Minimal Detectable and Identifiable Biases for quality control

The Minimal Detectable Bias (MDB) is an important diagnostic tool in data quality control. The MDB is traditionally computed for the case of testing the null hypothesis against a single alternative hypothesis. In the actual practice of statistical testing and data quality control, however, multiple alternative hypotheses are considered. We show that this has two important consequences for one's interpretation and use of the popular MDB. First, we demonstrate that care should be exercised in using the single-hypothesis-based MDB for the multiple hypotheses case. Second, we show that for identification purposes, not the MDB, but the Minimal Identifiable Bias (MIB) should be used as the proper diagnostic tool. We analyse the circumstances that drive the differences between the MDBs and MIBs, show how they can be computed using Monte Carlo simulation and illustrate by means of examples the significant differences that one can experience between detectability and identifiability

Risking to underestimate the integrity risk

As parameter estimation and statistical testing are often intimately linked in the processing of observational data, the uncertainties involved in both estimation and testing need to be properly propagated into the final results produced. This necessitates the use of conditional distributions when evaluating the quality of the resulting estimator. As the conditioning should be on the identified hypothesis as well as on the corresponding testing outcome, omission of the latter will result in an incorrect description of the estimator’s distribution. In this contribution, we analyse the impact this omission or approximation has on the considered distribution of the estimator and its integrity risk. For a relatively simple observational model it is mathematically proven that the rigorous integrity risk exceeds the approximation for the contributions under the null hypothesis, which typically has a much larger probability of occurrence than an alternative. Actual GNSS-based positioning examples confirm this finding. Overall we observe a tendency of the approximate integrity risk being smaller than the rigorous one. The approximate approach may, therefore, provide a too optimistic description of the integrity risk and thereby not sufficiently safeguard against possibly hazardous situations. We, therefore, strongly recommend the use of the rigorous approach to evaluate the integrity risk, as underestimating the integrity risk in practice, and also the risk to do so, cannot be acceptable particularly in critical and safety-of-life applications

A comparison of TCAR, CIR and LAMBDA GNSS ambiguity resolution

With the envisioned introduction of three-carrier GNSS's (modernized GPS, Galileo), new methods of ambiguity resolution have been developed. In this contribution we will compare two important candidate methods for triple-frequency ambiguity resolution with the already existing LAMBDA (Least-squares Ambiguity Decorrelation Adjustment) method; the TCAR (Three-Carrier Ambiguity Resolution) method; and the CIR (Cascading Integer Resolution) method. It will be shown that for their estimation principle, both TCAR and CIR rely on integer bootstrapping, whereas LAMBDA is based on integer least-squares, of which optimality has been proven, that is, highest probability of success. In TCAR and CIR pre-defined ambiguity transformation are used, whereas LAMBDA exploits the information content of the full ambiguity variance-covariance matrix, with statistical decorrelation the objective in constructing the ambiguity transformation. For the aspect of resolving the ambiguities, TCAR and CIR are designed for use with the geometry-free model. LAMBDA can intrinsically handle any GNSS model with integer ambiguities and thereby utilize satellite geometry to its benefit in geometry-based models

A Framework for Low Complexity Least-Squares Localization With High Accuracy

In this paper, a new framework is proposed for least-squares localization based on estimated ranges, coveringtime-difference-of-arrival (TDoA), time-of-arrival (ToA), and received signal strength (RSS) cases. The multidimensional nonlinear localization problem is first transformed to a lower dimension and then solved iteratively. Within the proposed transformed least-squares (TLS) framework, we introduce a method in which the localization problem is transformed to one dimension (1-D). In this way, compared to the classical nonlinear least-squares (NLS) type of methods, the amount of computations in each iteration is greatly reduced; a reduction of 67% for a 3-D positioning system is shown. Hence, the introduced 1-D iterative (1DI) method is fairly light on the computational load.The way to choose the 1-D parameter is proposed, and theoretical expressions for the convergence rate and the root- mean-squared error (RMSE) of the 1DI estimator are derived. Validation is performed mainly based on actual ultra-wideband (UWB) radio measurements, collected in typical office environments, with signal bandwidths varying from 0.5 to 7.5 GHz. Supplementary simulations are also included for validation. Results show that, in terms of RMSE, the 1DI method performs better than the linear least-squares (LLS) method, where the solution is obtained noniteratively, and performs similarly as NLS, especially in TDoA cases

A hybrid optical-wireless network for decimetre-level terrestrial positioning

Global navigation satellite systems (GNSS) are widely used for navigation and time distribution, features indispensable for critical infrastructure such as mobile communication networks, as well as emerging technologies like automated driving and sustainable energy grids. While GNSS can provide centimetre-level precision, GNSS receivers are prone to many-metre errors due to multipath propagation and obstructed view of the sky, which occur especially in urban areas where accurate positioning is needed most. Moreover, the vulnerabilities of GNSS, combined with the lack of a back-up system, pose a severe risk to GNSS-dependent technologies. Here, we demonstrate a terrestrial positioning system which is independent of GNSS and offers superior performance through a constellation of radio transmitters, connected and time-synchronised at the sub-nanosecond level through a fibre-optic Ethernet network. Employing optical and wireless transmission schemes similar to those encountered in mobile communication networks, and exploiting spectrally efficient virtual wideband signals, the detrimental effects of multipath propagation are mitigated, thus enabling robust decimetre-level positioning and sub-nanosecond timing in a multipath-prone outdoor environment. This work provides a glimpse of a future in which telecommunication networks provide not only connectivity, but also GNSS-independent timing and positioning services with unprecedented accuracy and reliability.Comment: 38 pages, 9 figures, 3 table

In Defence of Modest Doxasticism About Delusions

Here I reply to the main points raised by the commentators on the arguments put forward in my Delusions and Other Irrational Beliefs (OUP, 2009). My response is aimed at defending a modest doxastic account of clinical delusions, and is articulated in three sections. First, I consider the view that delusions are in-between perceptual and doxastic states, defended by Jacob Hohwy and Vivek Rajan, and the view that delusions are failed attempts at believing or not-quite-beliefs, proposed by Eric Schwitzgebel and Maura Tumulty. Then, I address the relationship between the doxastic account of delusions and the role, nature, and prospects of folk psychology, which is discussed by Dominic Murphy, Keith Frankish, and Maura Tumulty in their contributions. In the final remarks, I turn to the continuity thesis and suggest that, although there are important differences between clinical delusions and non-pathological beliefs, these differences cannot be characterised satisfactorily in epistemic terms. \u