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It is known, that nowadays almost every indoor positioning and navigation system (IPNS) consists of a radio signals part (Wi-Fi or BLE) and a part based on smartphone inertial sensors. Both parts contain a number of challenges complicating a precise user positioning using mobile phones or tablets. In the paper, we describe several contributions. Firstly, a problem of BLE packets recovering is considered. A specific version of a Kalman filter for received signal strength indicator (RSSI) data analysis is developed. The proposed modification allows recovering lost data as well as providing sufficient signal smoothing. Secondly, a custom step detection procedure based on an inertial navigation system (INS) is developed. Unlike to a common solution based on the thresholding of linear acceleration amplitude, an advanced version of the detector is highlighted. Finally, a hybrid indoor localization and navigation (HILN) system developed on the basis of a particle filter (PF) and the proposed modifications for BLE and INS parts is described. Experimental results are provided.