An Efficient Quadratic Constrained Least Squares Localization Method for Narrow Space With Ranging Measurement

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.