can outperform the unbiased algorithms, e.g., maximum likelihood, as if the estimation bias were attained. The second contribution is that we propose a hybrid Kalman filtering algorithm while employing the min-max to construct a constrain region and using the dynamic Gaussian model for calculation in non-Gaussian environments. Our algorithm is robust to complicated environments with high accuracy. And, we implement it in an IoT target tracking platform. Both theoretical analysis and experimental evaluation indicate that the proposed algorithm outperform the unbiased optimal estimation methods. And our algorithm can control the estimation error in only 1 m.