Observability-based optimization for flow sensing and control of an underwater vehicle in a uniform flowfield

DeVries, Levi; Paley, Derek A.

doi:10.1109/acc.2013.6580030

Cited by 34 publications

(37 citation statements)

References 20 publications

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“…In their work, Ham and Brown demonstrated that the eigenvalues and eigenvectors of the error covariance matrix, when properly normalized, provide more insight into the estimability of linear combination of states, thereby supplying the previously commented deficiency of the covariance analysis. Ham and Brown’s estimability approach had been successfully employed for the evaluation of the multiposition alignment [53], in-flight alignment [46,54], aided alignment [55,56], alignment on a rocking base [57], INS/GNSS integration [48,58], as well as in several other applications not related to inertial navigation [59,60,61]. …”

Section: Introductionmentioning

confidence: 99%

On the Error State Selection for Stationary SINS Alignment and Calibration Kalman Filters—Part II: Observability/Estimability Analysis

Silva

Hemerly

Filho

2017

Sensors

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This paper presents the second part of a study aiming at the error state selection in Kalman filters applied to the stationary self-alignment and calibration (SSAC) problem of strapdown inertial navigation systems (SINS). The observability properties of the system are systematically investigated, and the number of unobservable modes is established. Through the analytical manipulation of the full SINS error model, the unobservable modes of the system are determined, and the SSAC error states (except the velocity errors) are proven to be individually unobservable. The estimability of the system is determined through the examination of the major diagonal terms of the covariance matrix and their eigenvalues/eigenvectors. Filter order reduction based on observability analysis is shown to be inadequate, and several misconceptions regarding SSAC observability and estimability deficiencies are removed. As the main contributions of this paper, we demonstrate that, except for the position errors, all error states can be minimally estimated in the SSAC problem and, hence, should not be removed from the filter. Corroborating the conclusions of the first part of this study, a 12-state Kalman filter is found to be the optimal error state selection for SSAC purposes. Results from simulated and experimental tests support the outlined conclusions.

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Section: Introductionmentioning

confidence: 99%

On the Error State Selection for Stationary SINS Alignment and Calibration Kalman Filters—Part II: Observability/Estimability Analysis

Silva

Hemerly

Filho

2017

Sensors

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“…measurements (see, e.g., [12,30]). For a discrete set of measurements in time, the output of the linear time-varying system (5) can be written as …”

Section: B Observability Gramianmentioning

confidence: 99%

“…The observability of vortex flows was studied by Krener [11], where it was shown that Lagrangian measurements provide improved observability compared with Eulerian measurements. In [12], an observability-based sensor placement problem was solved by exhaustive search for sensor locations on a hydrofoil that improves angle-of-attack estimates, which were used in a feedback control of a Joukowski-foil model of an underwater vehicle. Wake estimation in aircraft formation flight was studied in [13], where pressure sensors on the leading edge of the trailing aircraft's wing were used in a vortex lattice simulation to track the lead aircraft's wake.…”

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confidence: 99%

Observability-Based Optimal Sensor Placement for Flapping Airfoil Wake Estimation

