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Pose error estimation of a quadcopter in the outdoors

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P♦s❡ ❊rr♦r ❊st✐♠❛t✐♦♥ ♦❢ ❛ ◗✉❛❞❝♦♣t❡r ✐♥

t❤❡ ❖✉t❞♦♦rs

❜②

❏❛❝♦❜✉s ❈✳ ▲♦❝❦

❚❤❡s✐s ♣r❡s❡♥t❡❞ ✐♥ ♣❛rt✐❛❧ ❢✉❧✜❧♠❡♥t ♦❢ t❤❡ r❡q✉✐r❡♠❡♥ts ❢♦r

t❤❡ ❞❡❣r❡❡ ♦❢ ▼❛st❡r ♦❢ ❊♥❣✐♥❡❡r✐♥❣ ✭▼❡❝❤❛tr♦♥✐❝✮ ✐♥ t❤❡

❋❛❝✉❧t② ♦❢ ❊♥❣✐♥❡❡r✐♥❣ ❛t ❙t❡❧❧❡♥❜♦s❝❤ ❯♥✐✈❡rs✐t②

❙✉♣❡r✈✐s♦r✿ ❉r✳ ❲❏ ❙♠✐t ❈♦✲s✉♣❡r✈✐s♦r✿ ▼r✳ ❏ ❚r❡✉r♥✐❝❤t ▼❛r❝❤ ✷✵✶✻

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❉❡❝❧❛r❛t✐♦♥

❇② s✉❜♠✐tt✐♥❣ t❤✐s t❤❡s✐s ❡❧❡❝tr♦♥✐❝❛❧❧②✱ ■ ❞❡❝❧❛r❡ t❤❛t t❤❡ ❡♥t✐r❡t② ♦❢ t❤❡ ✇♦r❦ ❝♦♥t❛✐♥❡❞ t❤❡r❡✐♥ ✐s ♠② ♦✇♥✱ ♦r✐❣✐♥❛❧ ✇♦r❦✱ t❤❛t ■ ❛♠ t❤❡ s♦❧❡ ❛✉t❤♦r t❤❡r❡♦❢ ✭s❛✈❡ t♦ t❤❡ ❡①t❡♥t ❡①♣❧✐❝✐t❧② ♦t❤❡r✇✐s❡ st❛t❡❞✮✱ t❤❛t r❡♣r♦❞✉❝t✐♦♥ ❛♥❞ ♣✉❜✲ ❧✐❝❛t✐♦♥ t❤❡r❡♦❢ ❜② ❙t❡❧❧❡♥❜♦s❝❤ ❯♥✐✈❡rs✐t② ✇✐❧❧ ♥♦t ✐♥❢r✐♥❣❡ ❛♥② t❤✐r❞ ♣❛rt② r✐❣❤ts ❛♥❞ t❤❛t ■ ❤❛✈❡ ♥♦t ♣r❡✈✐♦✉s❧② ✐♥ ✐ts ❡♥t✐r❡t② ♦r ✐♥ ♣❛rt s✉❜♠✐tt❡❞ ✐t ❢♦r ♦❜t❛✐♥✐♥❣ ❛♥② q✉❛❧✐✜❝❛t✐♦♥✳ ❋❡❜r✉❛r② ✶✽✱ ✷✵✶✻ ❉❛t❡✿ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ❈♦♣②r✐❣❤t ➞ ✷✵✶✻ ❙t❡❧❧❡♥❜♦s❝❤ ❯♥✐✈❡rs✐t② ❆❧❧ r✐❣❤ts r❡s❡r✈❡❞✳ ✐

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❆❜str❛❝t

P♦s❡ ❊rr♦r ❊st✐♠❛t✐♦♥ ♦❢ ❛ ◗✉❛❞❝♦♣t❡r ✐♥ t❤❡ ❖✉t❞♦♦rs

❏❈ ▲♦❝❦ ❉❡♣❛rt♠❡♥t ♦❢ ▼❡❝❤❛♥✐❝❛❧ ❛♥❞ ▼❡❝❤❛tr♦♥✐❝ ❊♥❣✐♥❡❡r✐♥❣✱ ❯♥✐✈❡rs✐t② ♦❢ ❙t❡❧❧❡♥❜♦s❝❤✱ Pr✐✈❛t❡ ❇❛❣ ❳✶✱ ▼❛t✐❡❧❛♥❞ ✼✻✵✷✱ ❙♦✉t❤ ❆❢r✐❝❛✳ ❚❤❡s✐s✿ ▼❊♥❣ ✭▼❡❝❤✮ ▼❛r❝❤ ✷✵✶✻ ❚❤❡ q✉❛❞❝♦♣t❡r ✐♥❞✉str② ✐s ❛ ❢❛st✲❣r♦✇✐♥❣ ❛♥❞ ♠❛t✉r✐♥❣ ✐♥❞✉str② ✇❤✐❝❤ ♣r♦✲ ❞✉❝❡s ❵❞✉♠❜✬ ✭♦r ♠❛♥✉❛❧❧② ❝♦♥tr♦❧❧❡❞✮ ✉♥♠❛♥♥❡❞ ❛❡r✐❛❧ ✈❡❤✐❝❧❡s ✭❯❆❱s✮✳ ❚❤❡② ❛r❡ ❛❧s♦ ❝♦♠♠♦♥❧② ❡q✉✐♣♣❡❞ ✇✐t❤ ❝♦♥tr♦❧❧❡rs ✇❤✐❝❤ ♠❛❦❡ t❤❡♠ ❛❜❧❡ t♦ ❛✉✲ t♦♥♦♠♦✉s❧② ❝❛rr② ♦✉t ❛ ✢✐❣❤t ♠✐ss✐♦♥ ✇✐t❤♦✉t ❛ ❤✉♠❛♥ ♣✐❧♦t✳ ■♥❞✉str② ✐s ❜❡❝♦♠✐♥❣ ✐♥❝r❡❛s✐♥❣❧② ✐♥t❡r❡st❡❞ ✐♥ ✐♥t❡❣r❛t✐♥❣ q✉❛❞❝♦♣t❡rs ✐♥t♦ t❤❡✐r r❡s♣❡❝✲ t✐✈❡ ✇♦r❦❢♦r❝❡s ✐♥ ❛♥ ❛tt❡♠♣t t♦ ❛✉t♦♠❛t❡ s♦♠❡ ♣r♦❝❡ss❡s✳ ❍♦✇❡✈❡r✱ ♥❛t✐♦♥❛❧ ❣♦✈❡r♥♠❡♥ts ❛r❡ ✇♦rr✐❡❞ t❤❛t ✐❢ ❧❡❢t ✉♥r❡❣✉❧❛t❡❞✱ ❯❆❱ q✉❛❞❝♦♣t❡rs ♠❛② ♣♦s❡ ❛ s❛❢❡t② ❛♥❞ s❡❝✉r✐t② t❤r❡❛t t♦ s♦❝✐❡t②✱ ♣❛rt✐❝✉❧❛r❧② ✐❢ t❤❡② ❛r❡ t♦ ✇♦r❦ ❛✉✲ t♦♥♦♠♦✉s❧② ✐♥ t❤❡ ♦✉t❞♦♦rs✳ ❚❤❡r❡ ❛r❡ ❛ ♥✉♠❜❡r ♦❢ ✐♠♣r♦✈❡♠❡♥ts t❤❛t ❝❛♥ ❜❡ ♠❛❞❡ t♦ ✐♥❝r❡❛s❡ t❤❡ s❛❢❡t② ♦❢ q✉❛❞❝♦♣t❡rs✳ ❚❤✐s r❡s❡❛r❝❤ ♣r♦❥❡❝t ✐♥✈❡st✐❣❛t❡s ❤♦✇ ✇❡❧❧ q✉❛❞❝♦♣t❡rs ❝❛♥ ❡st✐♠❛t❡ t❤❡✐r ♣♦s✐t✐♦♥ ❛♥❞ ♦r✐❡♥t❛t✐♦♥✱ ♦r ♣♦s❡✳ ■❢ t❤✐s ✐s ❦♥♦✇♥✱ ✐t ❝❛♥ ❜❡ ✐♥t❡❣r❛t❡❞ ✐♥t♦ ❛ ❝♦♥tr♦❧ ♠♦❞❡❧ ❛s ❛♥ ❡rr♦r t❡r♠ t♦ ✐♠♣r♦✈❡ t❤❡ ♣❡r❢♦r♠❛♥❝❡ ❛♥❞ s❛❢❡t② r❛t✐♥❣ ♦❢ ❛ q✉❛❞❝♦♣t❡r✳ ■♥❞♦♦r ♠❡❛s✉r❡♠❡♥t t♦♦❧s ❝❛♥♥♦t ❜❡ ✉s❡❞✱ s✐♥❝❡ t❤❡ q✉❛❞❝♦♣t❡rs ♦❢ ✐♥t❡r❡st r❡❧② ♦♥ ●P❙ ❞❛t❛✳ ❚❤❡r❡❢♦r❡✱ ❛ ❝♦♠♣✉t❡r ✈✐s✐♦♥✲❜❛s❡❞ ♣♦s❡ ♠❡❛s✉r❡♠❡♥t s②st❡♠ ✭❈❱❙✮ ✇❛s ✐♥✈❡st✐❣❛t❡❞✱ ❞❡s✐❣♥❡❞ ❛♥❞ ✐♠♣❧❡♠❡♥t❡❞ t♦ ♠❡❛s✉r❡ t❤❡ ♣♦s❡ ♦❢ ❛ q✉❛❞❝♦♣t❡r ✐♥ t❤❡ ♦✉t❞♦♦rs✳ ❚❤❡ s②st❡♠✬s ♠❡❛s✉r❡♠❡♥ts ✇❡r❡ ❝♦♠♣❛r❡❞ t♦ ❛ q✉❛❞❝♦♣t❡r✬s ♣♦s❡ ❡st✐♠❛t❡s r❡❝♦r❞❡❞ ❞✉r✐♥❣ ❛♥ ♦✉t❞♦♦r t❡st ✢✐❣❤t✳ ❚❤❡ r❡s✉❧ts s❤♦✇ t❤❛t t❤❡ ❈❱❙✬s ♠❡❛s✉r❡♠❡♥ts ❛r❡ ♠♦r❡ ❛❝❝✉r❛t❡ t❤❛♥ t❤❡ q✉❛❞❝♦♣t❡r✬s ✐♥ ❛❧❧ t❤❡ ❞✐♠❡♥s✐♦♥s ❡①❝❡♣t ❢♦r t❤❡ ②❛✇✳ ■t ✇❛s ❢♦✉♥❞ t❤❛t t❤❡ q✉❛❞❝♦♣t❡r✬s ♣♦s✐t✐♦♥ ❡st✐♠❛t✐♦♥ ❡rr♦r ✐s ❛♣♣r♦①✐♠❛t❡❧② 150 ♠♠ ❢♦r x✱ y ❛♥❞ z✱ ❛♥❞ 3.27➦ ❛♥❞ 1.9➦ ❢♦r t❤❡ r♦❧❧ ❛♥❞ ♣✐t❝❤ ❞✐♠❡♥s✐♦♥s✳ ❚❤❡s❡ r❡s✉❧ts ❝❛♥ ❜❡ ✉s❡❞ ❛♥❞ ✐♥t❡❣r❛t❡❞ ✐♥t♦ ❛ q✉❛❞❝♦♣t❡r✬s ❝♦♥tr♦❧ ♠♦❞❡❧✳ ✐✐

