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In this paper, we study the performance of two algorithms for tensor reconstruction in the presence of random uncertainties: the first one is the non-blind state-of-the-art, and the second one, new, is blind and is designed to deal with such uncertainties. Using coupled tensor LL1 models, we show that the proposed algorithm performs better than the stateof-the-art, which naturally raises the question of its efficiency. In that perspective, the standard approach is to resort to the usual constrained Cramér-Rao bound (CCRB), which appears to be only partially informative when addressing the asymptotic achievable performance of the considered model. Indeed, the usual CCRB is not able to account for randomness in the set of constraints. To fill this gap, we also introduce a new randomlyconstrained Cramér-Rao bound and we illustrate its relevance to analyze the relative efficiency of the proposed algorithm. As a by-product, we provide closed-form expressions for the Fisher information matrices based on the LL1 model.

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.