# Browsing by Department "Aerospace Engineering"

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Item A complete and fast survey of the orbital insertion design space for planetary moon missions(2017-08-10) See, Robert Harding; Russell, Ryan Paul, 1976-Show more The most expensive maneuver for an interplanetary spacecraft is the orbital injection. One approach to find minimum fuel-cost trajectories is to preform a search over a number of design parameters such as radius of periapse, apoapse of the insertion orbit, and angle of approach. The so-called V-infinity leveraging maneuver has been shown to reduce the design space by implementing a small burn at apoapse to modify the velocity vector at a flyby body. The focus of the present work is orbital insertion of a science mission at Jupiter or Saturn, with the end goal of rendezvousing with a high-science priority moon such at Titan or Europa. The orbital insertion phase is framed as a boundary-value problem with a 1-D minimization over Time-Of-Flight (TOF) and assumes two body dynamics which enables both rapid and broad trajectory searches. Specifically, a search over Body-Plane (B-Plane) Angle and TOF is presented and then, upon finding a minimum-[Delta] V B-Plane Angle, searches over radius of periapse. Additionally, analytic solutions for B-Plane Angle are derived for the special cases of minimum inclination, node/apse alignment, and moon/apse alignment.Show more Item A comprehensive proposal for securing terrestrial radionavigation systems(2021-05-07) Kor, Ronnie Xian Thong; Humphreys, Todd Edwin; Iannucci, Peter A.Show more The security of terrestrial radionavigation systems (TRNS) has not yet been addressed in the literature. This proposal builds on what is known about securing global navigation satellite systems (GNSS) to address this gap, re-evaluating proposals for GNSS security in light of the distinctive properties of TRNS. TRNS of the type envisioned in this paper are currently in their infancy, unburdened by considerations of backwards compatibility: security for TRNS is a clean slate. This thesis argues that waveform- or signal-level security measures are irrelevant for TRNS, preventing neither spoofing nor unauthorized use of the service. Thus, only security measures which modify navigation message bits merit consideration. This thesis proposes orthogonal mechanisms combining navigation message encryption (NME) and navigation message authentication (NMA), constructed from standard cryptography primitives and specialized to TRNS: message encryption allows providers to offer tiered access to navigation parameters on a bit-by-bit basis, and message authentication disperses the bits of a message authentication code across all data packets, posing an additional challenge to spoofers. This cryptographic proposal, however, is still vulnerable to certain types of replay threats. This thesis addresses this gap by augmenting TRNS with autonomous signal-situational-awareness (SSA) capability, allowing TRNS operators to detect spoofing and meaconing attacks. Two signal authentication techniques for SSA are developed to detect a weak spoofing signal in the presence of static and dynamic multipath. This thesis also proposes enhancements to these signal authentication techniques. These enhancements exploit the synergy from combining information across multiple epochs, or over multiple monitoring beacons, to further lower the spoofer detection threshold. Both techniques with their enhancements are shown to be effective in simulations of the varied operating environments that a generic TRNS will encounter. With both proposed cryptographic NME+NMA scheme and autonomous SSA in place, TRNS gains a defensive capability that GNSS cannot easily match: a comprehensive defense against most man-in-the-middle attacks on position, navigation and timing services.Show more Item A comprehensive study of a coaxial, co-rotating rotor in hover(2023-04-18) Johnson, Chloe Marie; Sirohi, Jayant; Clemens, Noel; Goldstein, David; Hamilton, Mark; McDonald, RobShow more Recent innovations in electric vertical takeoff and landing technologies have spurred research of coaxial, co-rotating (stacked) rotors. A stacked rotor employs two sets of two-bladed rotors offset axially and azimuthally. This thesis focuses on the experimental measurements of a 1.108 m stacked rotor in hover at a tip Mach number of 0.42. The goal of this work is to quantify the effects of rotor geometry and operating conditions on the performance and noise in hover. A coaxial stacked rotor test stand was designed that allows for variable axial and azimuthal spacings and differential collective, or unequal collective on the upper and lower rotor blades. Axial spacings ranged from 0 to 1.75 blade chords and