A choice of positioning algorithm is a key issue when designing a navigation system. The paper presents an Unscented Kalman Filter (UKF) for a personal navigation system using range measurements between ultrawideband radio modules for positioning. The mentioned system is described by a linear dynamics model and a non-linear observation model, and therefore UKF can be successfully applied for its state estimation. The unscented Kalman filter is a suboptimal non-linear filtration algorithm, however, in contrast to algorithms such as EKF or LKF, it uses an unscented transformation (UT) as an alternative to a linearization of non-linear equations with the use of Taylor series expansion. The linearization considers only the first term of a Taylor series and its higher terms are omitted, which degrades estimation accuracy in highly non-linear systems. Lack of necessity of a linearization of the dynamics and observation models leads to a higher navigation system accuracy. It also facilitates an implementation of the algorithm as non-linear transformations of a set of deterministically chosen sigma points replaces calculations of Jacobian matrices. The paper presents a personal navigation system designed by the authors, describes its unscented Kalman filter used for a mobile user position estimation and contains chosen simulation results of the tests of the filter. Based on these data, efficiency of using this kind of filtration in non-linear navigation systems has been assessed.

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