Date of download: 12/17/2017 Copyright © ASME. All rights reserved. From: Conjugate Unscented Transformation: Applications to Estimation and Control J. Dyn. Sys., Meas., Control. 2017;140(3):030907-030907-22. doi:10.1115/1.4037783 Figure Legend: Unscented transformation points in 2D: (a) points with corresponding weights and (b) effect of κ on weight

Date of download: 12/17/2017 Copyright © ASME. All rights reserved. From: Conjugate Unscented Transformation: Applications to Estimation and Control J. Dyn. Sys., Meas., Control. 2017;140(3):030907-030907-22. doi:10.1115/1.4037783 Figure Legend: Symmetric set of points and axes 2D and 3D space: (a) 2D axes, (b) 3D first quadrant view 1, and (c) 3D first quadrant view 2

Date of download: 12/17/2017 Copyright © ASME. All rights reserved. From: Conjugate Unscented Transformation: Applications to Estimation and Control J. Dyn. Sys., Meas., Control. 2017;140(3):030907-030907-22. doi:10.1115/1.4037783 Figure Legend: Comparison of number of points for Gaussian PDF: (a) fifth-order, (b) seventh-order, and (c) ninth-order

Date of download: 12/17/2017 Copyright © ASME. All rights reserved. From: Conjugate Unscented Transformation: Applications to Estimation and Control J. Dyn. Sys., Meas., Control. 2017;140(3):030907-030907-22. doi:10.1115/1.4037783 Figure Legend: Comparison of number of points for uniform PDF: (a) fifth-order, (b) seventh-order, (c) seventh-order (CUT versus Sparse GLgn4), and (d) ninth-order

Date of download: 12/17/2017 Copyright © ASME. All rights reserved. From: Conjugate Unscented Transformation: Applications to Estimation and Control J. Dyn. Sys., Meas., Control. 2017;140(3):030907-030907-22. doi:10.1115/1.4037783 Figure Legend: Simulation results for polar to Cartesian transformation: (a) μr=1 m, μθ=90 deg, σr2=0.022 m2, σθ2=152 deg2 and (b) μr=50 m, μθ=0 deg, σr2=0.022 m2, σθ2=302 deg2

Date of download: 12/17/2017 Copyright © ASME. All rights reserved. From: Conjugate Unscented Transformation: Applications to Estimation and Control J. Dyn. Sys., Meas., Control. 2017;140(3):030907-030907-22. doi:10.1115/1.4037783 Figure Legend: Nonpolynomial function-uniform PDF: % relative error: (a) Gauss–Legendre, (b) sparse grid Gauss–Legendre, and (c) 10% relative error GLgn versus CUT-U

Date of download: 12/17/2017 Copyright © ASME. All rights reserved. From: Conjugate Unscented Transformation: Applications to Estimation and Control J. Dyn. Sys., Meas., Control. 2017;140(3):030907-030907-22. doi:10.1115/1.4037783 Figure Legend: Air traffic scenario: (a) typical aeroplane trajectory and (b) estimated aeroplane trajectory

Date of download: 12/17/2017 Copyright © ASME. All rights reserved. From: Conjugate Unscented Transformation: Applications to Estimation and Control J. Dyn. Sys., Meas., Control. 2017;140(3):030907-030907-22. doi:10.1115/1.4037783 Figure Legend: Iterative block schematic of the filtering algorithm

Date of download: 12/17/2017 Copyright © ASME. All rights reserved. From: Conjugate Unscented Transformation: Applications to Estimation and Control J. Dyn. Sys., Meas., Control. 2017;140(3):030907-030907-22. doi:10.1115/1.4037783 Figure Legend: State estimation error versus the measurement time interval, T for the air traffic problem: (a) position (all filters), (b) velocity (all filters), (c) angular rate (all filters), (d) position (PF, CUT4, CUT6, CUT8), (e) velocity (PF, CUT4, CUT6, CUT8), and (f) angular rate (PF, CUT4, CUT6, CUT8)

Date of download: 12/17/2017 Copyright © ASME. All rights reserved. From: Conjugate Unscented Transformation: Applications to Estimation and Control J. Dyn. Sys., Meas., Control. 2017;140(3):030907-030907-22. doi:10.1115/1.4037783 Figure Legend: Lorenz system

Date of download: 12/17/2017 Copyright © ASME. All rights reserved. From: Conjugate Unscented Transformation: Applications to Estimation and Control J. Dyn. Sys., Meas., Control. 2017;140(3):030907-030907-22. doi:10.1115/1.4037783 Figure Legend: Comparison of filters for Lorenz model with varying measurement time intervals T: (a) 2-norm of RMSE and (b) max of RMSE

Date of download: 12/17/2017 Copyright © ASME. All rights reserved. From: Conjugate Unscented Transformation: Applications to Estimation and Control J. Dyn. Sys., Meas., Control. 2017;140(3):030907-030907-22. doi:10.1115/1.4037783 Figure Legend: Example 2: three mass system: uncertain spring and damping constants

Date of download: 12/17/2017 Copyright © ASME. All rights reserved. From: Conjugate Unscented Transformation: Applications to Estimation and Control J. Dyn. Sys., Meas., Control. 2017;140(3):030907-030907-22. doi:10.1115/1.4037783 Figure Legend: Distribution of cost function J under parametric uncertainty: (a) up to second moment) cost, (b) up to fourth moment) cost, (c) up to sixth moment) cost, and (d) min–max control cost