azimuthal spacing ranged from -90° to 90°. A method to characterize the acoustic facility was developed and implemented to quantify the effects of reflections on acoustic measurements. Stacked rotor performance measurements revealed significant variations of individual rotor thrust (67% upper rotor thrust, 50% lower rotor thrust) and power with azimuthal spacing, leading to total rotor thrust and power variations. Variations were greatest at small axial spacings and unequal collective pitch angles on the upper and lower rotor (differential collective), achieving 16.4% thrust change with 15.3% power change at zero differential collective and 76.5% thrust change with 46% power change at negative differential collectives. Moreover, large thrust variations with small azimuthal spacing changes suggest a new method for rotor thrust control. A numerical model was developed that coupled blade element momentum theory with a vortex panel method, with which it was revealed that chordwise circulation along the rotor blades is the dominant factor resulting in measured thrust variations. Rotor noise measurements revealed that at the given operating conditions, tonal and broadband noise are of similar magnitude and are both sensitive to stacked rotor parameters. Tonal noise increased at nonorthogonal azimuthal spacings due to a larger 2/rev noise component. This phenomenon was most pronounced at zero differential collective and nonzero axial spacings. Broadband noise variations were examined through tip vortex trajectory measurements extracted from flow visualization images. It was found that broadband noise around 3 kHz was greatest when the lower rotor operated below the upper rotor tip vortex. Broadband noise decreased by 1.5 dB as the distance between the rotor blade and vortex increased to 0.6 blade chords. Furthermore, if the blade operated in the vortex core or passed above it, broadband noise was reduced by 4.5 dB. The distance between the lower rotor blade and upper rotor blade tip vortex was highly dependent on azimuthal spacing and blade tip clearance. From these results, a quiet stacked rotor was obtained by optimizing tonal and broadband noise through rotor spacing and differential collective. Tonal noise variations are achieved by changing the axial and azimuthal spacing, while broadband noise can be controlled by altering the vortex trajectories with differential collective. This resulted in a mode of operation with 20% more power but a 2.5 dB reduction of total noise.Show more Item A constructionist course for aerodynamic design and simulation analysis(2020-12) Shelburne, William Daniel; Bisetti, FabrizioShow more An undergraduate design-build-test course was created to offer students experience with a variety of modern engineering tools including CAD, additive manufacturing, wind tunnels, and computational fluid dynamics solvers. The course is organized so students may take an aerodynamic design from an idea to prototype testing with simulation data for comparison. This report focuses on the key lessons from the preparation of the course, so adequate direction may be given to provide students a path to success during a typical semester. An example consisting of the design of an airplane wing is used to demonstrate those problems and some solutionsShow more Item A hierarchical multi-robot mapping architecture subject to communication constraints(2020-12) Cappel, Henry Fielding; Sentis, LuisShow more Multi-robot systems are an efficient method to explore and map an unknown environment. The simulataneous localization and mapping (SLAM) algorithm is common for single robot systems, however multiple robots can share respective map data in order to merge a larger global map. This thesis contributes to the multi-robot mapping problem by considering cases in which robots have communication range limitations. The architecture coordinates a team of robots and the central server to explore an unknown environment by exploiting a hierarchical choice structure. The coordination algorithms ensure that the hierarchy of robots choose frontier points that provide maximum information gain, while maintaining viable communication amongst themselves and the central computer through an ad-hoc relay network. In addition, the robots employ a backup choice algorithm in cases when no valid frontier points remain by arranging the communication relay network as a fireline back to the source. This work contributes a scalable, efficient, and robust architecture towards hybrid multi-robot mapping systems that take into account communication range limitations. The architecture is tested in a simulation environment using various maps.Show more Item A homotopic approach to solve the fuel optimal spacecraft proximity operations