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The use of carrier phase data is the main driver for high-precision Global Navigation Satellite Systems (GNSS) positioning solutions, such as Real-Time Kinematic (RTK). However, carrier phase observations are ambiguous by an unknown number of cycles, and their use in RTK relies on the process of mapping real-valued ambiguities to integer ones, so-called Integer Ambiguity Resolution (IAR). The main goal of IAR is to enhance the position solution by virtue of its correlation with the estimated integer ambiguities. With the deployment of new GNSS constellations and frequencies, a large number of observations is available. While this is generally positive, positioning in medium and long baselines is challenging due to the atmospheric residuals. In this context, the process of solving the complete set of ambiguities, so-called Full Ambiguity Resolution (FAR), is limiting and may lead to a decreased availability of precise positioning. Alternatively, Partial Ambiguity Resolution (PAR) relaxes the condition of estimating the complete vector of ambiguities and, instead, finds a subset of them to maximize the availability. This article reviews the state-of-the-art PAR schemes, addresses the analytical performance of a PAR estimator following a generalization of the Cramér–Rao Bound (CRB) for the RTK problem, and introduces Precision-Driven PAR (PD-PAR). The latter constitutes a new PAR scheme which employs the formal precision of the (potentially fixed) positioning solution as selection criteria for the subset of ambiguities to fix. Numerical simulations are used to showcase the performance of conventional FAR and FAR approaches, and the proposed PD-PAR against the generalized CRB associated with PAR problems. Real-data experimental analysis for a medium baseline complements the synthetic scenario. The results demonstrate that (i) the generalization for the RTK CRB constitutes a valid lower bound to assess the asymptotic behavior of PAR estimators, and (ii) the proposed PD-PAR technique outperforms existing FAR and PAR solutions as a non-recursive estimator for medium and long baselines.

Received Signal Strength (RSS) for indoor localization is widely used due to its simplicity and availability in most mobile devices. The RSS channel model is defined by the propagation losses and the shadow fading. This paper studies two-slope RSS channel model and compares its validity to classical one-slope path loss model. Particularly, the work presents real-data results of a Bayesian calibration method. Validation of the model fitting is then performed in a dynamic scenario where the distance to a reference node is tracked by a Kalman Filter. Results show the superiority of two-slope model, specially at large distances.

This paper addresses the problem of determining the Cramér-Rao lower bound (CRLB) for the parameters and breakpoint distance in a Path-Loss Channel model for Received Signal Strength (RSS) measurements. The path loss model is usually assumed for corrupted RSS measurements due to the shadow fading channel feature. In this paper the two-slope path loss model is considered, in which RSS measurements are modeled differently for close and far distances. Closed-form expressions for the CRLB parameters are derived for unknown breakpoint distance. For unknown parameters and breakpoint distance value, a Bayesian estimation method is proposed. The CRLB is then compared with the performance of the herein proposed method. The comparison illustrates convergence and efficiency of the Bayesian estimator.