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❯✐ttr❡❦s❡❧

P♦s✐s✐❡ ❡♥ ❖r✐ë♥t❛s✐❡ ❆❢s❦❛tt✐♥❣ ✈❛♥ ✬♥ ❱✐❡r❜❡❡♥

❍❡❧✐❦♦♣t❡r ✐♥ ❞✐❡ ❇✉✐t❡❧✉❣

❏❈ ▲♦❝❦ ❉❡♣❛rt❡♠❡♥t ▼❡❣❛♥✐❡s❡ ❡♥ ▼❡❣❛tr♦♥✐❡s❡ ■♥❣❡♥✐❡✉rs✇❡s❡✱ ❯♥✐✈❡rs✐t❡✐t ✈❛♥ ❙t❡❧❧❡♥❜♦s❝❤✱ Pr✐✈❛❛ts❛❦ ❳✶✱ ▼❛t✐❡❧❛♥❞ ✼✻✵✷✱ ❙✉✐❞ ❆❢r✐❦❛✳ ❚❡s✐s✿ ▼■♥❣ ✭▼❡❣✮ ▼❛❛rt ✷✵✶✻ ❉✐❡ ✈✐❡r❜❡❡♥ ♦♥❜❡♠❛♥❞❡✈❧✐❡❣t✉✐❣❜❡❞r②❢ ✐s ✬♥ s♥❡❧❣r♦❡✐❡♥❞❡ ✐♥❞✉str✐❡ ✇❛t ✈❧✐❡❣✲ t✉✐❡ ♣r♦❞✉s❡❡r ✇❛t ♠❡t ❞✐❡ ❤❛♥❞ ♦❢ ❤❡❡❧t❡♠❛❧ ♦✉t♦♥♦♦♠✱ s♦♥❞❡r ✬♥ ♠❡♥s❧✐❦❡ ✈❧✐❡ë♥✐❡r s❡ ✐♥s❡t✱ ✬♥ ✈❧✉❣♦♣❞r❛❣ ❦❛♥ ✈♦❧t♦♦✐✳ ■♥❞✉str✐❡ st❡❧ t♦❡♥❡♠❡♥❞ ❜❡❧❛♥❣ ❞❛❛r✐♥ ♦♠ s✉❧❦❡ ♦♥❜❡♠❛♥❞❡ ✈❧✐❡❣t✉✐❡ ✐♥ ❤✉❧ ✇❡r❦s♠❛❣ t❡ ✐♥t❡❣r❡❡r ♦♠ ♣r♦s❡ss❡ t♦t ✬♥ ♠❛t❡ t♦ ♦✉t♦♠❡❡r✳ ❲êr❡❧❞sr❡❣❡r✐♥❣s ✐s ❡❣t❡r ❜❡❦♦♠♠❡r❞ ❞❛t ✐♥❞✐❡♥ ❞✐❡ ♦♥❜❡♠❛♥❞❡✈❡❧✐❡❣t✉✐❣❜❡❞r②❢ ♦♥❣❡r❡❣✉❧❡❡r❞ ❣❡❧❛❛t ✇♦r❞✱ s✉❧❦❡ ✈❧✐❡❣t✉✐❡ ✬♥ ❣❡✲ ✈❛❛r s❛❧ ✐♥❤♦✉ ✈✐r ❞✐❡ s❛♠❡❧✇❡✐♥❣✱ ✈❡r❛❧ ❛s ❤✉❧❧❡ ❣❡❧❛❛t ✇♦r❞ ♦♠ ♦✉t♦♥♦♦♠ ✐♥ ❞✐❡ ❜✉✐t❡❧✉❣ t❡ ✇❡r❦✳ ❉❛❛r ✐s ✈❡rs❦❡✐❡ ✈❡r❜❡t❡r✐♥❣s ✇❛t ❣❡♠❛❛❦ ❦❛♥ ✇♦r❞ ♦♠ ❞✐❡ t❡❣♥♦❧♦❣✐❡ s❡ ✈❡✐❧✐❣❤❡✐❞ t❡ ✈❡r❤♦♦❣✳ ❍✐❡r❞✐❡ ♥❛✈♦rs✐♥❣s♣r♦❥❡❦ st❡❧ ♦♥❞❡rs♦❡❦ ✐♥ ♦♠ ✈❛s t❡ st❡❧ ❤♦❡ ❛❦❦✉r❛❛t ✬♥ ♦♥❜❡♠❛♥❞❡ ✈❧✐❡❣t✉✐❣ s② ♣♦s✐s✐❡ ❡♥ ♦r✐ë♥t❛s✐❡ ❦❛♥ ❛❢s❦❛t✳ ■♥❞✐❡♥ ❤✐❡r❞✐❡ ✇❛❛r❞❡s ❜❡❦❡♥❞ ✐s✱ ❦❛♥ ❞✐t ❣❡ï♥t❡❣r❡❡r ✇♦r❞ ✐♥ ✬♥ ❜❡❤❡❡r♠♦❞❡❧ ♦♠ s♦ ✬♥ ✈❧✐❡❣t✉✐❣ s❡ ✇❡r❦s✈❡rr✐❣t✐♥❣ ❡♥ ✈❡✐❧✐❣❤❡✐❞ t❡ ✈❡r❤♦♦❣✳ ❇✐♥♥❡♠✉✉rs❡ ♠❡❡t✐♥str✉♠❡♥t❡ ❦❛♥ ♥✐❡ ❣❡❜r✉✐❦ ✇♦r❞ ❤✐❡r ♥✐❡✱ ❛❛♥❣❡s✐❡♥ ❞✐❡ ♦♥❜❡♠❛♥❞❡ ✈❧✐❡❣t✉✐❡ ✈❛♥ ❤✐❡r❞✐❡ ♣r♦❥❡❦ st❛❛t♠❛❛❦ ♦♣ ❤✉❧ ●P❙ ❧❡s✐♥❣s✳ ❉✉s✱ ✐♥ ❤✐❡r❞✐❡ ♣r♦❥❡❦ ✐s ❞❛❛r ✬♥ r❡❦❡♥❛❛r✈✐s✐❡st❡❧s❡❧ ♦♥t✇❡r♣✱ ❣❡t♦❡ts ❡♥ ❣❡ï♠♣❧✐♠❡♥✲ t❡❡r ♦♠ ✬♥ ✈✐❡r❜❡❡♥ ❤❡❧✐❦♦♣t❡r s❡ ♣♦s✐s✐❡ ❛❢ t❡ s❦❛t ✐♥ ❞✐❡ ❜✉✐t❡❧✉❣✳ ❉✐❡ ✈✐❡r❜❡❡♥ ❤❡❧✐❦♦♣t❡r s❡ ❛❢s❦❛tt✐♥❣s❛❦❦✉r❛❛t❤❡✐❞ ✇❛s ❞❛♥ ❣❡✈✐♥❞ ❞❡✉r s② ❛❢s❦❛tt✐♥❣ t❡ ✈❡r✲ ❣❡❧②❦ ♠❡t ❞✐é ✈❛♥ ❞✐❡ r❡❦❡♥❛❛r✈✐s✐❡st❡❧s❡❧ ✐♥ ✬♥ ❜✉✐t❡♠✉✉rs❡ ✈❧✉❣t♦❡ts✳ ❚❤❡ r❡s✉❧t❛t❡ t♦♦♥ ❞❛t ❞✐❡ r❡❦❡♥❛❛r✈✐s✐❡st❡❧s❡❧ s❡ ♠❡t✐♥❣s ♠❡❡r ❛❦❦✉r❛❛t ✐s ❛s ❞✐❡ ✈✐❡r❜❡❡♥ ❤❡❧✐❦♦♣t❡r s✬♥ ✈✐r ❛❧❧❡ ♠❡❡t❞✐♠❡♥s✐❡s✱ ❜✉✐t❡♥ ❞✐❡ ❛❢✇②❦✐♥❣s❤♦❡❦✳ ❉✐t ✇❛s ❣❡✈✐♥❞ ❞❛t ❞✐❡ ❤❡❧✐❦♦♣t❡r s❡ ♣♦s✐s✐❡❛❢❦s❛tt✐♥❣s❢♦✉t ♦♥❣❡✈❡❡r 150 ♠♠ ✐s ✐♥ ❞✐❡ x✱ y ❡♥ z ❞✐♠❡♥s✐❡s✱ t❡r✇②❧ ❞✐❡ ❤♦❡❦❛❢s❦❛tt✐♥❣s❢♦✉t 3.27➦ ❡♥ 1.9➦ ✐s ✈✐r ❞✐❡ r♦❧✲ ❡♥ ❤❡❧❧✐♥❣s❤♦❡❦❡✳ ❍✐❡r❞✐❡ r❡s✉❧t❛t❡ ❦❛♥ ❣❡ï♠♣❧✐♠❡♥t❡❡r ✇♦r❞ ✐♥ ✬♥ ✈✐❡r❜❡❡♥ ❤❡❧✐❦♦♣t❡r s❡ ❜❡❤❡❡r♠♦❞❡❧✳ ✐✐✐

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❆❝❦♥♦✇❧❡❞❣❡♠❡♥ts

❇❡s✐❞❡s ♠② s✉♣❡r✈✐s♦r✱ ❉r✳ ❲❏ ❙♠✐t✱ ■ ✇♦✉❧❞ ❧✐❦❡ t♦ t❤❛♥❦ ❙❚❊❘● ❢♦r t❤❡ ♦♣♣♦rt✉♥✐t② t♦ st✉❞② ✇✐t❤ t❤❡♠ ❛♥❞ t❤❡ ❢❛❝✐❧✐t✐❡s t❤❡② ♣r♦✈✐❞❡❞✳ ❋✉rt❤❡r♠♦r❡✱ ■ ✇♦✉❧❞ ❧✐❦❡ t♦ t❤❛♥❦ ❈❘❙❊❙ ❢♦r t❤❡ ❢✉♥❞✐♥❣ t❤❡② ♣r♦✈✐❞❡❞✳ ■ ✇♦✉❧❞ ❛❧s♦ ❧✐❦❡ t♦ ❛❝❦♥♦✇❧❡❞❣❡ t❤❡ st❛✛ ❛t ❚②❣❡r❜❡r❣✬s t❤r❡❡✲❞✐♠❡♥s✐♦♥❛❧ ▼♦t✐♦♥ ❈❛♣t✉r❡ ❧❛❜♦r❛t♦r② ❛♥❞ t❤❡ r❡st ♦❢ t❤❡ ❙t❡❧❧❡♥❜♦s❝❤ ❯♥✐✈❡rs✐t② st❛✛ ✇❤♦ ❤❛❞ ❛ ❤❛♥❞ ✐♥ t❤✐s ♣r♦❥❡❝t✳ ✐✈

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❉❡❞✐❝❛t✐♦♥s

■ ❞❡❞✐❝❛t❡ t❤✐s t❤❡s✐s t♦ ♠② ♣❛r❡♥ts ❛♥❞ ❜r♦t❤❡rs✱ ✇❤♦s❡ ✉♥✇❛✈❡r✐♥❣ ❧♦✈❡ ❛♥❞ s✉♣♣♦rt ♣✉s❤❡s ♠❡ t♦ ❜❡ t❤❡ ❜❡st ♠❛♥ ■ ❝❛♥ ♣♦ss✐❜❧② ❜❡✳ ❆♥❞ t♦ ❛❧❧ ♠② ❢r✐❡♥❞s ✇❤♦ tr✐❡❞ t❤❡✐r ❜❡st t♦ ❦❡❡♣ ♠❡ ❢r♦♠ ✜♥✐s❤✐♥❣ ♠② ♣r♦❥❡❝t✿ ♥✐❝❡ tr②✳ ❊❦ ❞r❛ ❤✐❡r❞✐❡ t❡s✐s ♦♣ ♥❛ ♠② ♦✉❡rs✱ ❜r♦❡rs✱ ❏❛②✱ ❡♥ ❤✉❧❧❡ ♦♥✇r✐❦❜❛r❡ ❧✐❡❢❞❡ ❡♥ ♦♥❞❡rst❡✉♥✐♥❣✱ ✇❛❛rs♦♥❞❡r ❡❦ ♥✐❡ s♦✉ ✇❡❡s ✇❛❛r ❡❦ ✈❛♥❞❛❣ ✐s ♥✐❡✳ ❈❤r✐st✐❛♥✱ ❞✐❡ ❡❡♥ ✐s ✈✐r ❥♦✉✳ ✈