problem(2017-05) Gulino, Marco; Akella, Maruthi Ram, 1972-Show more This report focuses on finding the low-thrust fuel optimal solution to a class of spacecraft proximity operations subject to path constraints. The mission is for a service spacecraft to perform a surveying orbit relative to a reference within a prescribed period, without violating a no fly zone represented by a sphere centered on the reference vehicle. Clohessy-Wiltshire equations are used, together with the controllability Gramian of the resulting linear system, to obtain an analytical solution to the energy optimal problem. A homotopic approach is subsequently shown to serve as an effective bridge from the energy optimal solution toward the fuel optimal solution.Show more Item A lightweight semantic slam solution for small form factor autonomous vehicles(2023-04-21) Wiberg, Dallin Clark; Akella, Maruthi Ram, 1972-Show more As the interest in autonomous vehicles continues to increase, much effort has gone into developing technologies that enable vehicles to independently and reliably navigate in poorly mapped environments. Nonetheless, reliable navigation in GPS-denied scenarios or through indoor environments continues to present many challenges. Further, the very nature of these scenarios often necessitates certain size, weight, power, and cost (SWaP-C) constraints on the vehicle. This places an additional computational burden on a system’s ability for accurate navigation and path-planning. To this end, this work first proposes the design and development of a unique RGB-LiDAR computer vision pipeline for low SWaP-C 3D object bounding box estimation. This thesis then details the design and implementation of this pipeline into a Simultaneous Localization and Mapping (SLAM) solution for small form factor autonomous vehicles. Computer vision, in conjunction with the proliferation of neural networks, has been an asset of increasing promise within the endeavor for autonomous navigation. With a clever architecture of the sensor suite, RGB and LiDAR data can be aligned and fused in such a way to identify and produce valuable information about surrounding objects. Computationally lightweight algorithms have been developed that reliably estimate not only the range and bearing to the object but also the object’s physical dimensions in the form of a 3-dimensional bounding box. In unknown or GPS-constrained environments, SLAM is a common method for providing an autonomous navigation solution. Among computer vision methods, the great bulk of SLAM solutions employ the tracking of low context features such as points, corners, or edges sensed in the environment around the vehicle. The relatively heavy computational burden of such algorithms renders implementation onto small form factor vehicles exceptionally challenging. In contrast, the ability to track high-context features from the environment, such as complete objects, provides two distinct benefits. First, this provides a means of reducing the dimensionality of the SLAM problem, thereby lending itself nicely to design with an Extended Kalman Filter (EKF) architecture. This further assists the low SWaP-C objective. Secondly, this naturally produces information about and a map of the environment with a higher semantic value. This has large implications and benefits in its ability to feed valuable information into higher level autonomy and decision making.Show more Item A multiplicative multi-state constraint Kalman filter(2021-01-26) Michaelson, Kristen Alyssa; Zanetti, Renato, 1978-Show more A multi-state constraint Kalman filter (MSCKF) is implemented with a multiplicative quaternion update. The filter is tested on data from simulated inertial measurement unit (IMU) and camera measurements. In the simulation, a vehicle views feature points in the environment as it travels along a circular path. The MSCKF is demonstrated to be consistent using Monte Carlo analysisShow more Item A non-linear batch information filter with auto-tuning(2022-12-02) Durant, Dalton; Zanetti, Renato, 1978-; Akella, Maruthi RShow more A non-linear batch information filter provides pose estimation solutions at multiple epochs. The filter estimates dynamic states by using simulated measurement data coming from an inertial measurement unit (IMU), radar range stations, and GPS receivers. This filter has the ability to auto-tune measurement noise covariance matrices using a sliding window technique aided by an introduced smoothing algorithm. This filter is demonstrated to be consistent using Monte Carlo analysis and other methods found in literature.Show more Item A numerical study on mechanical properties of low-density two-dimensional networks of crosslinked long fibers(2023-04-03) Mane, Soham Manohar; Huang, Rui, doctor of civil and