Performance Analysis of Fingerprint-Based Indoor Localization

Fingerprint-based indoor localization holds great potential for the Internet of Things. Despite numerous studies focusing on its algorithmic and practical aspects, a notable gap exists in theoretical performance analysis in this domain. This paper aims to bridge this gap by deriving several lower bounds and approximations of mean square error (MSE) for fingerprint-based localization. These analyses offer different complexity and accuracy trade-offs. We derive the equivalent Fisher information matrix and its decomposed form based on a wireless propagation model, thus obtaining the Cramér-Rao bound (CRB). By approximating the Fisher information provided by constraint knowledge, we develop a constraint-aware CRB. To more accurately characterize nonlinear transformation and constraint information, we introduce the Ziv-Zakai bound (ZZB) and modify it for adapt deterministic parameters. The Gauss–Legendre quadrature method and the trust-region reflective algorithm are employed to make the calculation of ZZB tractable. We introduce a tighter extrapolated ZZB by fitting the quadrature function outside the well-defined domain based on the Q-function. For the constrained maximum likelihood estimator, an approximate MSE expression, which can characterize map constraints, is also developed. The simulation and experimental results validate the effectiveness of the proposed bounds and approximate MSE.