We construct a practical and real-time probabilistic framework for fine target tracking. In our scenario, a Bluetooth Low-Energy (BLE) device navigating in the environment publishes BLE packets that are captured by stationary BLE sensors. The aim is to accurately estimate the live position of the BLE device emitting these packets. The framework is built upon a hidden Markov model (HMM), the components of which are determined with a combination of heuristic and data-driven approaches. In the data-driven part, we rely on the fingerprints formed priorly by extracting received signal strength indicators (RSSI) from the packets. These data are then transformed into probabilistic radio-frequency maps that are used for measuring the likelihood between an RSSI data and a position. The heuristic part involves the movement of the tracked object. Having no access to any inertial information of the object, this movement is modeled with Gaussian densities with variable model parameters that are to be determined heuristically. The practicality of the framework comes from the associated small parameter set used to discretize the components of the HMM. By tuning these parameters, such as the grid size of the area, the mask size and the covariance of the Gaussian; a probabilistic filtering becomes tractable for discrete state spaces. The filtering is then performed by the forward algorithm given the instantaneous sequential RSSI measurements. The performance of the system is evaluated by taking the mean squared errors of the most probable positions at each time step to their corresponding ground-truth positions. We report the statistics of the error distributions and see that we achieve promising results. The approach is also finally evaluated by its runtime and memory usage.