environmental engineering; Liechti, K. M.; Kyriakides, Stelios; Rausch, Manuel; Bonnecaze, RogerShow more In this dissertation, we study mechanical properties of low-density two-dimensional (2D) networks by finite element methods. Fiber-based materials are prevalent in nature and in engineering applications. To understand the relationship between the effective mechanical properties and the underlying microstructures, we consider a variety of periodic and random 2D networks of crosslinked long fibers. The linearly elastic properties of periodic 2D networks (e.g., square, triangular and Kagome) are well understood. However, for low-density networks, cooperative buckling of the fiber segments can take place at small strains, leading to nonlinear, anisotropic elastic behaviors. A transition from stretch to bending and then back to stretch dominated deformation is predicted for the Kagome and triangular networks. For random 2D networks, the stress-strain behavior is statistically isotropic and slightly nonlinear under uniaxial tension, dominated by stretch of the fibers aligned closely to the loading direction. Meanwhile, stochastic buckling occurs continuously in the random networks, leading to significant lateral contraction. Consequently, while the effective Young’s modulus follows a nearly linear scaling with respect to the relative density, the effective Poisson’s ratio exhibits a transition from stretch to bending dominated mode as the relative density decreases. The comparison between the periodic and random 2D networks highlights the profound effects of the network topology on the effective elastic properties. Furthermore, we study the strength of 2D periodic networks. First we present the elastic beam models to predict the effective tensile strength of the rotated square, triangular and Kagome networks. Next we conduct finite element analyses to simulate the damage initiation and progression in the periodic 2D networks assuming elastic-brittle fibers. For the Kagome networks subject to uniaxial tension in the y-direction, four different failure modes (including post-buckling modes) are predicted, depending on the relative density and the fiber strength. The elastic beam model does not consider the nonlinear elastic behavior due to buckling and thus generally overestimates the tensile strength. Moreover, for Kagome networks consisting of many unit cells, the effective tensile strength depends on the boundary conditions, and the presence of a crack-like defect could reduce the strength considerably.Show more Item A reactor scale gas dynamics model of an industrial multi-wafer atomic layer deposition reactor using direct simulation Monte Carlo approach(2021-05-06) Thiruppathiraj, Sudharshanaraj; Raja, Laxminarayan L.Show more Atomic layer deposition (ALD) using multi-wafer batch reactors has now emerged as the manufacturing process of choice for modern microelectronics at a massive scale. Stringent process requirements of thin film deposition uniformity within wafer (WiW) and wafer-wafer (WTW) in the batch, film conformity along submicron wafer features, thin film quality, and the utilization of expensive precursors in the reactor dictate ALD reactor design and process parameter optimization. This research discusses a particle-based direct-simulation Monte Carlo (DSMC) of the full reactor scale simulation that overcomes the low Knudsen number limitation of typical continuum computational fluid dynamics (CFD) approaches used for modeling low-pressure ALD reactors. A representative industrial multi-wafer batch reactor used for the deposition of Si-based thin films with N₂ and Si₂Cl₆ (hexachlorodisilane - HCD) as process feed gases with pressures in the range 43 Pa to 130 Pa and uniform reactor temperature of 600°C is simulated. The model provides detailed insights into the flow physics associated with the transport of the precursor species from the inlets, through wafer feed nozzles, into the inter-wafer regions, and finally through the outlet. The reactor operating conditions are shown to be in the slip/transitional flow regime for much of the reactor volume and especially the feed gas nozzle and inter wafer regions (where the Knudsen number approaches ~0.2), justifying the need for a high-Knudsen number DSMC approach as in this work. For the simulated conditions, the non-uniformity of precursor species immediately above the wafer surface is predicted to be within < 1% for a given wafer and < 2% across the entire multi-wafer stack. Results indicate that higher pressure degrades WiW and WTW uniformity. A precursor-wafer interaction efficiency of ~99% is observed, irrespective of chamber pressure.Show more Item A simulation study towards local mass anomaly estimation using GRACE