Investigation of MEMS inertial sensors and aircraft dynamic models in global positioning system integrity monitoring for approaches with vertical guidance

An Approach with Vertical Guidance (APV) is an instrument approach procedure which provides horizontal and vertical guidance to a pilot on approach to landing in reduced visibility conditions. APV approaches can greatly reduce the safety risk to general aviation by improving the pilot’s situational awareness. In particular the incidence of Controlled Flight Into Terrain (CFIT) which has occurred in a number of fatal air crashes in general aviation over the past decade in Australia, can be reduced. APV approaches can also improve general aviation operations. If implemented at Australian airports, APV approach procedures are expected to bring a cost saving of millions of dollars to the economy due to fewer missed approaches, diversions and an increased safety benefit. The provision of accurate horizontal and vertical guidance is achievable using the Global Positioning System (GPS). Because aviation is a safety of life application, an aviation-certified GPS receiver must have integrity monitoring or augmentation to ensure that its navigation solution can be trusted. However, the difficulty with the current GPS satellite constellation alone meeting APV integrity requirements, the susceptibility of GPS to jamming or interference and the potential shortcomings of proposed augmentation solutions for Australia such as the Ground-based Regional Augmentation System (GRAS) justifies the investigation of Aircraft Based Augmentation Systems (ABAS) as an alternative integrity solution for general aviation. ABAS augments GPS with other sensors at the aircraft to help it meet the integrity requirements. Typical ABAS designs assume high quality inertial sensors to provide an accurate reference trajectory for Kalman filters. Unfortunately high-quality inertial sensors are too expensive for general aviation. In contrast to these approaches the purpose of this research is to investigate fusing GPS with lower-cost Micro-Electro-Mechanical System (MEMS) Inertial Measurement Units (IMU) and a mathematical model of aircraft dynamics, referred to as an Aircraft Dynamic Model (ADM) in this thesis. Using a model of aircraft dynamics in navigation systems has been studied before in the available literature and shown to be useful particularly for aiding inertial coasting or attitude determination. In contrast to these applications, this thesis investigates its use in ABAS. This thesis presents an ABAS architecture concept which makes use of a MEMS IMU and ADM, named the General Aviation GPS Integrity System (GAGIS) for convenience. GAGIS includes a GPS, MEMS IMU, ADM, a bank of Extended Kalman Filters (EKF) and uses the Normalized Solution Separation (NSS) method for fault detection. The GPS, IMU and ADM information is fused together in a tightly-coupled configuration, with frequent GPS updates applied to correct the IMU and ADM. The use of both IMU and ADM allows for a number of different possible configurations. Three are investigated in this thesis; a GPS-IMU EKF, a GPS-ADM EKF and a GPS-IMU-ADM EKF. The integrity monitoring performance of the GPS-IMU EKF, GPS-ADM EKF and GPS-IMU-ADM EKF architectures are compared against each other and against a stand-alone GPS architecture in a series of computer simulation tests of an APV approach. Typical GPS, IMU, ADM and environmental errors are simulated. The simulation results show the GPS integrity monitoring performance achievable by augmenting GPS with an ADM and low-cost IMU for a general aviation aircraft on an APV approach. A contribution to research is made in determining whether a low-cost IMU or ADM can provide improved integrity monitoring performance over stand-alone GPS. It is found that a reduction of approximately 50% in protection levels is possible using the GPS-IMU EKF or GPS-ADM EKF as well as faster detection of a slowly growing ramp fault on a GPS pseudorange measurement. A second contribution is made in determining how augmenting GPS with an ADM compares to using a low-cost IMU. By comparing the results for the GPS-ADM EKF against the GPS-IMU EKF it is found that protection levels for the GPS-ADM EKF were only approximately 2% higher. This indicates that the GPS-ADM EKF may potentially replace the GPS-IMU EKF for integrity monitoring should the IMU ever fail. In this way the ADM may contribute to the navigation system robustness and redundancy. To investigate this further, a third contribution is made in determining whether or not the ADM can function as an IMU replacement to improve navigation system redundancy by investigating the case of three IMU accelerometers failing. It is found that the failed IMU measurements may be supplemented by the ADM and adequate integrity monitoring performance achieved. Besides treating the IMU and ADM separately as in the GPS-IMU EKF and GPS-ADM EKF, a fourth contribution is made in investigating the possibility of fusing the IMU and ADM information together to achieve greater performance than either alone. This is investigated using the GPS-IMU-ADM EKF. It is found that the GPS-IMU-ADM EKF can achieve protection levels approximately 3% lower in the horizontal and 6% lower in the vertical than a GPS-IMU EKF. However this small improvement may not justify the complexity of fusing the IMU with an ADM in practical systems. Affordable ABAS in general aviation may enhance existing GPS-only fault detection solutions or help overcome any outages in augmentation systems such as the Ground-based Regional Augmentation System (GRAS). Countries such as Australia which currently do not have an augmentation solution for general aviation could especially benefit from the economic savings and safety benefits of satellite navigation-based APV approaches.

