Indoor Map Boundary Correction Based on Normalized Total Least Squares of Condition Equation

Abstract

Indoor high-precision maps are necessary for many applications, including robot navigation and location-based services. Raw indoor map boundaries are too irregular and coarse to be used in practical applications directly; thus, correction for indoor map boundaries is necessarily carried out. Considering that least-square (LS) methods cannot process the errors in a coefficient matrix, we proposed a normalized total least-squares of condition (NTLSC) equation method to solve for polylines. The proposed NTLSC is more robust than LS with respect to the ill-posed problem in iteration, and linearization need not be employed, which simplifies the complexity of the formula. Aiming at the curves in the map, an iterative LS (ILS) strategy was designed to rectify it for high precision. However, due to the use of different correction models, there will be some tiny gaps between the curve and polylines. Therefore, a junction processing method was put forward, which is an indispensable step to preserve the integrality of the indoor map boundary. Finally, the indoor map boundaries of two scenes were refined by the proposed method, and the results of two perspectives of qualitative and quantitative evaluations indicate that the proposed method can effectively correct irregular and coarse map boundaries.