This paper provides an overview of the most significant existing methods for indoor positioning on a contemporary smartphone. The approaches include Wi-Fi and Bluetooth based positioning, magnetic field fingerprinting, map aided navigation using building floor plans, and aiding from self-contained sensors. Wi-Fi and Bluetooth based positioning methods considered in this survey are fingerprint approaches that determine a user's position using a database of radio signal strength measurements that were collected earlier at known locations. Magnetic field fingerprinting can be used in an information fusion algorithm to improve positioning. The map-matching algorithms include application of wall constraints, topological indoor maps, and building geometry for heading correction. Finally, methods for step counting, step length and direction estimation, orientation tracking, motion classification, transit mode detection, and floor change detection in multi-storey buildings are discussed.

The term ldquolocation fingerprintingrdquo covers a wide variety of methods for determining receiver position using databases of radio signal strength measurements from different sources. In this work we present a survey of location fingerprinting methods, including deterministic and probabilistic methods for static estimation, as well as filtering methods based on Bayesian filter and Kalman filter. We present a unified mathematical formulation of radio map database and location estimation, point out the equivalence of some methods from the literature, and present some new variants. A set of tests in an indoor positioning scenario using WLAN signal strengths is performed to determine the influence of different calibration and location method parameters. In the tests, the probabilistic method with the kernel function approximation of signal strength histograms was the best static positioning method. Moreover, all filters improved the results significantly over the static methods.

Filtering and smoothing algorithms for linear discrete- time state-space models with skewed and heavy-tailed measurement noise are presented. The algorithms use a variational Bayes approximation of the posterior distribution of models that have normal prior and skew- $t$ -distributed measurement noise. The proposed filter and smoother are compared with conventional low- complexity alternatives in a simulated pseudorange positioning scenario. In the simulations the proposed methods achieve better accuracy than the alternative methods, the computational complexity of the filter being roughly 5 to 10 times that of the Kalman filter.

Nonlinear Kalman filter and Rauch-Tung-Striebel smoother type recursive estimators for nonlinear discrete-time state space models with multivariate Student's t-distributed measurement noise are presented. The methods approximate the posterior state at each time step using the variational Bayes method. The nonlinearities in the dynamic and measurement models are handled using the nonlinear Gaussian filtering and smoothing approach, which encompasses many known nonlinear Kalman-type filters. The method is compared to alternative methods in a computer simulation.