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❈♦♥t❡♥ts

❉❡❝❧❛r❛t✐♦♥ ✐ ❆❜str❛❝t ✐✐ ❯✐ttr❡❦s❡❧ ✐✐✐ ❆❝❦♥♦✇❧❡❞❣❡♠❡♥ts ✐✈ ❉❡❞✐❝❛t✐♦♥s ✈ ❈♦♥t❡♥ts ✈✐ ▲✐st ♦❢ ❋✐❣✉r❡s ✈✐✐✐ ▲✐st ♦❢ ❚❛❜❧❡s ① ▲✐st ♦❢ ❆❧❣♦r✐t❤♠s ①✐ ◆♦♠❡♥❝❧❛t✉r❡ ①✐✐ ✶ ■♥tr♦❞✉❝t✐♦♥ ✶ ✶✳✶ Pr♦❜❧❡♠ ❙t❛t❡♠❡♥t ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶ ✶✳✷ Pr♦❥❡❝t ▼♦t✐✈❛t✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷ ✶✳✸ P♦t❡♥t✐❛❧ ❯s❡ ❈❛s❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸ ✶✳✹ ❊①✐st✐♥❣ ❛♥❞ Pr♦♣♦s❡❞ ❙♦❧✉t✐♦♥s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺ ✶✳✺ Pr♦❥❡❝t ❖❜❥❡❝t✐✈❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺ ✶✳✻ ❉♦❝✉♠❡♥t ❙tr✉❝t✉r❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻ ✷ ▲✐t❡r❛t✉r❡ ❘❡✈✐❡✇ ✼ ✷✳✶ ■♥tr♦❞✉❝t✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼ ✷✳✷ ◗✉❛❞❝♦♣t❡rs ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼ ✷✳✸ ❈♦♠♣✉t❡r ❱✐s✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷ ✷✳✹ ▼❛❝❤✐♥❡ ▲❡❛r♥✐♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻ ✷✳✺ ❈♦♥❝❧✉s✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✸ P♦s❡ ▼❡❛s✉r❡♠❡♥t ❙②st❡♠ ❉❡s✐❣♥ ✷✷ ✈✐

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❈❖◆❚❊◆❚❙ ✈✐✐ ✸✳✶ ■♥tr♦❞✉❝t✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✸✳✷ ❙②st❡♠ ▲❛②♦✉t ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✸✳✸ ▼❡❛s✉r❡♠❡♥t ❚❡st ❉❡s✐❣♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✸✳✹ ❘❡s✉❧ts ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✸✳✺ ❈♦♥❝❧✉s✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻ ✹ ❈❱❙ P♦s❡ ▼❡❛s✉r❡♠❡♥t ❊rr♦r ✹✽ ✹✳✶ ■♥tr♦❞✉❝t✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ✹✳✷ ▼♦❞❡❧ ❉❡s✐❣♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ✹✳✸ ❘❡s✉❧ts ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ✹✳✹ ❈♦♥❝❧✉s✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺ ✺ ◗✉❛❞❝♦♣t❡r ❚❡st ✺✼ ✺✳✶ ■♥tr♦❞✉❝t✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼ ✺✳✷ ❋❧✐❣❤t ❚❡st ❉❡s✐❣♥ ❛♥❞ Pr♦❝❡❞✉r❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼ ✺✳✸ ❘❡s✉❧ts ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸ ✺✳✹ ❈♦♥❝❧✉s✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽ ✻ ❈♦♥❝❧✉s✐♦♥ ✼✶ ✻✳✶ ■♥tr♦❞✉❝t✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶ ✻✳✷ ❚❤❡s✐s ❙✉♠♠❛r② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶ ✻✳✸ ❋✐♥❞✐♥❣s ❛♥❞ ❈♦♥tr✐❜✉t✐♦♥s t♦ ❇♦❞② ♦❢ ❑♥♦✇❧❡❞❣❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷ ✻✳✹ ❙❤♦rt❝♦♠✐♥❣s ❛♥❞ ❋✉t✉r❡ ❲♦r❦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹ ✻✳✺ ❈♦♥❝❧✉s✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻ ❆♣♣❡♥❞✐❝❡s ✼✼ ❆ P✐①❤❛✇❦ ❙♣❡❝✐✜❝❛t✐♦♥s ✼✽ ❇ ▲✐❢❡❝❛♠ ❍❉✲✺✵✵✵ ❙♣❡❝✐✜❝❛t✐♦♥s ✽✵ ❈ ❋❧✐❣❤t ❚❡st ■♠❛❣❡s ✽✶ ❉ ❍❡❧✐♦✶✵✵ ❙✐t❡ ❲❡❛t❤❡r ❉❛t❛ ✽✺ ▲✐st ♦❢ ❘❡❢❡r❡♥❝❡s ✽✼

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▲✐st ♦❢ ❋✐❣✉r❡s

✶✳✶ ❆ s✐❞❡✲❜②✲s✐❞❡ ❝♦♠♣❛r✐s♦♥ ♦❢ ❤♦✇ ❤❡❧✐♦st❛ts ❛r❡ ❝✉rr❡♥t❧② ❝❛❧✐❜r❛t❡❞ ❛♥❞ ❤♦✇ ❤❡❧✐♦st❛ts ❝❛♥ ❜❡ ❝❛❧✐❜r❛t❡❞ ❜② ❛✉t♦♥♦♠♦✉s q✉❛❞❝♦♣t❡rs✳ ✳ ✹ ✷✳✶ ❆ ♣✐❝t✉r❡ ♦❢ t❤❡ ❙✉♥❝♦♣t❡r ✉s❡❞ ❜② ❙❚❊❘●✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼ ✷✳✷ ❉✐❛❣r❛♠ ♣r❡s❡♥t✐♥❣ t❤❡ ♦♣♣♦s✐♥❣ ❛①✐s r♦t❛t✐♦♥s ❞✐r❡❝t✐♦♥s✳ ✳ ✳ ✳ ✳ ✳ ✽ ✷✳✸ ❉✐❛❣r❛♠ ♦❢ t❤❡ q✉❛❞❝♦♣t❡r ♠♦❞❡❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾ ✷✳✹ ❉✐❛❣r❛♠ s❤♦✇✐♥❣ ✇❤❛t t❤❡ ❢♦❝❛❧ ❧❡♥❣t❤ ❛♥❞ ♣r✐♥❝✐♣❧❡ ♣♦✐♥t ♣❛r❛♠✲ ❡t❡rs r❡♣r❡s❡♥t✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸ ✷✳✺ ❆♥ ❡①❛♠♣❧❡ ♦❢ ❛ t②♣✐❝❛❧ ❝❤❡ss❜♦❛r❞ ♣❛tt❡r♥ ✉s❡❞ ❢♦r ❝❛❧✐❜r❛t✐♦♥✳ ✳ ✳ ✶✹ ✷✳✻ ❉✐❛❣r❛♠ ♦❢ ❛ s✐♠♣❧❡ ❆◆◆✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼ ✷✳✼ ❉✐❛❣r❛♠ ♦❢ ❛ s✐♠♣❧❡ ❘◆◆✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✷✳✽ ❈♦♠♣❛r✐s♦♥ ❜❡t✇❡❡♥ t❤❡ ❘❇❋ ❛♥❞ ❘◆◆ ❝❧❛ss✐✜❡rs✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✷✳✾ ❙❱▼ ✇✐t❤ ❛ ❧✐♥❡❛r ❤②♣❡r♣❧❛♥❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✷✳✶✵ ❊①❛♠♣❧❡ ♦❢ ❛♥ ❙❱▼ ✇✐t❤ ❛ ♥♦♥✲❧✐♥❡❛r ❦❡r♥❡❧ s❡♣❛r❛t♦r✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✸✳✶ ❚♦♣ ✈✐❡✇ ♦❢ t❤❡ ❱✐❝♦♥ ♠♦t✐♦♥ ❝❛♣t✉r❡ s②st❡♠✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✸✳✷ ❚❤❡ ❛①✐s ♦r✐❡♥t❛t✐♦♥s ♦❢ t❤❡ ❱✐❝♦♥ ❛♥❞ ❈❱ s②st❡♠s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✸✳✸ ❱✐❝♦♥♠❛r❦❡r ♣❧❛❝❡♠❡♥t ♦♥ t❤❡ ❝❛❧✐❜r❛t✐♦♥ ❜♦❛r❞ ❛♥❞ ❝❛♠❡r❛ ❢r❛♠❡✳ ✷✽ ✸✳✹ P✐❝t✉r❡ ♦❢ t❤❡ ❱✐❝♦♥ t❡st ❧❛②♦✉t✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✸✳✺ ❉✐❛❣r❛♠s ♦❢ t❤❡ r❡❧❛t✐♦♥s❤✐♣s ❜❡t✇❡❡♥ t❤❡ ♣♦s❡ ✈❡❝t♦rs ❣✐✈❡♥ ❜② t❤❡ ❱✐❝♦♥ ❛♥❞ ❈❱❙✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✸✳✻ ■♠❛❣❡s ❞❡♠♦♥str❛t✐♥❣ t❤❡ ♦♣t✐♠✐s❛t✐♦♥ ♣r♦❝❡❞✉r❡✬s s❡♥s✐t✐✈✐t② t♦ t❤❡ ♦r✐❡♥t❛t✐♦♥ ❞✐♠❡♥s✐♦♥s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✸✳✼ P❧♦ts s❤♦✇✐♥❣ ❡rr♦r ❝♦♥✈❡r❣❡♥❝❡ ❢♦r t❤❡ ♦♣t✐♠s❛t✐♦♥ ♣r♦❝❡❞✉r❡✳ ✳ ✳ ✸✻ ✸✳✽ P❧♦t ♦❢ t❤❡ ♠✐♥✐♠✉♠ ♥♦r♠ ✈❛❧✉❡s ❢♦r t❤❡ ♣♦s✐t✐♦♥ ❞✐♠❡♥s✐♦♥s✳ ✳ ✳ ✳ ✸✼ ✸✳✾ ❋r❡q✉❡♥❝② ❤✐st♦❣r❛♠s ♦❢ t❤❡ ❡rr♦r ❞❛t❛ ✐♥ ❡❛❝❤ ❞✐♠❡♥s✐♦♥✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✸✳✶✵ P❧♦t ❝♦♠♣❛r✐♥❣ t❤❡ ❱✐❝♦♥✱ ♦r✐❣✐♥❛❧ ❛♥❞ ✐♠♣r♦✈❡❞ ❈❱❙ ♠❡❛s✉r❡✲ ♠❡♥ts ✐♥ t❤❡ x ❞✐♠❡♥s✐♦♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✸✳✶✶ P❧♦t ❝♦♠♣❛r✐♥❣ t❤❡ ❱✐❝♦♥✱ ♦r✐❣✐♥❛❧ ❛♥❞ ✐♠♣r♦✈❡❞ ❈❱❙ ♠❡❛s✉r❡✲ ♠❡♥ts ✐♥ t❤❡ y ❞✐♠❡♥s✐♦♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✸✳✶✷ P❧♦t ❝♦♠♣❛r✐♥❣ t❤❡ ❱✐❝♦♥✱ ♦r✐❣✐♥❛❧ ❛♥❞ ✐♠♣r♦✈❡❞ ❈❱❙ ♠❡❛s✉r❡✲ ♠❡♥ts ✐♥ t❤❡ z ❞✐♠❡♥s✐♦♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷ ✸✳✶✸ P❧♦t ❝♦♠♣❛r✐♥❣ t❤❡ ❱✐❝♦♥✱ ♦r✐❣✐♥❛❧ ❛♥❞ ✐♠♣r♦✈❡❞ ❈❱❙ ♠❡❛s✉r❡✲ ♠❡♥ts ✐♥ t❤❡ roll ❞✐♠❡♥s✐♦♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✈✐✐✐

