Introduction, discussion and evaluation of recursive Bayesian filters for linear and nonlinear filtering problems in indoor localization

Linear and nonlinear filtering for state estimation (e.g. position estimation or sensor fusion) for indoor positioning and navigation applications is a challenging task. Sensor fusion becomes more important with cost-effective sensors being readily available. However, state estimation with recursive Bayesian filters for sensor fusion and filtering are difficult to apply. We present an overview for the general Bayesian filter and derive the most commonly used recursive Bayesian filters, namely the Kalman, extended Kalman and the unscented Kalman filter along with the particle filter. The later Kalman filters are extension of the original Kalman filter, which are able to solve nonlinear filtering problems. The particle filter is also able to solve nonlinear filtering problems. We evaluate the recursive Bayesian filters for linear and nonlinear filtering problems for sensor fusion from relative dead reckoning positioning data and absolute positioning data from an UWB positioning system. We discuss and evaluate performance and computational complexity and provide recommendations for the use case of the recursive Bayesian filters.