An instrumental-variable method for bearing-only localization under small noise

In this paper,we propose a k-nearest-neighbor (knn) instrumental-variable (IV) method to solve the nonlinear bearing-only localization under small measurement noise. The IV matrix is constructed by the k Euclidean nearest row neighbors in the regressor. Our estimator is proven to be consistent with a closed-form expression of the asymptotic covariance matrix. In order to improve the positioning accuracy, a weight matrix to the knn-IV estimator can be added. In simulation, the positioning accuracy of our method is validated based on the mean square error (MSE) and bias norm as the evalution indicators. The theoretical link between our method and other methods is also analysed.