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▲■❙❚ ❖❋ ❋■●❯❘❊❙ ✐① ✸✳✶✹ P❧♦t ❝♦♠♣❛r✐♥❣ t❤❡ ❱✐❝♦♥✱ ♦r✐❣✐♥❛❧ ❛♥❞ ✐♠♣r♦✈❡❞ ❈❱❙ ♠❡❛s✉r❡✲ ♠❡♥ts ✐♥ t❤❡ pitch ❞✐♠❡♥s✐♦♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ✸✳✶✺ P❧♦t ❝♦♠♣❛r✐♥❣ t❤❡ ❱✐❝♦♥✱ ♦r✐❣✐♥❛❧ ❛♥❞ ✐♠♣r♦✈❡❞ ❈❱❙ ♠❡❛s✉r❡✲ ♠❡♥ts ✐♥ t❤❡ yaw ❞✐♠❡♥s✐♦♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺ ✸✳✶✻ P❧♦ts ❞❡♠♦♥str❛t✐♥❣ t❤❡ ❝♦♠♣❧❡①✐t② ♦❢ t❤❡ ❡rr♦r ❞❛t❛ ❢♦r t❤❡ z ❞✐✲ ♠❡♥s✐♦♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼ ✹✳✶ ◆❡✉r❛❧ ♥❡t✇♦r❦ ✐♠♣❧❡♠❡♥t✐♥❣ t❤❡ ❜❛❝❦♣r♦♣❛❣❛t✐♦♥ ♣r♦❝❡❞✉r❡✳ ✳ ✳ ✳ ✺✵ ✹✳✷ ❋✐❣✉r❡ s❤♦✇✐♥❣ t❤❡ ❝♦♥✜❣✉r❛t✐♦♥ ❢♦r t❤❡ ❞✉❛❧ ❘❇❋◆◆ ❝♦♥✜❣✉r❛t✐♦♥✳ ✺✷ ✹✳✸ ❙❝❛tt❡r ♣❧♦ts ♦❢ t❤❡ tr❛✐♥✐♥❣ ❛♥❞ ✈❛❧✐❞❛t✐♦♥ ❞❛t❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ✹✳✹ ❖✉t♣✉t ♦❢ t❤❡ ❘❇❋◆◆s ✇❤❡♥ ✉s❡❞ ✇✐t❤ t❤❡ tr❛✐♥✐♥❣ s❡t ✐♥♣✉t✳ ✳ ✳ ✳ ✺✹ ✹✳✺ ❖✉t♣✉t ♦❢ t❤❡ ❘❇❋◆◆s ✇✐t❤ t❤❡ ✈❛❧✐❞❛t✐♦♥ s❡t ✐♥♣✉t✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺ ✺✳✶ ❙❤❡♠❛t✐❝ ♦❢ t❤❡ t❡st ✢✐❣❤t ❧❛②♦✉t✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷ ✺✳✷ ❙❝❛tt❡r ♣❧♦ts ♦❢ ✢✐❣❤t ❞❛t❛ ✈s✳ tr❛✐♥✐♥❣ ❞❛t❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹ ✺✳✸ ❘❡s✉❧ts ♦❢ t❤❡ ✢✐❣❤t t❡st✱ ❝♦♠♣❛r✐♥❣ t❤❡ ❈❱❙ ❛♥❞ q✉❛❞❝♦♣t❡r✬s ♠❡❛s✉r❡♠❡♥ts ✐♥ t❤❡ x ❞✐♠❡♥s✐♦♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺ ✺✳✹ ❘❡s✉❧ts ♦❢ t❤❡ ✢✐❣❤t t❡st✱ ❝♦♠♣❛r✐♥❣ t❤❡ ❈❱❙ ❛♥❞ q✉❛❞❝♦♣t❡r✬s ♠❡❛s✉r❡♠❡♥ts ✐♥ t❤❡ y ❞✐♠❡♥s✐♦♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻ ✺✳✺ ❘❡s✉❧ts ♦❢ t❤❡ ✢✐❣❤t t❡st✱ ❝♦♠♣❛r✐♥❣ t❤❡ ❈❱❙ ❛♥❞ q✉❛❞❝♦♣t❡r✬s ♠❡❛s✉r❡♠❡♥ts ✐♥ t❤❡ z ❞✐♠❡♥s✐♦♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻ ✺✳✻ ❘❡s✉❧ts ♦❢ t❤❡ ✢✐❣❤t t❡st✱ ❝♦♠♣❛r✐♥❣ t❤❡ ❈❱❙ ❛♥❞ q✉❛❞❝♦♣t❡r✬s ♠❡❛s✉r❡♠❡♥ts ✐♥ t❤❡ roll ❞✐♠❡♥s✐♦♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼ ✺✳✼ ❘❡s✉❧ts ♦❢ t❤❡ ✢✐❣❤t t❡st✱ ❝♦♠♣❛r✐♥❣ t❤❡ ❈❱❙ ❛♥❞ q✉❛❞❝♦♣t❡r✬s ♠❡❛s✉r❡♠❡♥ts ✐♥ t❤❡ pitch ❞✐♠❡♥s✐♦♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼ ✺✳✽ ❘❡s✉❧ts ♦❢ t❤❡ ✢✐❣❤t t❡st✱ ❝♦♠♣❛r✐♥❣ t❤❡ ❈❱❙ ❛♥❞ q✉❛❞❝♦♣t❡r✬s ♠❡❛s✉r❡♠❡♥ts ✐♥ t❤❡ yaw ❞✐♠❡♥s✐♦♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽ ✺✳✾ ❙❡t ♦❢ ❢r❡q✉❡♥❝② ❤✐st♦❣r❛♠s ❞✐s♣❧❛②✐♥❣ t❤❡ q✉❛❞❝♦♣t❡r✬s ♣♦s❡ ❡st✐✲ ♠❛t❡ ❞❡✈✐❛t✐♦♥ ❢r♦♠ t❤❡ ❈❱❙✬s ♠❡❛s✉r❡♠❡♥ts✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾ ❇✳✶ ❚❤❡ s♣❡❝✐✜❝❛t✐♦♥s ♦❢ t❤❡ ▼✐❝r♦s♦❢t ❍❉✲✺✵✵✵ ▲✐❢❡❈❛♠ ✇❡❜❝❛♠✳ ✳ ✳ ✳ ✽✵ ❈✳✶ P✐❝t✉r❡ ♦❢ ❛ t②♣✐❝❛❧ t❡st ✐♠❛❣❡ ✇❤❡r❡ t❤❡ ❈❱❙ ❞r❡✇ ❛♥ ❛①✐s s②st❡♠ ♦♥ t❤❡ ❜♦❛r❞✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✶ ❈✳✷ P✐❝t✉r❡ ♦❢ ✇❤❡r❡ t❤❡ ❜♦❛r❞ ✐s ♣❛rt✐❛❧❧② ♦✉t ♦❢ t❤❡ ❝❛♠❡r❛✬s ✈✐❡✇✳ ❚❤❡ ❈❱❙ ❝♦✉❧❞ ♥♦t ❝❛♣t✉r❡ ❛❧❧ t❤❡ ❝♦r♥❡r ❞❛t❛ ✐t r❡q✉✐r❡❞ ❛♥❞ ❝♦✉❧❞ ♥♦t ❞r❛✇ ❛♥ ❛①✐s s②st❡♠ ♦♥ t❤❡ ❜♦❛r❞✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷ ❈✳✸ P✐❝t✉r❡ ♦❢ ✇❤❡r❡ t❤❡ ❜♦❛r❞ ✐s t♦♦ ❢❛r ❛✇❛② ❢r♦♠ t❤❡ ❝❛♠❡r❛ ❢♦r t❤❡ ❈❱❙ t♦ ❝❛♣t✉r❡ t❤❡ ❝♦r♥❡r ❞❛t❛ ❛♥❞ ❞r❛✇ ❛♥ ❛①✐s s②st❡♠✳ ✳ ✳ ✳ ✳ ✳ ✽✸ ❈✳✹ P✐❝t✉r❡ ✇✐t❤ ❛♥ ✐♥❝♦rr❡❝t❧② ❞r❛✇♥ ❛①✐s s②st❡♠✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✹ ❉✳✶ ❲✐♥❞ s♣❡❡❞ ❞❛t❛ t❛❦❡♥ ❞✉r✐♥❣ t❤❡ ✢✐❣❤t t❡sts✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✺ ❉✳✷ ❍✉♠✐❞✐t② ❞❛t❛ t❛❦❡♥ ❞✉r✐♥❣ t❤❡ ✢✐❣❤t t❡st✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✻

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▲✐st ♦❢ ❚❛❜❧❡s

✺✳✶ ❙✉♥❝♦♣t❡r s♣❡❝✐✜❝❛t✐♦♥s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽ ✺✳✷ P✐①❤❛✇❦ s♣❡❝✐✜❝❛t✐♦♥s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ✺✳✸ P✐①❤❛✇❦ s❡♥s♦r s♣❡❝✐✜❝❛t✐♦♥s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾

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▲✐st ♦❢ ❆❧❣♦r✐t❤♠s

✶ ❖♣t✐♠✐s❡ ❈❛♠❡r❛ ❋♦❝❛❧ ▲❡♥❣t❤ P❛r❛♠❡t❡r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺

(13)

◆♦♠❡♥❝❧❛t✉r❡

❱❛r✐❛❜❧❡s f ❋♦❝❛❧ ▲❡♥❣t❤ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ❬ Pixels ❪ x ❳✲❈♦♦r❞✐♥❛t❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ❬ m ❪ y ❨✲❈♦♦r❞✐♥❛t❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ❬ m ❪ z ❩✲❈♦♦r❞✐♥❛t❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ❬ m ❪ θ P✐t❝❤ ❆♥❣❧❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ❬ ➦ ❪ φ ❘♦❧❧ ❆♥❣❧❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ❬ ➦ ❪ ψ ❨❛✇ ❆♥❣❧❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ❬ ➦ ❪ ❱❡❝t♦rs ❛♥❞ ▼❛tr✐❝❡s C ❈❛♠❡r❛ ▼❛tr✐① N ■♥tr✐♥s✐❝ ❈❛♠❡r❛ P❛r❛♠❡t❡r ▼❛tr✐① P P♦s❡ ▼❛tr✐① \bfitP P♦s❡ ❱❡❝t♦r R ❘♦t❛t✐♦♥ ▼❛tr✐① \bfitT ❚r❛♥s❧❛t✐♦♥ ❱❡❝t♦r \bfitx ❚✇♦✲❉✐♠❡♥s✐♦♥❛❧ ❈❛♠❡r❛ ❈♦♦r❞✐♥❛t❡ ❱❡❝t♦r \bfitX ❚❤r❡❡✲❉✐♠❡♥s✐♦♥❛❧ ❲♦r❧❞ ❈♦♦r❞✐♥❛t❡ ❱❡❝t♦r \bfitepsilon ❊rr♦r ❱❡❝t♦r Σ ❈♦✈❛r✐❛♥❝❡ ▼❛tr✐① ❙✉❜s❝r✐♣ts b ❇♦❛r❞ c ❈❛♠❡r❛ i ■♥❞❡①❡r M ◆✉♠❜❡r ♦❢ s❛♠♣❧❡s ✐♥ ❞❛t❛ s❡t ①✐✐

