I. INTRODUCTION

II. PROBLEM STATEMENT

III. MODEL AND ALGORITHM

IV. NUMERICAL SIMULATIONS AND EXPERIMENTAL TESTS

V. CONCLUSION

REFERENCES

The localization algorithm for mobile robots working in narrow space needs to handle the scenario that the geometric shape of reference nodes tends to a line, which results in the matrix of least squares localization approaches ill-conditioned. Estimator bias becomes an important factor that can degrade the localization performance. In this paper, we present a fast unbiased range-based localization algorithm to resist the ill-conditioned problem. The main strategy is to augment objective function in the resultant optimization formulations via introducing a measurement distance into the locating model, which forms a least squares problem with cone constrained. The proposed model decouples the measurement distances from the matrix of least squares, which avoids the ill-conditioned problem when the target is around the geometric center. The closed-form expression of locating position ensures that the proposed algorithm is unbiased and low computation burden in the presence of zero-mean disturbance. Moreover, the robustness improvement of the augmented objective function is analyzed. Numerical simulations are used to corroborate the analytic results which demonstrate the good performance, robustness, and fastness of the proposed method.

INTRODUCTION

Indoor localization for autonomous robots becomes an attractive subject with the rapid development and application of the autonomous robots technology [1], [2]. The robots need localization systems to provide position information which is critical and fundamental for the control algorithm. Since the distance information can be sourced from various physical signals, such as, laser, ultrasound, ultrawideband (UWB), time-of-arrival (TOA), time-difference-of-arrival (TDOA), received signal strength (RSS), channel state information (CSI) and in various combinations [3]–[۹], the robots can flexibly equip the suitable ranging device to adapt working circumstance. Therefore, range-based localization algorithms, which estimate the target position by using distance information, are widely used for robot navigation. To pursue efficient localization performance, methods are proposed, such as using more sensitive ranging sensors, optimizing calculation methods, cooperating localization among the target nodes, etc. Since cooperative localization [10], which utilizes the information among the target nodes, significantly improves the localization accuracy, it has become the current lines of research. However, only a single robot is deployed in some applications, such as inspecting the safety of the underground tunnel. In this paper, we focus on the range-based localization algorithm for a single target node.