Observability-based Optimization of Coordinated Sampling Trajectories for Recursive Estimation of a Strong, Spatially Varying Flowfield

DeVries, Levi; Majumdar, Sharanya J.; Paley, Derek A.

doi:10.1007/s10846-012-9718-1

Cited by 24 publications

(24 citation statements)

References 31 publications

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“…Observability-based trajectory optimization for flowfield estimation has been proposed in Ref. 34, for example. Such a process would be akin to designing system identification maneuvers for estimating aircraft aerodynamic parameters.…”

Section: B Observability Analysismentioning

confidence: 99%

Coupled Inertial Navigation and Flush Air Data Sensing Algorithm for Atmosphere Estimation

Karlgaard

Kutty

Schoenenberger

2015

AIAA Atmospheric Flight Mechanics Conference

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This paper describes an algorithm for atmospheric state estimation that is based on a coupling between inertial navigation and flush air data sensing pressure measurements. In this approach, the full navigation state is used in the atmospheric estimation algorithm along with the pressure measurements and a model of the surface pressure distribution to directly estimate atmospheric winds and density using a nonlinear weighted least-squares algorithm. The approach uses a highfidelity model of atmosphere stored in table-look-up form, along with simplified models of that are propagated along the trajectory within the algorithm to provide prior estimates and covariances to aid the air data state solution. Thus, the method is essentially a reduced-order Kalman filter in which the inertial states are taken from the navigation solution and atmospheric states are estimated in the filter. The algorithm is applied to data from the Mars Science Laboratory entry, descent, and landing from August 2012. Reasonable estimates of the atmosphere and winds are produced by the algorithm. The observability of winds along the trajectory are examined using an index based on the discrete-time observability Gramian and the pressure measurement sensitivity matrix. The results indicate that bank reversals are responsible for adding information content to the system. The algorithm is then applied to the design of the pressure measurement system for the Mars 2020 mission. The pressure port layout is optimized to maximize the observability of atmospheric states along the trajectory. Linear covariance analysis is performed to assess estimator performance for a given pressure measurement uncertainty. The results indicate that the new tightly-coupled estimator can produce enhanced estimates of atmospheric states when compared with existing algorithms. Nomenclature C = Backward smoothing gain F = Linearization of f with respect to x f = Low-fidelity atmospheric model equations of motion G = Linearization of f with respect to u g = Gravitational acceleration, m/s 2 H = Linearization of h with respect to x h = Pressure distribution model, Pa I = Identity matrix J = Linearization of h with respect to u k = Integer time index N = Integer time index of final pressure measurement P = Covariance of x after the measurement model update = Static pressure, Pa p = Pressure measurement vector, Pa Q = Process noise spectral densitỹ Q = Process noise covariance R = Pressure measurement covariance matrix R = Pressure measurement covariance matrix augmented with navigation uncertainty R = Planetary radius, m = Specific gas constant, J/kg-K S = Prior covariance of x from low fidelity model T = Prior covariance of x from high fidelity model T = Atmospheric temperature, K u = Vehicle inertial state v n , v e , v d = Vehicle planet-relative north, east, and down velocity components, m/s W o = Discrete-time observability Gramian w n , w e , w d = North, east, and down wind velocity components, m/s X 11 , X 12 , X 22 = Van Loan integral sub-matrices x = Atmospheric sta...

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Section: B Observability Analysismentioning

confidence: 99%

Coupled Inertial Navigation and Flush Air Data Sensing Algorithm for Atmosphere Estimation

Karlgaard

Kutty

Schoenenberger

2015

AIAA Atmospheric Flight Mechanics Conference

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“…Equation (7) depends on Ω indirectly through the circulation strength distribution Γ(y) of the horseshoe vortices, which motivates the need to quantitatively assess the observability of the parameters Ω as part of the implementation of an observer-based controller. This section provides a brief overview of observability in the context of linear and nonlinear systems and reviews the empirical observability gramian 22,23,27 used to assess the observability of the wake parameters in the aerodynamic model of Section II.A. A dynamical system is said to be observable if its initial conditions can be determined from a time history of output measurements h(t) and control inputs u(t) over some time interval.…”