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◆❖▼❊◆❈▲❆❚❯❘❊ ①✐✐✐ ❆❜❜r❡✈✐❛t✐♦♥s ❆◆◆ ❆rt✐✜❝✐❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦ ❈❙P ❈♦♥❝❡♥tr❛t✐♥❣ ❙♦❧❛r P♦✇❡r ❈❱❙ ❈♦♠♣✉t❡r ❱✐s✐♦♥ ❙②st❡♠ ❋❋◆◆ ❋❡❡❞✲❢♦r✇❛r❞ ◆❡✉r❛❧ ◆❡t✇♦r❦ ●P❙ ●❧♦❜❛❧ P♦s✐t✐♦♥✐♥❣ ❙②st❡♠ ❍inf ❍✲✐♥✜♥✐t② ■▼❯ ■♥❡rt✐❛ ▼❡❛s✉r❡♠❡♥t ❯♥✐t ▲◗❘ ▲✐♥❡❛r ◗✉❛❞r❛t✐❝ ❘❡❣✉❧❛t♦r ▼P❈ ▼♦❞❡❧ Pr❡❞✐❝t✐✈❡ ❈♦♥tr♦❧❧❡r ▼❙❊ ▼❡❛♥ ❙q✉❛r❡ ❊rr♦r P■❉ Pr♦♣♦rt✐♦♥❛❧ ■♥t❡❣r❛❧ ❉❡r✐✈❛t✐✈❡ P♥P P❡rs♣❡❝t✐✈❡ ♥✲P♦✐♥ts ❘❆◆❙❆❈ ❘❛♥❞♦♠ ❙❛♠♣❧❡ ❈♦♥s❡♥s✉s ❘❇❋◆◆ ❘❛❞✐❛❧ ❇❛s✐s ❋✉♥❝t✐♦♥ ◆❡✉r❛❧ ◆❡t✇♦r❦ ❘◆◆ ❘❡❝✉rr❡♥t ◆❡✉r❛❧ ◆❡t✇♦r❦ ❙❚❊❘● ❙♦❧❛r ❚❤❡r♠❛❧ ❊♥❡r❣② ❘❡s❡❛r❝❤ ●r♦✉♣ ❙❯ ❙t❡❧❧❡♥❜♦s❝❤ ❯♥✐✈❡rs✐t② ❯❆❱ ❯♥♠❛♥♥❡❞ ❆❡r✐❛❧ ❱❡❤✐❝❧❡

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❈❤❛♣t❡r ✶

■♥tr♦❞✉❝t✐♦♥

✶✳✶ Pr♦❜❧❡♠ ❙t❛t❡♠❡♥t

❘❡♠♦t❡ ❝♦♥tr♦❧❧❡❞ ♠♦❞❡❧ ❛❡r♦♣❧❛♥❡s ❤❛✈❡ ❜❡❡♥ ✐♥ ✉s❡ ❢♦r ❞❡❝❛❞❡s ❛♥❞ ❤❛✈❡ ❜❡❡♥ ❛ ❢❛✈♦✉r✐t❡ ❛♠♦♥❣ ❤♦❜❜②✐sts ❢♦r ❛❧♠♦st ❡q✉❛❧❧② ❧♦♥❣✳ ❍♦✇❡✈❡r✱ t❤❡ ♣❛st ❞❡❝❛❞❡ ❤❛s ❛r❣✉❛❜❧② s❡❡♥ t❤❡ ❣r❡❛t❡st ✐♥❝r❡❛s❡ ✐♥ ❝♦♠♣✉t✐♥❣ ♣♦✇❡r ❛♥❞ ❡❢✲ ✜❝✐❡♥❝② s✐♥❝❡ t❤❡ s✐❧✐❝♦♥ tr❛♥s✐st♦r ✇❛s ✜rst ✐♥✈❡♥t❡❞ ✭r❡❢❡r t♦ t❤❡ ❧❛✇ ♣♦♣✲ ✉❧❛r✐s❡❞ ❜② ▼♦♦r❡✱ ✶✾✻✺✮✳ ❚❤❛♥❦s t♦ t❤❡ ❣r♦✇t❤ ✐♥ t❤❡ ♠♦❜✐❧❡ t❡❝❤♥♦❧♦❣② ✐♥❞✉str✐❡s✱ ❝♦♠♣✉t❡rs ❤❛✈❡ ♥♦t ♦♥❧② ❣r♦✇♥ ♠♦r❡ ♣♦✇❡r❢✉❧✱ ❜✉t ❛❧s♦ s♠❛❧❧❡r✱ ❧✐❣❤t❡r✱ ❝❤❡❛♣❡r ❛♥❞ ♠♦r❡ ♣♦✇❡r ❡✣❝✐❡♥t✳ ❚❤❡ ✐♥❝r❡❛s❡ ✐♥ ❝♦♠♣✉t✐♥❣ ♣♦✇❡r ❛♥❞ ❞❡❝r❡❛s❡ ✐♥ s✐③❡ ❛♥❞ ❝♦st ❤❛✈❡ ♠❛❞❡ ✐t ♣♦ss✐❜❧❡ t♦ ♣❧❛❝❡ s♠❛❧❧ ❝♦♠♣✉t❡rs ♦♥t♦ ❛ ♠♦❞❡❧ ❛❡r♦♣❧❛♥❡ ✇✐t❤ t❤❡ ❛✐♠ ♦❢ ❤❛✈✐♥❣ ✐t ❛✉t♦♥♦♠♦✉s❧② ❝♦♥tr♦❧✱ ♦r s❡♠✐✲❛✉t♦♥♦♠♦✉s❧② ❛ss✐st ✐♥ ❝♦♥tr♦❧❧✐♥❣✱ ❛ ♠♦❞❡❧ ❛❡r♦♣❧❛♥❡✳ ❈♦✉♣❧❡❞ ✇✐t❤ t❤❡ r✐s❡ ✐♥ ♠♦❜✐❧❡ ❝♦♠♣✉t✐♥❣ ♣♦✇❡r✱ ❝♦♥tr♦❧ t❤❡♦r② ❤❛s ❛❧s♦ r❡❛❝❤❡❞ ❛ ♣♦✐♥t ✇❤❡r❡ ✐t ❤❛s ❛ ❜❡tt❡r ✉♥❞❡rst❛♥❞✐♥❣ ♦❢ t❤❡ ✉♥st❛❜❧❡✱ ✉♥❞❡r❛❝t✉✲ ❛t❡❞ ♣❧❛♥t✱ s✉❝❤ ❛s ❛ ❙❡❣✇❛②✱ ❛♥❞ ♠❛♥❛❣❡s t♦ st❛❜✐❧✐s❡ ❛♥❞ ❝♦♥tr♦❧ s✉❝❤ ♣❧❛♥ts ✐♥ s♦♠❡ ❝❛s❡s✳ ❖♥❡ ❝❛s❡ ♦❢ ✐♥t❡r❡st ✐s ❛ ♠✉❧t✐r♦t♦r ✉♥♠❛♥♥❡❞ ❛❡r✐❛❧ ✈❡❤✐❝❧❡ ✭❯❆❱✮ ✇❤✐❝❤ r❡s❡♠❜❧❡s ❛ ♠♦❞❡❧ ❤❡❧✐❝♦♣t❡r ✇✐t❤ ♠✉❧t✐♣❧❡ r♦t♦rs✳ ❚❤❡ s♦✲❝❛❧❧❡❞ q✉❛❞❝♦♣t❡r ❝♦♥✜❣✉r❛t✐♦♥ ✐s ♦❢ s♣❡❝✐❛❧ ✐♥t❡r❡st ❢♦r t❤✐s r❡s❡❛r❝❤ ♣r♦❥❡❝t✳ ❆✉t♦♥♦♠♦✉s ❯❆❱s ❛r❡ t②♣✐❝❛❧❧② ✜tt❡❞ ✇✐t❤ ❛ ♠✉❧t✐t✉❞❡ ♦❢ s❡♥s♦rs t❤❛t ♣r♦✈✐❞❡ t❤❡ ❝♦♥tr♦❧ s②st❡♠ ✇✐t❤ t❤❡ ❯❆❱✬s ♦r✐❡♥t❛t✐♦♥ ❛♥❞ ❧♦❝❛❧✐s❛t✐♦♥ ❞❛t❛✳ ❚❤❡s❡ s❡♥s♦rs ♥♦r♠❛❧❧② ✐♥❝❧✉❞❡ ❛♥ ❛❝❝❡❧❡r♦♠❡t❡r✱ ❣②r♦s❝♦♣❡ ❛♥❞ ●P❙✱ ❛❧♦♥❣ ✇✐t❤ ♦t❤❡rs s✉❝❤ ❛s ❛ ❜❛r♦♠❡t❡r✱ ♦♣t✐❝ ✢♦✇ s❡♥s♦r✱ ♠❛❣♥❡t♦♠❡t❡r✱ ❡t❝✳ ■♥ ✐ts s❡♠✐✲❛✉t♦♥♦♠♦✉s st❛t❡✱ t❤❡ ❝♦♥tr♦❧ s②st❡♠ ✉s❡s t❤❡s❡ s❡♥s♦r r❡❛❞✐♥❣s t♦ ❦❡❡♣ t❤❡ ❯❆❱ ❧❡✈❡❧ ❛♥❞ st❛❜❧❡ ✇❤✐❧❡ ❢♦❧❧♦✇✐♥❣ ❛ ❤✉♠❛♥ ♣✐❧♦t✬s ✢✐❣❤t ✐♥str✉❝t✐♦♥s✳ ❖♣t✐♦♥❛❧❧②✱ t❤❡ ♣✐❧♦t ❝❛♥ ❡♥❣❛❣❡ t❤❡ ❯❆❱ ✐♥ ♠✐ss✐♦♥ ♠♦❞❡ ✇❤❡r❡ t❤❡ ❯❆❱ ❛✉t♦♥♦♠♦✉s❧② ❝♦♠♣❧❡t❡s ❛ ✢✐❣❤t ♠✐ss✐♦♥ s❡❧❡❝t❡❞ ❜② t❤❡ ♣✐❧♦t ✇✐t❤♦✉t t❤❡ ♣✐❧♦t ❝♦♥tr♦❧❧✐♥❣ ✐t✳ ❆ ♠✐ss✐♦♥ ❝♦♥s✐sts ♦❢ ❛ s❡t ♦❢ ●P❙ ❝♦♦r❞✐♥❛t❡ ✇❛②♣♦✐♥ts ❛♥❞ ❛❧t✐t✉❞❡s ❢♦r t❤❡ ❯❆❱ t♦ ❢♦❧❧♦✇✳ ❚❤❡ ♣✐❧♦t ❝❛♥ ❛❧s♦ s❡t t❤❡ ❯❆❱ t♦ ❧♦✐t❡r✐♥❣ ♠♦❞❡ ✇❤❡r❡ t❤❡ ❯❆❱✬s ❝♦♥tr♦❧ s②st❡♠ ✇✐❧❧ ❦❡❡♣ ✐t st❛❜❧❡ ❛♥❞ ❧❡✈❡❧ ✇❤✐❧❡ ❤♦❧❞✐♥❣ t❤❡ ②❛✇ ❛♥❣❧❡ ❛♥❞ ♣♦s✐t✐♦♥ ❝♦♥st❛♥t✳ ✶

