Detection-only versus detection and identification of model misspecifications

It is common practice to use the well-known concept of the minimal detectable bias (MDB) to assess the performance of statistical testing procedures. However, such procedures are usually applied to a null and a set of multiple alternative hypotheses with the aim of selecting the most likely one. Therefore, in the DIA method for the detection,...

A generalized Kalman filter with its precision in recursive form when the stochastic model is misspecified

In this contribution, we introduce a generalized Kalman filter with precision in recursive form when the stochastic model is misspecified. The filter allows for a relaxed dynamic model in which not all state vector elements are connected in time. The filter is equipped with a recursion of the actual error-variance matrices so as to provide an...

DIA-datasnooping and identifiability

In this contribution, we present and analyze datasnooping in the context of the DIA method. As the DIA method for the detection, identification and adaptation of mismodelling errors is concerned with estimation and testing, it is the combination of both that needs to be considered. This combination is rigorously captured by the DIA estimator....

A modified carrier-to-code leveling method for retrieving ionospheric observables and detecting short-term temporal variability of receiver differential code biases

Sensing the ionosphere with the global positioning system involves two sequential tasks, namely the ionospheric observable retrieval and the ionospheric parameter estimation. A prominent source of error has long been identified as short-term variability in receiver differential code bias (rDCB). We modify the carrier-to-code leveling (CCL), a...

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...

Multi-GNSS PPP-RTK: Mixed-receiver network and user scenarios

In this contribution, we present full-rank observation equations of the network and user receivers, of mixed types, through an application of S-system theory. We discuss the important roles played by the inter system biases (ISBs), and we show how the three-component structure of PPP-RTK is affected by the inclusion of the ISBs as extra...

Distributional theory for the DIA method

The DIA method for the detection, identification and adaptation of model misspecifications combines estimation with testing. The aim of the present contribution is to introduce a unifying framework for the rigorous capture of this combination. By using a canonical model formulation and a partitioning of misclosure space, we show that the...

Does RAIM with correct exclusion produce unbiased positions?

As the navigation solution of exclusion-based RAIM follows from a combination of least-squares estimation and a statistically based exclusion-process, the computation of the integrity of the navigation solution has to take the propagated uncertainty of the combined estimation-testing procedure into account. In this contribution, we analyse,...

Characterization of multi-GNSS between-receiver differential code biases using zero and short baselines

Care should be taken to minimize adverse impact of receiver differential code biases (DCBs) on global navigation satellite system (GNSS)-derived ionospheric parameters. It is therefore of importance to ascertain the intrinsic characteristics of receiver DCBs, preferably in the context of new-generation GNSS. In this contribution, we present a...

Single-receiver single-channel multi-frequency GNSS integrity: Outliers, slips, and ionospheric disturbances

In this contribution the integrity of single- receiver, single-channel, multi-frequency GNSS models is studied. The uniformly most powerful invariant test statistics for spikes and slips are derived and their detection capabilities are described by means of minimal detectable biases (MDBs). Analytical closed-form expressions of the phase-slip,...

A novel un-differenced PPP-RTK concept

In this contribution, a novel un-differenced (UD) (PPP-RTK) concept, i.e. a synthesis of Precise Point Positioning and Network-based Real-Time Kinematic concept, is introduced. In the first step of our PPP-RTK approach, the UD GNSS observations from a regional reference network are processed based upon re-parameterised observation equations,...

Next generation GNSS single receiver cycle slip reliability

In this contribution we study the multi-frequency, carrier-phase slip detection capabilities of a single receiver. Our analysis is based on an analytical expression that we present for themulti-frequencyminimal detectable carrier phase cycle slip.