data(2019-01-30) Köhne, Tobias; Bettadpur, Srinivas Viswanath, 1963-Show more Since the dawn of spaceborne Earth Science missions like the Gravity Recovery and Climate Experiment (GRACE), our understanding of global geophysical processes has increased significantly. As measurements get more precise, it is necessary to improve the accuracy of our models to explain observations more precisely. In the case of GRACE-produced gravity solutions, postfit residuals show spatial patterns that indicate unmodeled influences and motivate further investigation. The purpose of this work is to assess the potential of dividing Earth into a grid and using GRACE observations to investigate local mass anomalies, in contrast to the global fields generated usually. Starting from the equations of motion of the N-body problem, a framework is developed and implemented to allow for the simulation of GRACE-like orbits, and generation of inter-satellite range measurements. After differentiating twice using a digital filter, the acceleration observables can be used to estimate excess or default mass, as they are proportional to the forces acting on the spacecraft. Using analytical formulations to generate the true inter-satellite range accelerations, grid-by-grid least squares solutions allow for the estimation of the respective local mass anomaly. However, as there is no knowledge about the true accelerations in reality, this only proves theoretical feasibility. When imitating the process flow of GRACE to generate observed range accelerations from range measurements, numerical insufficiencies stemming from a suboptimal orbit propagator are too large to yield accurate and stable estimates. A sensitivity analysis is included to determine the impact of several simulation parameters and inform future studies of critical design choices, if any emerge. Lastly, an effort is made to search for unmodeled forces in GRACE acceleration residuals. Applying the same grid-based models as used in the simulation setup, a curve is fit through the data spanning the entire mission. The result is a global, coarse estimate of the location and amplitude of model inaccuracies, serving as a starting point for future studies into their causes.Show more Item Ablation onset in unsteady hypersonic flow about nose-tips with a forward-facing cavity(2001-08) Silton, Sidra Idelle, 1973-; Goldstein, David Benjamin, doctor of aeronauticsShow more A forward-facing cavity is examined as a means of reducing the severe heating and delaying ablation onset at the nose-tip of a hypersonic vehicle. Whereas previous studies have concentrated on heating rates alone, the present study addresses the e ect of the cavity on ablation onset times through experiments and joined ow- eld/heat conduction simulations. A viable experimental technique is developed to study ablation in the Mach 5 blow down wind tunnel at the University of Texas at Austin J.J. Pickle Research Center. This technique is utilized to determine the time to ablation onset for nosetip con gurations against which the computational technique could be compared. The computational technique included the linking of commercial computational uid dynamic and solid body heat conduction software. Agreement between the experimental and computational ablation onset times is quite good. Thus, a benchmark is achieved in the computational technique for use in determining the ow eld physics of the complex, hypersonic ow problem. vi An experimental parameter study is then undertaken to optimize the forwardfacing cavity geometry, for a given nose-tip diameter, for the most delayed ablation onset. The parameters of cavity length, lip radius, and diameter are independently optimized. Numerical simulations are conducted for each parametrically optimized con guration in order to investigate the ow physics. The impact of the forwardfacing cavity on the aerodynamic drag is also considered.Show more Item Accuracy limitations of GPS surveying using mixed receiver types(1990) Dahlke, Scott Raymond, 1965-; Not availableShow more Item Accuracy Limits for Globally-Referenced Digital Mapping Using Standard GNSS(IEEE, 2018) Narula, Lakshay; Murrian, Matthew J.; Humphreys, Todd E.Show more Exchange of location and sensor data among connected and automated vehicles will demand accurate global referencing of the digital maps currently being developed to aid positioning for automated driving. This paper explores the limit of such maps’ globally-referenced position accuracy when the mapping agents are equipped with low-cost Global Navigation Satellite System (GNSS) receivers performing standard codephase-based navigation. The key accuracy-limiting factor is shown to be the asymptotic average of the error sources that impair standard GNSS positioning. Asymptotic statistics of