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❈❍❆P❚❊❘ ✶✳ ■◆❚❘❖❉❯❈❚■❖◆ ✷ ❆ ❝♦♥s❡q✉❡♥❝❡ ♦❢ t❤❡ s♠❛❧❧❡r ❛♥❞ ❧✐❣❤t❡r s❡♥s♦rs ❯❆❱s ❛r❡ t②♣✐❝❛❧❧② ❡✲ q✉✐♣♣❡❞ ✇✐t❤ ✐s t❤❛t t❤❡② ❛r❡ ♦❢t❡♥ ❧❡ss ❛❝❝✉r❛t❡ t❤❛♥ t❤❡✐r ❧❛r❣❡r✱ ♠♦r❡ ♣♦✇✲ ❡r❢✉❧ ❝♦✉♥t❡r♣❛rts✳ ❚❤❡ ✐♠♣❧✐❝❛t✐♦♥ t❤✐s ❤♦❧❞s ❢♦r ❯❆❱s ✐♥ ❣❡♥❡r❛❧ ❝❛♥ r❡❛❞✐❧② ❜❡ ♦❜s❡r✈❡❞ ❢r♦♠ ♠♦st ❯❆❱s ✐♥ ❧♦✐t❡r ♠♦❞❡ ✇❤❡r❡ t❤❡r❡ ✐s ♦❢t❡♥ s✐❣♥✐✜❝❛♥t ❞r✐❢t ❛r♦✉♥❞ ✐ts s❡t ♣♦✐♥t✳ ❚❤❡ ❛❝❝✉r❛❝② ♦❢ t❤❡ ✐♥❞✐✈✐❞✉❛❧ s❡♥s♦rs ❛r❡ ♦❢t❡♥ ❦♥♦✇♥ ♦r ❝❛♥ ❜❡ ❞❡t❡r♠✐♥❡❞✱ ❜✉t ❞✉❡ t♦ t❤❡ ♠❛t❤❡♠❛t✐❝❛❧ ✜❧t❡r✐♥❣ ❛♥❞ ❢✉s✐♦♥ ♦❢ t❤❡ ❞✐✛❡r❡♥t s❡♥s♦r r❡❛❞✐♥❣s✱ ❛s ✇❡❧❧ ❛s ♦t❤❡r ♦♣❡r❛t✐♦♥s t❤❛t t❤❡ ❝♦♥tr♦❧ s②st❡♠ ♠❛② ♣❡r❢♦r♠ ♦♥ t❤❡ s❡♥s♦r ❞❛t❛✱ ✐t ✐s ❞✐✣❝✉❧t t♦ ❞❡t❡r♠✐♥❡ t❤❡ r❡s✉❧t✲ ✐♥❣ ❛❝❝✉r❛❝② ♦❢ t❤❡ ♣♦s✐t✐♦♥ ❛♥❞ ♦r✐❡♥t❛t✐♦♥ ♠❡❛s✉r❡♠❡♥ts ♠❛❞❡ ❜② t❤❡ ❯❆❱✬s s❡♥s♦r s✉✐t❡✳ ❆s ❛ r❡s✉❧t✱ t❤❡ ♣♦s❡ ✭❛ ✈❡❝t♦r ❞❡s❝r✐❜✐♥❣ ❛♥ ♦❜❥❡❝t✬s ♣♦s✐t✐♦♥ ❛♥❞ ♦r✐❡♥t❛t✐♦♥✮ ❡st✐♠❛t✐♦♥ ❛❝❝✉r❛❝② ♦❢ ❛♥ ♦✉t❞♦♦r ❯❆❱ ✐s ♥♦t ②❡t ❦♥♦✇♥✳ ❚❤✐s r❡s❡❛r❝❤ ♣r♦❥❡❝t ❛tt❡♠♣ts t♦ ✜♥❞ ❛♥❞ ✐♠♣❧❡♠❡♥t ❛♥ ❛✛♦r❞❛❜❧❡ ❛♥❞ r❡❧✐❛❜❧❡ ♠❡t❤♦❞ t♦ ❞❡t❡r♠✐♥❡ t❤❡ ♣♦s❡ ❡st✐♠❛t✐♦♥ ❡rr♦r ♦❢ ❛ t②♣✐❝❛❧ q✉❛❞❝♦♣t❡r ❯❆❱✳

✶✳✷ Pr♦❥❡❝t ▼♦t✐✈❛t✐♦♥

❋♦r ♠❛♥② ②❡❛rs✱ ❯❆❱s ❤❛✈❡ ♠♦st❧② ❜❡❡♥ t❤❡ ♣❧❛②t❤✐♥❣s ♦❢ ❤♦❜❜②✐sts ❛♥❞ t❤❡ r❡✲ s❡❛r❝❤❡rs st✉❞②✐♥❣ t❤❡♠✳ ■♥ r❡❝❡♥t ②❡❛rs✱ ❤♦✇❡✈❡r✱ t❤❡ ✐♠♣r♦✈❡♠❡♥ts t❤❛t ❤❛✈❡ ❜❡❡♥ ♠❛❞❡ t♦ ❯❆❱s✱ ✇❤✐❝❤ ✐♥❝❧✉❞❡ q✉❛❞✲✱ ❤❡①❛✲ ❛♥❞ ♦❝t♦❝♦♣t❡rs✱ ❛♥❞ t❤❡✐r ❝♦♥tr♦❧❧❡rs ❤❛✈❡ ❞r❛✇♥ t❤❡ ❛tt❡♥t✐♦♥ ♦❢ ❧❛r❣❡ ❝♦r♣♦r❛t✐♦♥s✱ s✉❝❤ ❛s ❆♠❛③♦♥ ❛♥❞ ❉❍▲✱ ❤❛✈❡ ❡①♣r❡ss❡❞ ✐♥t❡r❡st ✐♥ ✐♥❝♦r♣♦r❛t✐♥❣ ❯❆❱s ✐♥t♦ t❤❡✐r r❡s♣❡❝t✐✈❡ ✇♦r❦❢♦r❝❡s✳ ❙✐♠✐❧❛r❧②✱ ♥❛t✐♦♥❛❧ ❣♦✈❡r♥♠❡♥ts ❤❛✈❡ ❛❧s♦ ♥♦t✐❝❡❞ t❤❡ ✐♥❝r❡❛s✐♥❣ ❝♦♠♠❡r✲ ❝✐❛❧ ❛♥❞ ✐♥❞✉str✐❛❧ ♣♦t❡♥t✐❛❧ t❤❛t ❯❆❱s ❤❛✈❡✱ ✇❤✐❧❡ ❛❧s♦ r❡❝♦❣♥✐s✐♥❣ t❤❡ ❞❛♥❣❡rs t❤❛t t❤❡② ♣♦s❡ t♦ s♦❝✐❡t② ✐❢ ❧❡❢t ✉♥r❡❣✉❧❛t❡❞✳ ❆s s✉❝❤✱ ♠❛♥② ❣♦✈❡r♥♠❡♥ts ❤❛✈❡ ♠♦✈❡❞ t♦ r❡❣✉❧❛t❡ ❛♥❞ ♣❧❛❝❡ r❡str✐❝t✐♦♥s ♦♥ ❤♦✇ ❛♥❞ ✇❤❡r❡ ❯❆❱s ♠❛② ❜❡ ✉s❡❞✳ ❚❤❡ ❣❡♥❡r❛❧ tr❡♥❞ ♦❢ t❤❡ r❡❣✉❧❛t✐♦♥s✱ ❛s ❞❡♠♦♥str❛t❡❞ ❜② t❤❡ r❡❣✉❧❛t✐♦♥s r❡✲ ❧❡❛s❡❞ ❜② t❤❡ ❙♦✉t❤ ❆❢r✐❝❛♥ ❈✐✈✐❧ ❆✈✐❛t✐♦♥ ❆✉t❤♦r✐t② ✭✷✵✶✺✮✱ ✐s t❤❛t ❯❆❱s ♠❛② ❜❡ ♠❛♥✉❛❧❧② ✢♦✇♥ ❜② ❛ ♣✐❧♦t ❛♥②✇❤❡r❡ ❜❡❧♦✇ ❛♥ ❛❧t✐t✉❞❡ ♦❢ 120 ♠✱ 50 ♠ ❛✇❛② ❢r♦♠ ♣❡♦♣❧❡ ❛♥❞ ❜✉✐❧❞✐♥❣s ❛♥❞ 10 ❦♠ ❛✇❛② ❢r♦♠ ❛♥② ❛❡r♦❞r♦♠❡✳ ❚❤❡s❡ r❡❣✉❧❛t✐♦♥s ❛❧❧♦✇ ❢♦r ❛✉t♦♥♦♠♦✉s ❯❆❱ ✢✐❣❤t✱ ♣r♦✈✐❞❡❞ t❤❡ ❯❆❱ r❡♠❛✐♥ ✇✐t❤✐♥ r❛❞✐♦ ❧✐♥❡ ♦❢ s✐❣❤t ♦❢ ❛ ❤✉♠❛♥ ♦♣❡r❛t♦r t❤❛t ❝❛♥ ♠❛♥✉❛❧❧② t❛❦❡ ♦✈❡r ❝♦♥tr♦❧ ♦❢ t❤❡ ❯❆❱ ❛t ❛♥② t✐♠❡ s❤♦✉❧❞ s♦♠❡t❤✐♥❣ ❣♦ ✇r♦♥❣✳ ❆t t❤❡ ♠♦♠❡♥t✱ ❯❆❱s ❛r❡ ♥♦t ❛s s❛❢❡ ❛s t❤❡② s❤♦✉❧❞ ❜❡ ❛♥❞ ❝❛♥ ♣♦s❡ ❛ s❡r✐♦✉s ❤❡❛❧t❤ ❤❛③❛r❞ t♦ t❤❡✐r s✉rr♦✉♥❞✐♥❣s ❛♥❞ ♣❡♦♣❧❡ ✐❢ ❤❛♥❞❧❡❞ ✐♥❝♦rr❡❝t❧②✳ ❚❤✐s✱ ❝♦✉♣❧❡❞ ✇✐t❤ ❛ ❣❡♥❡r❛❧ ❧❛❝❦ ♦❢ ❤❛r❞✇❛r❡✲ ❛♥❞ s♦❢t✇❛r❡✲❜❛s❡❞ ❝♦❧❧✐s✐♦♥ ❛✈♦✐❞❛♥❝❡ ❝❛♣❛❜✐❧✐t✐❡s✱ ♠❛❦❡s ❛✈✐❛t✐♦♥ ❛✉t❤♦r✐t✐❡s ✈❡r② ❝❛✉t✐♦✉s ❛❜♦✉t ❛❧❧♦✇✐♥❣ ❢✉❧❧② ❛✉t♦♥♦♠♦✉s ✢✐❣❤t ✭✐✳❡✳ ♦✉t ♦❢ r❛❞✐♦ ❧✐♥❡ ♦❢ s✐❣❤t✮✳ ❚❤❡r❡ ❛r❡ ♠❛♥② s❛❢❡t② ✐♠♣r♦✈❡♠❡♥ts t❤❛t ❝❛♥ ❜❡ ♠❛❞❡ t♦ ❯❆❱s✱ s✉❝❤ ❛s ❛♥ ✐♠♣r♦✈❡❞ ❝♦♥tr♦❧ str❛t❡❣②✱ ❤❛r❞✇❛r❡ ✐♠♣r♦✈❡♠❡♥ts ✭s✉❝❤ ❛s r♦t♦r s❤r♦✉❞s✮ ❛♥❞ ♦t❤❡r ❢❛✐❧✲s❛❢❡ ❛♥❞ ❝♦❧❧✐s✐♦♥ ❛✈♦✐❞❛♥❝❡ s②st❡♠s✳ ❍❛✈✐♥❣ ❛❝❝✉r❛t❡ ♣♦s❡ ❞❛t❛ ♦❢ ❛ ❯❆❱ ✐♥ ✢✐❣❤t ❛✈❛✐❧❛❜❧❡ ✐s ❝r✉❝✐❛❧ t♦ ✐♠✲ ♣❧❡♠❡♥t✐♥❣ ❛♥ ❡✛❡❝t✐✈❡ ❝♦♥tr♦❧ str❛t❡❣② ❛♥❞ ❝♦❧❧✐s✐♦♥ ❛✈♦✐❞❛♥❝❡ s②st❡♠✳ ❆s

(17)

❈❍❆P❚❊❘ ✶✳ ■◆❚❘❖❉❯❈❚■❖◆ ✸ ♠❡♥t✐♦♥❡❞ ✐♥ ❙❡❝t✐♦♥ ✶✳✶✱ ❯❆❱s ❞♦ ♥♦t ❡st✐♠❛t❡ t❤❡✐r ♦✇♥ ♣♦s❡ ✈❡r② ✇❡❧❧ ❛♥❞ ❛r❡ ♣r♦♥❡ t♦ s❡♥s♦r ❞r✐❢t ♦✈❡r t✐♠❡✳ ❚❤✐s ❛❧❧♦✇s ❢♦r ❛ ❵❜✉❜❜❧❡✬ ♦❢ ♣♦s❡ ✉♥❝❡r✲ t❛✐♥t② t♦ ❜❡ ❞r❛✇♥ ❛r♦✉♥❞ ❛ ❯❆❱ ✐♥ ✢✐❣❤t✱ ✇❤❡r❡ t❤❡ tr✉❡ ♣♦s❡ ♦❢ ❛ ❯❆❱ ✇✐❧❧ ❜❡ s♦♠❡✇❤❡r❡ ✇✐t❤✐♥ t❤❡ ❜✉❜❜❧❡✱ ❜✉t t❤❡ tr✉❡ ♣♦s❡ ✐s ✐♥❞❡t❡r♠✐♥❛❜❧❡✳ ■❢ t❤❡ ❜✉❜❜❧❡✬s ✈♦❧✉♠❡ ❝❛♥ ❜❡ ❞❡t❡r♠✐♥❡❞✱ ✐t ✇✐❧❧ ❛❧❧♦✇ ❛ ❯❆❱✬s ❝♦♥tr♦❧ s②st❡♠ t♦ ❣❡♥❡r❛t❡ s❛❢❡r✱ ♠♦r❡ ❡✣❝✐❡♥t ✢✐❣❤t ♣❛t❤s✱ ✇❤✐❝❤ ✇✐❧❧ ✐♠♣r♦✈❡ t❤❡ ❯❆❱s ♣❡r✲ ❢♦r♠❛♥❝❡ ❛♥❞ ♠❛❦❡ t❤❡♠ ❛ ♠♦r❡ ❛ttr❛❝t✐✈❡ ❛♥❞ s❛❢❡ ♦♣t✐♦♥ ❢♦r ❣♦✈❡r♥♠❡♥ts ❛♥❞ ✐♥❞✉str②✳ ❋✉rt❤❡r♠♦r❡✱ t❤❡ ♠❡❛s✉r❡♠❡♥t s②st❡♠ ❝❛♥ ❜❡ ✉s❡❞ t♦ ❡✈❛❧✉❛t❡ ❛♥❞ ✐♠♣r♦✈❡ t❤❡ ✢✐❣❤t ♣❡r❢♦r♠❛♥❝❡ ♦❢ ❛ ❯❆❱✳

