This contribution investigates four members of the class of Detection, Identification, and Adaptation (DIA) estimators, which integrate parameter estimation with hypothesis testing. Using the framework of minimum mean penalty testing, we analyze and compare the misclosure-space partitionings of the traditional DIA procedure, which combines the overall model test with likelihood-ratio-based tests, and those maximizing the probabilities of correct hypothesis identification and parameter estimation. A constrained version of the latter, with the null hypothesis acceptance region fixed to the traditional procedure, is also examined. Our study focuses on cases where the biases under alternative hypotheses are fully known. Next to the conceptual comparison, we also assess, through a number of examples, misclosure-space partitionings and the probabilities of DIA estimators falling within a defined elliptical safety region. The results highlight the relationships and distinctions among the DIA estimators, revealing the influence of penalty functions, bias magnitude, safety region size, and false alarm probability.

While integer ambiguity resolution (IAR) enables GNSS to achieve real-time sub-centimeter-level positioning in open-sky environments, it can be easily hindered if the involved receivers are situated in areas with limited satellite visibility, such as in dense city environments. In such GNSS-challenged cases, commercial Low Earth Orbit (LEO) communication satellites can potentially augment GNSS by providing additional measurements. However, LEO satellites often lack code measurements, mainly transmitting satellite-specific frequency-varying carrier phase signals. This contribution aims to study the ambiguity-resolved baseline positioning performance of such phase-only signals, addressing the extent to which LEO constellations can realize near real-time positioning in standalone and GNSS-combined modes. Through a simulation platform, we analyze the distinct response of each LEO constellation (Iridium, Globalstar, Starlink, OneWeb, and Orbcomm) to IAR under various circumstances. Although achieving single-receiver high-precision positioning can be challenged by inaccuracies in the LEO satellite orbit products, the relative distance between two receivers can help overcome this limitation. As a result, centimeter-level relative positioning over short baselines can be made possible, even with a satellite elevation cut-off angle of 50 degrees, making it suitable for GNSS-challenged environments. This can be achieved with high-grade receiver clocks over very short baselines (∼5 km) and access to decimeter-level orbit products.

Customary confidence regions do not truly reflect in the majority of our geodetic applications the confidence one can have in one’s produced estimators. As it is common practice in our daily data analyses to combine methods of parameter estimation and hypothesis testing before the final estimator is produced, it is their combined uncertainty that has to be taken into account when constructing confidence regions. Ignoring the impact of testing on estimation will produce faulty confidence regions and therefore provide an incorrect description of estimator’s quality. In this contribution, we address the interplay between estimation and testing and show how their combined non-normal distribution can be used to construct truthful confidence regions. In doing so, our focus is on the designing phase prior to when the actual measurements are collected, where it is assumed that the working (null) hypothesis is true. We discuss two different approaches for constructing confidence regions: Approach I in which the region’s shape is user-fixed and only its size is determined by the distribution, and Approach II in which both the size and shape are simultaneously determined by the estimator’s non-normal distribution. We also prove and demonstrate that the estimation-only confidence regions have a poor coverage in the sense that they provide an optimistic picture. Next to the provided theory, we provide computational procedures, for both Approach I and Approach II, on how to compute confidence regions and confidence levels that truthfully reflect the combined uncertainty of estimation and testing.