each GNSS error source are analyzed through both simulation and empirical data to show that sub-50-cm accurate digital mapping is feasible in moderately urban environments in the horizontal plane after multiple mapping sessions with standard GNSS, but larger biases persist in the vertical direction.Show more Item Achieving the Cramer-Rao Lower Bound in GPS Time-of-Arrival Estimation: A Frequency Domain Weighted Least-Squares Estimator Approach(2013) Wesson, Kyle; Humphreys, Todd E.Show more Item Acoustic waveforms produced by a laboratory scale supersonic jet(2014-08) Fiévet, Romain; Tinney, Charles Edmund, 1975-Show more The spatial evolution of acoustic waveforms produced by a Mach 3 jet are investigated using both 1/4 inch and 1/8 inch pressure field microphones located along rays emanating from the post potential core where the peak sound emission is found to occur. The measurements are acquired in a fully anechoic chamber where ground, or other large surface reflections are minimal. The calculation of the OASPL along an arc located at 95 jet diameters using 120 planar grid measurements are shown to collapse remarkably well when the arc array is centered on the post potential core region. Various statistical metrics, including the quadrature spectral density, number of zero crossings, the skewness of the pressure time derivative and the integral of the negative part of the quadrature spectral density, are exercised along the peak emission path. These metrics are shown to undergo rapid changes within 2 meters from the source regions of this laboratory scale jet. The sensitivity of these findings to both transducer size and humidity effects are discussed. A visual extrapolation of these nonlinear metrics toward the jet shear layer suggests that these waveforms are initially skewed at the source. An experimentally validated wave packet model is used to confirm the location where the pressure decay law transition from cylindrical to spherical. It is then used to estimate the source intensity, which is required to predict the effective Gol'dberg number.Show more Item Acoustics from high-speed jets with crackle(2013-05) Baars, Woutijn Johannes; Tinney, Charles Edmund, 1975-Show more A scaling model based on an effective Gol'dberg number is proposed for predicting the presence of cumulative nonlinear distortions in the acoustic waveforms produced by high-speed jets. Two acoustic length scales, the shock formation distance and the absorption length are expressed in terms of jet exit parameters. This approach allows one to compute the degree of cumulative nonlinear distortion in a full-scale scenario, from laboratory-scale observations, or vice versa. Surveys of the acoustic pressure waveforms emitted by a laboratory-scale, shock-free and unheated Mach 3 jet are used to support the findings of the model. These acoustic waveforms are acquired on a planar grid in an acoustically treated and range-restricted environment. Various statistical metrics are employed to examine the degree of local and cumulative nonlinearity in the measured waveforms and their temporal derivatives. This includes skewness, kurtosis, the number of zero crossings in the waveform, a wave steepening factor, the Morfey-Howell nonlinearity indicator and an application of the generalized Burgers equation. It is advocated that in order for the Morfey-Howell indicator to be used as an investigative tool for the presence of cumulative nonlinear waveform distortion, that it be applied as a multi-point indicator. Based on findings of the model and the spatial topography of the metrics, it is concluded that cumulative nonlinear steepening effects are absent in the current data set. This implies that acoustic shock-structures in the waveforms are generated by local mechanisms in, or in close vicinity to, the jet's hydrodynamic region. Furthermore, these shock-structures induce the crackle noise component. The research aims to quantify crackle in a temporal and spectral fashion, and is motivated by the fact that (1) it is perceived as the most annoying component of jet noise, (2) no unique measures of crackle exist, and (3) significant reductions in jet noise will be achieved when crackle can be controlled. A unique detection algorithm is introduced which isolates the shock-structures in the temporal waveform that are responsible for crackle. Ensemble-averages of the identified waveform sections are employed to gain an in-depth understanding of the crackling structures. Moreover, PDF's of the temporal intermittence of these shocks reveal modal trends and show evidence that crackling shock-structures are present in groups of multiple shocks. A spectral measure of crackle is considered by using wavelet-based time-frequency analyses. The increase in