Section: B Measures Of Leader Aircraft Observabilitymentioning

confidence: 99%

“…When applied to close formation flight, observability analysis provides a method of mapping "blind spots" in which the follower aircraft may not be able to estimate the leader aircraft wake parameters because they are highly unobservable. Analytical approaches to nonlinear system observability were introduced by Hermann 27,28 To the authors' knowledge this paper is the first instance in which empirical observability measures have been applied to wake sensing in close-formation flight. The contributions of this paper are (1) a method for quantitative analysis of the nonlinear observability of a leader aircraft's wake parameters given distributed measurements of differential pressure collected by the follower aircraft; (2) a recursive Bayesian filtering framework allowing the follower aircraft to assimilate distributed noisy measurements of differential pressure and a low-fidelity (binary) measurement of relative altitude to resolve the leader aircraft wake parameters; and (3) an optimal control algorithm to steer the follower aircraft to a desired vertical/lateral position relative to the leader aircraft while maximizing observability of the leader's parameters along the trajectory.…”

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confidence: 99%

Wake Estimation and Optimal Control for Autonomous Aircraft in Formation Flight

DeVries

Paley

2013

AIAA Guidance, Navigation, and Control (GNC) Conference

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The continued development of sophisticated aircraft with high fidelity control systems will enable autonomous execution of challenging tasks such as aerial refueling and close formation flight. In order to achieve such tasks in autonomous flight, an aircraft must sense other aircraft in close proximity and position itself relative to them. For example, aerial refueling requires the follower aircraft to intercept the filling nozzle attached to the leader aircraft; also, formation-flying aircraft must position themselves strategically to realize benefits of aerodynamic efficiency. This paper uses lifting-line theory to represent a two-aircraft formation and presents a grid-based, recursive Bayesian filter for estimating the wake parameters of the leader aircraft using noisy pressure measurements distributed along the trailing aircraft's wing; the estimator also requires a binary, relative-altitude measurement to break the vertical symmetry. Optimal control strategies are presented to steer the follower aircraft to a desired position relative to the leader while simultaneously optimizing the observability of the leader's relative position. The control algorithms guide the follower aircraft along trajectories that maintain adequate observability, thereby guaranteeing estimator performance. Theoretical results are illustrated using numerical examples of two-aircraft formations.

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“…This task is motivated through problems where the reconstruction of the state proves to be challenging and it becomes imperative to actively acquire, sense, and estimate it; an example of such a problem is robot localization operating in an unknown environment, when the robot only has access to range/bearing measurements [9]. In this context, a robot can use a path that leads to more effective localization of itself or to construct a map of the environment [9,10]. For example, in [10], sampling trajectories for autonomous vehicles are selected from a finite sampling of trajectories through an exhaustive search.…”

Section: Introductionmentioning

confidence: 99%

Augmented state feedback for improving observability of linear systems with nonlinear measurements

Alaeddini

Morgansen

Mesbahi

2019

Systems & Control Letters

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This paper is concerned with the design of an augmented state feedback controller for finite-dimensional linear systems with nonlinear observation dynamics. Most of the theoretical results in the area of (optimal) feedback design are based on the assumption that the state is available for measurement. In this paper, we focus on finding a feedback control that avoids state trajectories with undesirable observability properties. In particular, we introduce an optimal control problem that specifically considers an index of observability in the control synthesis. The resulting cost functional is a combination of LQR-like quadratic terms and an index of observability. The main contribution of the paper is presenting a control synthesis procedure that on one hand, provides closed loop asymptotic stability, and addresses the observability of the system-as a transient performance criteria-on the other.

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Observability-based Optimization of Coordinated Sampling Trajectories for Recursive Estimation of a Strong, Spatially Varying Flowfield

Cited by 24 publications

References 31 publications

Coupled Inertial Navigation and Flush Air Data Sensing Algorithm for Atmosphere Estimation

Coupled Inertial Navigation and Flush Air Data Sensing Algorithm for Atmosphere Estimation

Wake Estimation and Optimal Control for Autonomous Aircraft in Formation Flight

Augmented state feedback for improving observability of linear systems with nonlinear measurements

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