Practical aspects of frequency-domain identification of dynamic models of marine structures from hydrodynamic data

The motion response of marine structures in waves can be studied using finite-dimensional linear-time-invariant approximating models. These models, obtained using system identification with data computed by hydrodynamic codes, find application in offshore training simulators, hardware-in-the-loop simulators for positioning control testing, and also in initial designs of wave-energy conversion devices. Different proposals have appeared in the literature to address the identification problem in both time and frequency domains, and recent work has highlighted the superiority of the frequency-domain methods. This paper summarises practical frequency-domain estimation algorithms that use constraints on model structure and parameters to refine the search of approximating parametric models. Practical issues associated with the identification are discussed, including the influence of radiation model accuracy in force-to-motion models, which are usually the ultimate modelling objective. The illustration examples in the paper are obtained using a freely available MATLAB toolbox developed by the authors, which implements the estimation algorithms described.

In search of climate effects on Atlantic Croaker (Micropogonias undulatus) stock off the U.S. Atlantic coast with Bayesian state-space biomass dynamic models

Atlantic Croaker (Micropogonias undulatus) production dynamics along the U.S. Atlantic coast are regulated by fishing and winter water temperature. Stakeholders for this resource have recommended investigating the effects of climate covariates in assessment models. This study used state-space biomass dynamic models without (model 1) and with (model 2) the minimum winter estuarine temperature (MWET) to examine MWET effects on Atlantic Croaker population dynamics during 1972–2008. In model 2, MWET was introduced into the intrinsic rate of population increase (r). For both models, a prior probability distribution (prior) was constructed for r or a scaling parameter (r0); imputs were the fishery removals, and fall biomass indices developed by using data from the Multispecies Bottom Trawl Survey of the Northeast Fisheries Science Center, National Marine Fisheries Service, and the Coastal Trawl Survey of the Southeast Area Monitoring and Assessment Program. Model sensitivity runs incorporated a uniform (0.01,1.5) prior for r or r0 and bycatch data from the shrimp-trawl fishery. All model variants produced similar results and therefore supported the conclusion of low risk of overfishing for the Atlantic Croaker stock in the 2000s. However, the data statistically supported only model 1 and its configuration that included the shrimp-trawl fishery bycatch. The process errors of these models showed slightly positive and significant correlations with MWET, indicating that warmer winters would enhance Atlantic Croaker biomass production. Inconclusive, somewhat conflicting results indicate that biomass dynamic models should not integrate MWET, pending, perhaps, accumulation of longer time series of the variables controlling the production dynamics of Atlantic Croaker, preferably including winter-induced estimates of Atlantic Croaker kills.

Dynamic models of piled foundations

The vibration behavior of piled foundations is an important consideration in fields such as earthquake engineering, construction, machine-foundation design, offshore structures, nuclear energy, and road and rail development. This paper presents a review of the past 40 years' literature on modeling the frequency-dependent behavior of pile foundations. Beginning with the earliest model of a single pile, adapted from those for embedded footings, it charts the development of the four pile-modeling techniques: the "dynamic Winkler-foundation" approach that uses springs to represent the effect of the soil; elasticcontinuum-type formulations involving the analytical solutions for displacements due to a subsurface disk, cylinder, or other element; boundary element methods; and dynamic finite-element formulations with special nonreflecting boundaries. The modeling of pile groups involves accounting for pile-soil-pile interactions, and four such methods exist: interaction factors; complete pile models; the equivalent pier method; and periodic structure theory. Approaches for validating pile models are also explored. Copyright © 2013 by ASME.