✶✳✸ P♦t❡♥t✐❛❧ ❯s❡ ❈❛s❡

❚❤❡ r❡s✉❧ts ❢r♦♠ t❤✐s r❡s❡❛r❝❤ ♣r♦❥❡❝t ✇✐❧❧ ❜❡ ❛♣♣❧✐❝❛❜❧❡ t♦ ♠❛♥② ❞✐✛❡r❡♥t ✐♥❞✉str✐❡s ❛♥❞ ❛♣♣❧✐❝❛t✐♦♥s✳ ❚♦ ✐❧❧✉str❛t❡ t❤✐s✱ ❛♥ ❡①❛♠♣❧❡ ♦❢ ✇❤❡r❡ ✐t ✇♦✉❧❞ ❜❡ ❤❡❧♣❢✉❧ t♦ ❦♥♦✇ ❤♦✇ ❛❝❝✉r❛t❡❧② ❛ q✉❛❞❝♦♣t❡r ❝❛♥ ❡st✐♠❛t❡ ✐ts ♣♦s❡ ✐s ♣r❡s❡♥t❡❞ ❛♥❞ ❜r✐❡✢② ❞✐s❝✉ss❡❞✳ ❈♦♥❝❡♥tr❛t✐♥❣ s♦❧❛r ♣♦✇❡r ✭❈❙P✮ ✐s ❛♥ ❛ttr❛❝t✐✈❡ s♦✉r❝❡ ♦❢ r❡♥❡✇❛❜❧❡ ❡♥✲ ❡r❣② ✇❤✐❝❤ ❛❧❧♦✇s t❤❡r♠❛❧ ❡♥❡r❣② t♦ ❜❡ st♦r❡❞ ❢♦r ✉s❡ ❛t ♥✐❣❤t t✐♠❡✳ ❍♦✇❡✈❡r✱ ❛ ♠❛❥♦r ❤✉r❞❧❡ t♦ t❤❡ ❝♦♥str✉❝t✐♦♥ ♦❢ ❛ ❈❙P ♣❧❛♥t✱ ✐♥ ♣❛rt✐❝✉❧❛r t❤❡ ❝❡♥tr❛❧ r❡❝❡✐✈❡r ❝♦♥✜❣✉r❛t✐♦♥✱ ✐s ✐ts ❤❡❢t② ♣r✐❝❡ t❛❣✳ ❲✐t❤ ❈❙P ❝♦st✐♥❣ ♠♦r❡ ♣❡r ❲❛tt t❤❛♥ ❢♦ss✐❧ ❢✉❡❧s✱ ❛s ✇❡❧❧ ❛s ♦t❤❡r r❡♥❡✇❛❜❧❡ ❡♥❡r❣② s♦✉r❝❡s s✉❝❤ ❛s ♣❤♦t♦✲ ✈♦❧t❛✐❝ ♣❛♥❡❧s ♦r ✇✐♥❞ t✉r❜✐♥❡s ✭■❘❊◆❆✱ ✷✵✶✺✮✱ ✐t ✐s ♦❢t❡♥ ❞✐✣❝✉❧t t♦ ❝♦♥✈✐♥❝❡ ✜♥❛♥❝✐❡rs t♦ ✐♥✈❡st ✐♥ ❛ ❝❡♥tr❛❧ r❡❝❡✐✈❡r ❈❙P ♣❧❛♥t✳ ❚♦ ♣r❡✈❡♥t ♠✐rr♦r ❞❡❢♦r♠❛t✐♦♥✱ ✇✐♥❞ ❧♦❛❞s✱ ✐♠♣❛❝ts ❢r♦♠ ❢♦r❡✐❣♥ ♦❜❥❡❝ts ❛♥❞ ❣r♦✉♥❞ s❡tt❧✐♥❣ ❢r♦♠ ❛✛❡❝t✐♥❣ t❤❡ ❤❡❧✐♦st❛t✬s tr❛❝❦✐♥❣ ♣❛t❤✱ ❡❛❝❤ ❤❡❧✐♦st❛t ❢r❛♠❡ ✐s ❞❡s✐❣♥❡❞ t♦ ❜❡ ❤❡❛✈② ❛♥❞ st✉r❞② ❛♥❞ t❤❡② ❛r❡ ♣❧❛❝❡❞ ♦♥ str♦♥❣ ❢♦✉♥✲ ❞❛t✐♦♥s✳ ❚❤❡② ❛❧s♦ ❝♦♠❡ ❡q✉✐♣♣❡❞ ✇✐t❤ ❡①♣❡♥s✐✈❡ ❛❝t✉❛t♦rs ❛♥❞ ❣❡❛r❜♦①❡s ✇❤✐❝❤ ♠✐♥✐♠✐s❡ ❡rr♦r ❜✉✐❧❞✲✉♣s ❞✉r✐♥❣ ❛ ❤❡❧✐♦st❛t✬s ♦♣❡r❛t✐♦♥✱ ❝♦♥tr✐❜✉t✐♥❣ ❛ s✐❣♥✐✜❝❛♥t ♣♦rt✐♦♥ t♦ ✐ts t♦t❛❧ ❝♦st ❛♥❞ P✐t③✲P❛❛❧ ✭✷✵✵✺✮ ✜♥❞s t❤❛t ❛♣♣r♦①✐✲ ♠❛t❡❧② ✹✵ ✪ ♦❢ t❤❡ ✐♥✐t✐❛❧ ❝❛♣✐t❛❧ ❡①♣❡♥❞✐t✉r❡ ♦❢ ❛ ❈❙P ♣❧❛♥t ✐s s♣❡♥t ♦♥ t❤❡ t❤♦✉s❛♥❞s ♦❢ ❤❡❧✐♦st❛ts ♣❧❛❝❡❞ ❛r♦✉♥❞ t❤❡ r❡❝❡✐✈❡r t♦✇❡r✳ ❈❙P ❛s ❛ ❝♦♥❝❡♣t ✐s ♦❧❞ ❛♥❞ ✇❡❧❧ ❞♦❝✉♠❡♥t❡❞✱ ❜✉t t❤❡ t❡❝❤♥♦❧♦❣✐❡s ✉s❡❞ ❛r❡ st✐❧❧ r❡❧❛t✐✈❡❧② ♥❡✇ ❛♥❞ ✇✐❞❡❧② r❡s❡❛r❝❤❡❞✳ ❆s s✉❝❤✱ ❈❙P ♣❧❛♥t ❞❡s✐❣♥ ❤❛s ♥♦t ②❡t r❡❛❝❤❡❞ ❢✉❧❧ ♠❛t✉r✐t② ✐♥ t❡r♠s ♦❢ ❡✣❝✐❡♥❝② ❛♥❞ ♦♣t✐♠❛❧ ❞❡s✐❣♥✳ ❚❤❡r❡✲ ❢♦r❡✱ t❤❡r❡ ❛r❡ st✐❧❧ ✇❛②s t♦ r❡❞✉❝❡ t❤❡ ❝♦st ♦❢ ❈❙P ♣❧❛♥ts✱ s✉❝❤ ❛s ✐♠♣r♦✈✐♥❣ t❤❡ ❤❡❧✐♦st❛t ❝♦♥tr♦❧ s❝❤❡♠❡✱ ♦♣t✐♠✐s✐♥❣ ❤❡❧✐♦st❛t ❞❡s✐❣♥ ❛♥❞ ✐♠♣r♦✈✐♥❣ t❤❡ t❤❡r♠❛❧ st♦r❛❣❡ ♠❡❝❤❛♥✐s♠s✱ ❛♠♦♥❣st ♦t❤❡rs ✭■❘❊◆❆✱ ✷✵✶✷✮✳ ●✐✈❡♥ t❤❡ s❤❡❡r s✐③❡ ♦❢ ❛ t②♣✐❝❛❧ ❤❡❧✐♦st❛t ✜❡❧❞✱ ❛ s♠❛❧❧ ❞✐s♣❧❛❝❡♠❡♥t ✐♥ ❛ ♠✐rr♦r ❝♦✉❧❞ ✐♥✢✉❡♥❝❡ t❤❡ ❛❝❝✉r❛❝② ❛♥❞ ❡✛❡❝t✐✈❡♥❡ss ♦❢ t❤❛t ❤❡❧✐♦st❛t ✇❤✐❝❤ ✐s ❡①tr❡♠❡❧② ✉♥❞❡s✐r❛❜❧❡ ❣✐✈❡♥ t❤❡ ❧❡♥❣t❤② ❝❛❧✐❜r❛t✐♦♥ ♣r♦❝❡ss r❡q✉✐r❡❞✳ ❙t❡❧❧❡♥✲ ❜♦s❝❤ ❯♥✐✈❡rs✐t② ✭❙❯✮ ❛♥❞ ✐ts ❙♦❧❛r ❚❤❡r♠❛❧ ❊♥❡r❣② ❘❡s❡❛r❝❤ ●r♦✉♣ ✭❙❚❊❘●✮ ❛r❡ ❛tt❡♠♣t✐♥❣ t♦ ♠❛❦❡ ❤❡❧✐♦st❛ts ❧✐❣❤t❡r✱ ❝❤❡❛♣❡r ❛♥❞ r❡❞✉❝❡ t❤❡ ♥❡❡❞ ❢♦r ❡①✲ ♣❡♥s✐✈❡ ❛❝t✉❛t♦rs ❛♥❞ ❣❡❛r❜♦①❡s✱ t❤❡r❡❜② ❛❧❧♦✇✐♥❣ t❤❡ ❤❡❧✐♦st❛ts t♦ ❜❡ ♣❧❛❝❡❞

(18)