Hinson

Morgansen

2014

Journal of Guidance, Control, and Dynamics

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This work considers the optimal sensor placement problem for a general nonlinear system using the eigenvalues of the observability Gramian in the cost function. The problem is formulated as a mixed-integer convex optimization problem. Using the empirical observability Gramian, the input data to this optimization problem are computed from a simulation of the nonlinear system with no analytical model required. A piecewise linear approximation to the observability Gramian is proposed using special ordered sets of type two, allowing a coarser sensor location mesh and thus fewer binary variables and shorter solution times compared with standard gridded approaches. The solution methodology is applied to vortex estimation in the wake of a flapping airfoil using velocity sensors on the surface of the airfoil, which is modeled using unsteady potential flow and a Joukowski conformal mapping. Resulting optimal sensor sets are found near the trailing edge in pairs on the upper and lower surface. Although the observability Gramian is computed from the linearized system, the optimal sensor sets yield improved performance of an unscented Kalman filter estimating wake vortex structure on the nonlinear dynamics; the optimal sets outperform more than 99% of the sampled feasible sensor sets, thus validating the observability eigenvalues as a measure of nonlinear estimator performance. Nomenclature A, B, C = linearized system dynamics matrices a = Joukowski cylinder radius E = expectation operator F = Fisher information matrix f = nonlinear dynamics model H = linear measurement model h = nonlinear measurement model k = discrete time step k r = reduced frequency P = covariance matrix p = number of desired sensors r = number of candidate sensors s i = sensor location for sensor i u = control input u = control linearization deviation u 0 = control linearization trajectory v = measurement noise W = observability Gramiañ W = empirical observability Gramian W = interpolated observability Gramian W d = discrete-time observability Gramian w j = special ordered set weight vector for sensor j x = state vector x = state linearization deviation x 0 = state linearization trajectory

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“…From the viewpoint of the observer, the estimation problem can be likened to traditional target tracking [10]. This section provides the background on Bayes' theorem, Bayesian inference, and single target tracking with recursive Bayesian filtering.…”

Section: Recursive Bayesian Estimationmentioning

confidence: 99%

Randomized path optimization for the mitigated counter-detection of UAVs

Heaton

DeVries²,

Kutzer³

2017

2017 International Conference on Unmanned Aircraft Systems (ICUAS)

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Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instruction, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden to Washington The views expressed in this document are those of the author and do not reflect the official policy or position of the Department of Defense or the U.S. Government. IRB Protocol Number: N/A. 12a. DISTRIBUTION / AVAILABILITY STATEMENTApproved for public release. Distribution is unlimited.12b. DISTRIBUTION CODE ABSTRACT (maximum 200 words)UAVs provide exceptional capabilities and a myriad of potential mission sets, but the ability to disguise where the aircraft takes off and lands would expansively advance the abilities of UAVs. This thesis describes the development of a nonlinear estimation algorithm to predict the terminal location of an aircraft and a trajectory optimization strategy to mitigate the algorithm's success. Vehicle paths are generated using a matrix-based quadratic trajectory computation method. The paths are then tracked by recursively updating time-based observations of vehicle position using Bayesian filtering. The KL divergence is used to compare the probability density of aircraft termination to a normal distribution around the true terminal location. Results show that the optimal conditions to obfuscate path include waypoints at or beyond the vehicle terminal location, variations in velocity throughout the time of flight, and the minimal use of an aircraft's maximum potential time of flight. ABSTRACTUAVs provide exceptional capabilities and a myriad of potential mission sets, but the ability to disguise where the aircraft takes off and lands would expansively advance the abilities of UAVs. This thesis describes the development of a nonlinear estimation algorithm to predict the terminal location of an aircraft and a trajectory optimization strategy to mitigate the algorithm's success. Vehicle paths are generated using a matrix-based quadratic trajectory computation method. The paths are then tracked by recursively updating timebased observations of vehicle position using Bayesian filtering. The KL divergence is used to compare the probability density of aircraft termination to a normal distribution around the true terminal location. Results show that the optimal conditions to obfuscate path include waypoints at or beyond the vehicle terminal location, variations in velocity throughout the time of flight, and the minimal use of an aircraft's maximum potential time of flight.

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Observability-based optimization for flow sensing and control of an underwater vehicle in a uniform flowfield

Cited by 34 publications

References 20 publications

On the Error State Selection for Stationary SINS Alignment and Calibration Kalman Filters—Part II: Observability/Estimability Analysis

On the Error State Selection for Stationary SINS Alignment and Calibration Kalman Filters—Part II: Observability/Estimability Analysis

Observability-Based Optimal Sensor Placement for Flapping Airfoil Wake Estimation

Randomized path optimization for the mitigated counter-detection of UAVs

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