Prediction in dynamic models with time-dependent conditional variances

This paper considers forecasting the conditional mean and variance from a single-equation dynamic model with autocorrelated disturbances following an ARMA process, and innovations with time-dependent conditional heteroskedasticity as represented by a linear GARCH process. Expressions for the minimum MSE predictor and the conditional MSE are presented. We also derive the formula for all the theoretical moments of the prediction error distribution from a general dynamic model with GARCH(1, 1) innovations. These results are then used in the construction of ex ante prediction confidence intervals by means of the Cornish-Fisher asymptotic expansion. An empirical example relating to the uncertainty of the expected depreciation of foreign exchange rates illustrates the usefulness of the results. © 1992.

Bayesian Analysis of Latent Threshold Dynamic Models

We discuss a general approach to dynamic sparsity modeling in multivariate time series analysis. Time-varying parameters are linked to latent processes that are thresholded to induce zero values adaptively, providing natural mechanisms for dynamic variable inclusion/selection. We discuss Bayesian model specification, analysis and prediction in dynamic regressions, time-varying vector autoregressions, and multivariate volatility models using latent thresholding. Application to a topical macroeconomic time series problem illustrates some of the benefits of the approach in terms of statistical and economic interpretations as well as improved predictions. Supplementary materials for this article are available online. © 2013 Copyright Taylor and Francis Group, LLC.

Identification of greenhouse climate dynamic models

In this paper climate discrete-time dynamic models for the inside air temperature of two different greenhouses are identified, using data acquired during two different periods of the year. These models employ data from air temperature and relative humidity (both outside and inside the greenhouse), solar radiation, wind speed, and control inputs (ventialtion, etc.).

Parameter identification of structural dynamic models by inverse statistical analysis

Auf dem Gebiet der Strukturdynamik sind computergestützte Modellvalidierungstechniken inzwischen weit verbreitet. Dabei werden experimentelle Modaldaten, um ein numerisches Modell für weitere Analysen zu korrigieren. Gleichwohl repräsentiert das validierte Modell nur das dynamische Verhalten der getesteten Struktur. In der Realität gibt es wiederum viele Faktoren, die zwangsläufig zu variierenden Ergebnissen von Modaltests führen werden: Sich verändernde Umgebungsbedingungen während eines Tests, leicht unterschiedliche Testaufbauten, ein Test an einer nominell gleichen aber anderen Struktur (z.B. aus der Serienfertigung), etc. Damit eine stochastische Simulation durchgeführt werden kann, muss eine Reihe von Annahmen für die verwendeten Zufallsvariablengetroffen werden. Folglich bedarf es einer inversen Methode, die es ermöglicht ein stochastisches Modell aus experimentellen Modaldaten zu identifizieren. Die Arbeit beschreibt die Entwicklung eines parameter-basierten Ansatzes, um stochastische Simulationsmodelle auf dem Gebiet der Strukturdynamik zu identifizieren. Die entwickelte Methode beruht auf Sensitivitäten erster Ordnung, mit denen Parametermittelwerte und Kovarianzen des numerischen Modells aus stochastischen experimentellen Modaldaten bestimmt werden können.

Front spreading in population dynamic models. Theory and application to the Neolithic transition

This thesis presents population dynamics models that can be applied to predict the rate of spread of the Neolithic transition (change from hunter-gathering to farming economics) across the European continent, which took place about 9000 to 5000 years ago. The first models in this thesis provide predictions at a continental scale. We develop population dynamics models with explicit kernels and apply realistic data. We also derive a new time-delayed reaction-diffusion equation which yields speeds about a 10% slower than previous models. We also deal with a regional variability: the slowdown of the Neolithic front when reaching the North of Europe. We develop simple reaction-diffusion models that can predict the measured speeds in terms of the non-homogeneous distribution of pre-Neolithic (Mesolithic) population in Europe, which were present in higher densities at the North of the continent. Such models can explain the observed speeds.