sound energy is computed by considering the global pressure spectra of the waveforms and the ones that represent the spectral behavior during instances of crackle. This energy-based metric is postulated to be an appropriate metric for the level of crackle.Show more Item Adaptation, gyro-ree stabilization, and smooth angular velocity observers for attitude tracking control applications(2014-08) Thakur, Divya, active 21st century; Akella, Maruthi Ram, 1972-Show more This dissertation addresses the problem of rigid-body attitude tracking control under three scenarios of high relevance to many aerospace guidance and control applications: adaptive attitude-tracking control law development for a spacecraft with time-varying inertia parameters, velocity-free attitude stabilization using only vector measurements for feedback, and smooth angular velocity observer design for attitude tracking in the absence of angular velocity measurements. Inertia matrix changes in spacecraft applications often occur due to fuel depletion or mass displacement in a flexible or deployable spacecraft. As such, an adaptive attitude control algorithm that delivers consistent performance when faced with uncertain time-varying inertia parameters is of significant interest. This dissertation presents a novel adaptive control algorithm that directly compensates for inertia variations that occur as either pure functions of the control input, or as functions of time and/or the state. Another important problem considered in this dissertation pertains to rigid-body attitude stabilization of a spacecraft when only a set of inertial sensor measurements are available for feedback. A novel gyro-free attitude stabilization solution is presented that directly utilizes unit vector measurements obtained from inertial sensors without relying on observers to reconstruct the spacecraft's attitude or angular velocity. As the third major contribution of this dissertation, the problem of attitude tracking control in the absence of angular velocity measurements is investigated through angular velocity observer (estimator) design. A new angular velocity observer is presented which is smoothed and ensures asymptotic convergence of the estimation errors irrespective of the initial true states of the spacecraft. The combined implementation of a separately designed proportional-derivative type controller using estimates generated by the observer results in global asymptotic stability of the overall closed-loop tracking error dynamics. Accordingly, a separation-type property is established for the rigid-body attitude dynamics, the first such result to the author's best knowledge, using a smooth (switching-free) observer formulation.Show more Item Adaptive algorithms for identification of symmetric and positive definite matrices(2021-05-04) Moghe, Rahul; Akella, Maruthi Ram, 1972-; Zanetti, Renato, 1978-; Tanaka, Takashi; Bakolas, Efshtatios; D'Souza, ChristopherShow more Adaptive estimation and identification algorithms involving unknown symmetric and positive definite (SPD) matrix-valued parameters are ubiquitous in engineering applications. The problem of estimating the noise covariance matrices in estimation algorithms is considered first. An adaptive Kalman filter to estimate the noise covariance matrix of the noises entering a linear time invariant system is introduced first. The convergence of the estimates as well as the states is guaranteed with mild assumptions on the system. Conditions of estimability of the noise covariance matrix are discussed. The generalization of the adaptive Kalman fitler to the linear time varying case is introduced next. To maintain positive definiteness of the noise covariance estimates a differential geometric approach is adopted. The geometry of the manifold of SPD matrices is used to develop a Riemannian optimization based adaptive Kalman filter that ensure positive definiteness of the estimate. The convergence of the Riemannian optimization-based estimate and the adaptive Kalman filter is established under mild conditions of uniform observability and uniform controllability of the system. An adaptive control problem with an unknown SPD matrix is considered next. A novel projection scheme is introduced that ensures that the estimates of the unknown SPD matrix are SPD. Adaptive update laws for identifying the SPD matrix are also presented. The adaptive control laws are shown to globally stabilize systems in problems such as the adaptive angular velocity tracking, adaptive attitude control, and the adaptive trajectory tracking of robotic manipulators with parameter uncertainties within the generalized mass matrix. In general, such a method can be applied to estimation of symmetric matrices with eigenvalue constraints.Show more