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.

Received Signal Strength (RSS) localization is widely\ud used due to its simplicity and availability in most mobile devices.\ud The RSS channel model is defined by the propagation losses\ud and the shadow fading. These parameters might vary over time\ud because of changes in the environment. In this paper, the problem\ud of tracking a mobile node by RSS measurements is addressed,\ud while simultaneously estimating a two-slope RSS model. The\ud methodology considers a Kalman filter with Interacting Multiple\ud Model architecture, coupled to an on-line estimation of the\ud observation’s variance. The performance of the method is shown\ud through numerical simulations in realistic scenarios.Peer ReviewedPostprint (published version

Due to the vast increase in location-based services, currently there exists an actual need of robust and reliable indoor localization solutions. Received signal strength localization is widely used due to its simplicity and availability in most mobile devices. The received signal strength channel model is defined by the propagation losses and the shadow fading. In real-life applications, these parameters might vary over time because of changes in the environment. Thus, to obtain a reliable localization solution, they have to be sequentially estimated. In this article, the problem of tracking a mobile node by received signal strength measurements is addressed, simultaneously estimating the model parameters. Particularly, a two-slope path loss model is assumed for the received signal strength observations, which provides a more realistic representation of the propagation channel. The proposed methodology considers a parallel interacting multiple modelbased architecture for distance estimation, which is coupled with the on-line estimation of the model parameters and the final position determination via Kalman filtering. Numerical simulation results in realistic scenarios are provided to support the theoretical discussion and to show the enhanced performance of the new robust indoor localization approach. Additionally, experimental results using real data are reported to validate the technique.

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.

Global Navigation Satellite Systems (GNSS) have become the keystone and main information supplier for Positioning, Navigation and Timing (PNT) data. While providing an adequate open sky performance, the accuracy of standard code-based GNSS techniques is insufficient for applications requiring precise navigation. Additionally, GNSS positioning algorithms performance can be easily disturbed in signal-degraded environments due to space weather events, obstacles, urban areas, bridges, limited open sky view and/or low-elevation multipath effects. Hence, this study gives a comparative of the performance assessment for different high elevation masks of a multi-frequency multi-GNSS RTK method in a loose combination (a pivot satellite is chosen for each constellation and frequency) to avoid the case of the lack of coinciding frequencies and based in the code and carrier phase measurements of the integration of multiple GNSS constellations. The analysis of the Ambiguity Dilution of Precision (ADOP) and the number of fixed ratio epochs in both static and dynamic real scenarios, demonstrates that the dual frequency L1/E1+L5/E5a GPS+Galileo RTK positioning solution approach presented in this study has a good performance in terms of reliability, positioning accuracy and availability in comparative with a GPSonly RTK algorithm when high elevation mask values are used.

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.Peer ReviewedPostprint (published version

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The use of carrier phase data play an important role for high-precision Global Navigation Satellite Systems (GNSS) positioning solutions, such as Real-Time Kinematic (RTK). Similarly, precise orientation information can be obtained with multiantenna setups which exploit carrier phase observables. The availability of high precision navigation solutions is, however, subject to the Integer Ambiguity Resolution (IAR) performance. IAR is the process of mapping the real-valued carrier ambiguities to integer ones, enhancing the attitude solution by virtue of the cross-correlation with the estimated integer ambiguities. Unfortunately, IAR is known to suffer from dimensionality course or, in other words, the chances for finding the correct vector of integers reduces with the number of ambiguities.This work focuses on improving the availability of high precision attitude estimates by means of using a Partial Ambiguity Resolution (PAR) scheme. PAR relaxes the condition of estimating the complete vector of ambiguities and, instead and finds a subset of them to maximize the availability. A new formulation for attitude determination using quaternion rotation within a precision-driven PAR scheme is proposed. Numerical simulations are used to showcase the attitude determination performance with a conventional Full Ambiguity Resolution (FAR) and a precision-aided PAR approach.