Uncertainty Propagation for Inertial Navigation with Coning, Sculling, and Scrolling Corrections

This paper investigates the propagation of estimation errors through a common coning, sculling, and scrolling architecture used in modern-day inertial navigation systems. Coning, sculling, and scrolling corrections often have an unaccounted for effect on the error statistics of inertial measurements used to describe the state and uncertainty propagation for position, velocity, and attitude estimates. Through the development of an error analysis for a set of coning, sculling, and scrolling algorithms, mappings of the measurement and estimation errors through the correction term are adaptively generated. Using the developed mappings, an efficient and consistent propagation of the state and uncertainty, within the multiplicative extended Kalman filter architecture, is achieved. Monte Carlo analysis is performed, and results show that the developed system has favorable attributes when compared to the traditional mechanization.

Improved parameter estimation and uncertainty propagation in Bayesian Radiocarbon-dated Event Count [REC] models

Data about the past contain chronological uncertainty that needs to be accounted for in statistical models. Recently a method called Radiocarbon-dated Event Count (REC) modelling has been explored as a way to improve the handling of chronological uncertainty in the context of statistical regression. REC modelling has so far employed a Bayesian hierarchical framework for parameter estimation to account for chronological uncertainty in count series of radiocarbon-dates. This approach, however, suffers from a couple of limitations. It is computationally inefficient, which limits the amount of chronological uncertainty that can be accounted for, and the hierarchical framework can produce biased, but highly precise parameter estimates. Here we report the results of an investigation in which we compared hierarchical REC models to an alternative with simulated data and a new R package called "chronup". Our results indicate that the hierarchical framework can produce correct high-precision estimates given enough data, but it is susceptible to sampling bias and has an inflated Type I error rate. In contrast, the alternative better handles small samples and fully propagates uncertainty into parameter estimates. In light of these results, we think the alternative method is more generally suitable for Palaeo Science applications.

Uncertainty Quantification of Time-Dependent Quantities in a System with Adjustable Level of Smoothness

We summarise the results of a computational study involved with Uncertainty Quantification (UQ) in a benchmark turbulent burner flame simulation. UQ analysis of this simulation enables one to analyse the convergence performance of one of the most widely-used uncertainty propagation techniques, Polynomial Chaos Expansion (PCE) at varying levels of system smoothness. This is possible because in the burner flame simulations, the smoothness of the time-dependent temperature, which is the study's QoI is found to evolve with the flame development state. This analysis is deemed important as it is known that PCE cannot accurately surrogate non-smooth QoIs and thus perform convergent UQ. While this restriction is known and gets accounted for, there is no understanding whether there is a quantifiable scaling relationship between the PCE's convergence metrics and the level of QoI's smoothness. It is found that the level of QoI-smoothness can be quantified by its standard deviation allowing to observe the effect of QoI's level of smoothness on the PCE's convergence performance. It is found that for our flow scenario, there exists a power-law relationship between a comparative parameter, defined to measure the PCE's convergence performance relative to Monte Carlo sampling, and the QoI's standard deviation, which allows us to make a more weighted decision on the choice of the uncertainty propagation technique.

Variance in Variants: Propagating Genome Sequence Uncertainty into Phylogenetic Lineage Assignment

Genetic sequencing is subject to many different types of errors, but most analyses treat the resultant sequences as if they are known without error. Next generation sequencing methods rely on significantly larger numbers of reads than previous sequencing methods in exchange for a loss of accuracy in each individual read. Still, the coverage of such machines is imperfect and leaves uncertainty in many of the base calls. On top of this machine-level uncertainty, there is uncertainty induced by human error, such as errors in data entry or incorrect parameter settings. In this work, we demonstrate that the uncertainty in sequencing techniques will affect downstream analysis and propose a straightforward method to propagate the uncertainty. Our method uses a probabilistic matrix representation of individual sequences which incorporates base quality scores as a measure of uncertainty that naturally lead to resampling and replication as a framework for uncertainty propagation. With the matrix representation, resampling possible base calls according to quality scores provides a bootstrap- or prior distribution-like first step towards genetic analysis. Analyses based on these re-sampled sequences will include a more complete evaluation of the error involved in such analyses. We demonstrate our resampling method on SARS-CoV-2 data. The resampling procedures adds a linear computational cost to the analyses, but the large impact on the variance in downstream estimates makes it clear that ignoring this uncertainty may lead to overly confident conclusions. We show that SARS-CoV-2 lineage designations via Pangolin are much less certain than the bootstrap support reported by Pangolin would imply and the clock rate estimates for SARS-CoV-2 are much more variable than reported.