An affordable and reliable indoor positioning is a highly needed service. Moreover, maps of the indoor environment are vital to many applications. In this paper, a method for joint localization and mapping using multipath delay estimates is developed. Required high-resolution estimates of multipath delays may be obtained using radio frequency or acoustic measurements among a set of nodes in a network. In this paper, the problem is modeled in two-dimensional space with arbitrary node configuration and assuming a convex polygonal room shape. Joint localization and mapping is formulated as an optimization problem. It is subdivided and relaxed into two convex subproblems, which can be solved in an alternating manner. A method for data association and a low-complexity mapping algorithm stemming from Hough transform are proposed. Both the estimation performance and identifiability of the indoor localization problem are improved. Moreover, a basic map of the propagation environment is produced.
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