❈❍❆P❚❊❘ ✶✳ ■◆❚❘❖❉❯❈❚■❖◆ ✹ Heliostat Target Receiver Tower Calibration Target ✭❛✮ ❉✐❛❣r❛♠ ♦❢ t❤❡ ❝✉rr❡♥t ❤❡❧✐♦st❛t ❝❛❧✲ ✐❜r❛t✐♦♥ ♣r♦❝❡❞✉r❡ ✇❤❡r❡ t❤❡ ♣♦s✐t✐♦♥ ♦❢ t❤❡ r❡✢❡❝t❡❞ s✉♥ r❛②s ♦♥ t❤❡ t❛r❣❡t ❛r❡ ♠❡❛s✉r❡❞✳ Light Source Receiver Heliostat ✭❜✮ ❆ ❞✐❛❣r❛♠ ♦❢ ❛ ♣r♦♣♦s❡❞ ❝❛❧✐❜r❛t✐♦♥ ♣r♦❝❡❞✉r❡ ✉s✐♥❣ q✉❛❞❝♦♣t❡rs ✇❤❡r❡ t❤❡ t✇♦ q✉❛❞❝♦♣t❡r✬s ♣♦s✐t✐♦♥s ❛r❡ s✐♠✉❧t❛♥❡✲ ♦✉s❧② ♠❡❛s✉r❡❞✳ ❋✐❣✉r❡ ✶✳✶✿ ❆ s✐❞❡✲❜②✲s✐❞❡ ❝♦♠♣❛r✐s♦♥ ♦❢ ❤♦✇ ❤❡❧✐♦st❛ts ❛r❡ ❝✉rr❡♥t❧② ❝❛❧✐❜r❛t❡❞ ❛♥❞ ❤♦✇ ❤❡❧✐♦st❛ts ❝❛♥ ❜❡ ❝❛❧✐❜r❛t❡❞ ❜② ❛✉t♦♥♦♠♦✉s q✉❛❞❝♦♣t❡rs✳ ♦♥ ❝❤❡❛♣❡r ❢♦✉♥❞❛t✐♦♥s ✇✐t❤ ❝❤❡❛♣❡r✱ ❧❡ss ❛❝❝✉r❛t❡ ❛❝t✉❛t♦rs✳ ❚❤✐s ✇✐❧❧ ❧❡❛❞ t♦ s✐❣♥✐✜❝❛♥t ❝♦st s❛✈✐♥❣s ✐♥ ❛ ❈❙P ♣❧❛♥t✬s ♠❛♥✉❢❛❝t✉r✐♥❣ st❛❣❡✳ ❍♦✇❡✈❡r✱ t♦ ❛❝❤✐❡✈❡ t❤✐s ✇✐t❤♦✉t ❝♦♠♣r♦♠✐s✐♥❣ t❤❡ ❛❝❝✉r❛❝② ♦❢ t❤❡ ❤❡❧✐♦st❛ts ❞✉r✐♥❣ ♦♣❡r❛t✐♦♥✱ t❤❡ ❧❡♥❣t❤② ❝❛❧✐❜r❛t✐♦♥ ♣r♦❝❡❞✉r❡ ❝✉rr❡♥t❧② ✐♥ ✉s❡ ♠❛② ❤❛✈❡ t♦ ❜❡ ♦♣t✐♠✐s❡❞ ❛♥❞ ♣♦ss✐❜❧② r❡❞❡s✐❣♥❡❞ t♦ ❛❧❧♦✇ t❤❡ ❤❡❧✐♦st❛ts t♦ ❜❡ ❝❛❧✐❜r❛t❡❞ ♠♦r❡ ♦❢t❡♥ ♦♥ ❛ ♠♦♥t❤❧②✱ ♦r ❡✈❡♥ ✇❡❡❦❧②✱ ❜❛s✐s✳ ❚❤❡ ❝✉rr❡♥t ❝❛❧✐❜r❛t✐♦♥ ♣r♦❝❡❞✉r❡ ✉s❡s t❤❡ s✉♥ ❛s ❛ ❧✐❣❤t s♦✉r❝❡ ❛♥❞ ❛ s❡❝✲ t✐♦♥ ♦❢ t❤❡ r❡❝❡✐✈❡r t♦✇❡r ❛s ❛ r❡❢❡r❡♥❝❡ t❛r❣❡t✳ ❚❤✐s ❝♦♥str❛✐♥s t❤❡ ♣r♦❝❡ss t♦ t❛❦❡ ♣❧❛❝❡ ✐♥ ❞❛② t✐♠❡ ❛♥❞ ♦♥❧② ❛❧❧♦✇s ♦♥❡ ❤❡❧✐♦st❛t t♦ ❜❡ ❝❛❧✐❜r❛t❡❞ ❛t ❛ t✐♠❡✳ ❙✐♥❝❡ ❛ ❤❡❧✐♦st❛t ✜❡❧❞ t②♣✐❝❛❧❧② ❝♦♥t❛✐♥s s❡✈❡r❛❧ t❤♦✉s❛♥❞ ❤❡❧✐♦st❛ts✱ t❤✐s ♣r♦❝❡✲ ❞✉r❡ ♠❛② ❜❡❝♦♠❡ ✈❡r② t✐♠❡✲❝♦♥s✉♠✐♥❣✳ ❙❡❡ ❋✐❣✉r❡ ✶✳✶❛ ❢♦r ❛ ❞✐❛❣r❛♠♠❛t✐❝❛❧ ❡①❛♠♣❧❡ ♦❢ t❤❡ ❝❛❧✐❜r❛t✐♦♥ ♣r♦❝❡❞✉r❡✳ ■♥ t❤✐s r❡❣❛r❞✱ ❙❚❊❘● ✐s ✐♥✈❡st✐❣❛t✐♥❣ t❤❡ ♣♦ss✐❜✐❧✐t② ♦❢ ✉s✐♥❣ q✉❛❞❝♦♣t❡r ❯❆❱s t♦ ❛✉t♦♥♦♠♦✉s❧② ♣❡r❢♦r♠ ♦r ❛ss✐st ✇✐t❤ ❤❡❧✐♦st❛t ❝❛❧✐❜r❛t✐♦♥ ❜②✱ ❢♦r ❡①❛♠♣❧❡✱ ♠❛❦✐♥❣ ♦♥❡ q✉❛❞❝♦♣t❡r t❤❡ ❧✐❣❤t s♦✉r❝❡ ❛♥❞ ❛♥♦t❤❡r t❤❡ r❡❝❡✐✈❡r✳ ❚❤✐s ✇✐❧❧ ❛❧❧♦✇ ❛s ♠❛♥② ❤❡❧✐♦st❛ts t♦ ❜❡ ❝❛❧✐❜r❛t❡❞ s✐♠✉❧t❛♥❡♦✉s❧② ❛s t❤❡r❡ ❛r❡ ♣❛✐rs ♦❢ q✉❛❞❝♦♣t❡rs ❛✈❛✐❧❛❜❧❡✳ ❙❡❡ ❋✐❣✉r❡ ✶✳✶❜ ❢♦r ❛♥ ✐❧❧✉str❛t✐♦♥ ♦❢ t❤❡ ♣r♦♣♦s❡❞ ❝❛❧✐❜r❛t✐♦♥ ♣r♦❝❡❞✉r❡✳ ❙✐♥❝❡ t❤❡ ❤❡❧✐♦st❛ts ♠✉st ❜❡ ❝❛❧✐❜r❛t❡❞ ✇✐t❤ ❛ ✜♥❡ ❞❡❣r❡❡ ♦❢ ❛❝❝✉r❛❝②✱ t❤✐s ❛♣♣r♦❛❝❤ r❡q✉✐r❡s ❛♥ ❡st✐♠❛t❡ ♦❢ t❤❡ q✉❛❞❝♦♣t❡r✬s ♣♦s❡ ❡st✐♠❛t✐♦♥ ❡rr♦r✳ ❍❡r❡✱ t❤❡ ♣♦s❡ ❡st✐♠❛t✐♦♥ ❡rr♦r r❡❢❡rs t♦ t❤❡ ❞✐✛❡r❡♥❝❡ ❜❡t✇❡❡♥ ❛ q✉❛❞❝♦♣t❡r✬s ♦♥✲❜♦❛r❞ ♣♦s❡ ❡st✐♠❛t❡ ❛♥❞ ✐ts r❡❛❧ ♣♦s❡✳ ❙✐♥❝❡ ❛ q✉❛❞❝♦♣t❡r t②♣✐❝❛❧❧② ❞r✐❢ts ❛r♦✉♥❞ ✐ts s❡t✲♣♦✐♥t✱ s♦♠❡ ♣♦s❡ ❡rr♦r t❡r♠ ♠✉st ❜❡ ✐♥❝❧✉❞❡❞ ✐♥t♦ t❤❡ ❤❡❧✐♦st❛t ❝❛❧✐❜r❛t✐♦♥ ♣r♦❝❡❞✉r❡✳ ❋✐rst t❤❡ ❡①♣❡❝t❡❞ ♣♦s❡ ❡rr♦r✱ ♦r ❵❜✉❜❜❧❡✬ ♦❢ ♣♦s❡ ✉♥❝❡rt❛✐♥t②✱ ♥❡❡❞s t♦ ❜❡ ❞❡t❡r♠✐♥❡❞✳ ❆❢t❡r t❤✐s ✐s ❞♦♥❡✱ t❤❡ ♣♦s❡ ❡rr♦r ❝❛♥ ❜❡ ✐♥❝❧✉❞❡❞ ✐♥t♦ t❤❡ ❝❛❧✐❜r❛t✐♦♥ ♣r♦❝❡❞✉r❡ ❛♥❞ t❤❡ ♣r♦❝❡❞✉r❡ ❝❛♥ ❜❡ ❞❡s✐❣♥❡❞ ❛♥❞ r❡✜♥❡❞ ❛r♦✉♥❞ ✐t✳

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❈❍❆P❚❊❘ ✶✳ ■◆❚❘❖❉❯❈❚■❖◆ ✺ ❈✉rr❡♥t❧②✱ t❤❡ ♦♥❧② ♣♦s❡ ♠❡❛s✉r❡♠❡♥ts ♦❢ ❛ q✉❛❞❝♦♣t❡r ❛✈❛✐❧❛❜❧❡ ❛r❡ ✐ts ♦✇♥ ♦♥✲❜♦❛r❞ ❡st✐♠❛t❡s ♣r♦❞✉❝❡❞ ❜② ❛ ❝♦♠❜✐♥❛t✐♦♥ ♦❢ r❡❛❞✐♥❣s ❢r♦♠ ✐ts s❡♥s♦r s✉✐t❡✱ ✇❤✐❝❤ t②♣✐❝❛❧❧② ✐♥❝❧✉❞❡s ❛ ❣②r♦s❝♦♣❡✱ ❛❝❝❡❧❡r♦♠❡t❡r ❛♥❞ ●P❙✳ ❍♦✇❡✈❡r✱ t❤❡ ♦♥✲❜♦❛r❞ ❞❛t❛ ❝❛♥♥♦t ❜❡ ✉s❡❞ ❤❡r❡✱ s✐♥❝❡ ✐ts ❡rr♦r ❤❛s ♥♦t ②❡t ❜❡❡♥ q✉❛♥t✐✲ ✜❡❞✳ ❈♦♥s❡q✉❡♥t❧②✱ ❛♥♦t❤❡r ❛♣♣r♦❛❝❤ ✐s r❡q✉✐r❡❞ t♦ ❞❡t❡r♠✐♥❡ ❛ q✉❛❞❝♦♣t❡r✬s ♣♦s❡ ❡st✐♠❛t✐♦♥ ❡rr♦r✳ ❲✐t❤ ❛ q✉❛❞❝♦♣t❡r✬s ♣♦s❡ ❡st✐♠❛t✐♦♥ ❡rr♦r ❞❡t❡r♠✐♥❡❞✱ ✐t ✇♦✉❧❞ ❜❡ ♣♦ss✐❜❧❡ t♦ ❛✉t♦♥♦♠♦✉s❧② ❝❛❧✐❜r❛t❡ ❛ ❤❡❧✐♦st❛t ♦♥ ❛ r❡❣✉❧❛r ❜❛s✐s✱ ✇❤✐❝❤ ✇♦✉❧❞ ❧❡❛❞ t♦ s✐❣♥✐✜❝❛♥t ❝♦st s❛✈✐♥❣s ❛♥❞ ❛❧❧♦✇ ❈❙P t❡❝❤♥♦❧♦❣② t♦ ❜❡❝♦♠❡ ❛ ♠♦r❡ s❡r✐♦✉s ❝♦♠♣❡t✐t♦r ✐♥ t❤❡ r❡♥❡✇❛❜❧❡ ❡♥❡r❣② ❣❡♥❡r❛t✐♦♥ ❛r❡♥❛✳

✶✳✹ ❊①✐st✐♥❣ ❛♥❞ Pr♦♣♦s❡❞ ❙♦❧✉t✐♦♥s

❚❤❡ ❝✉rr❡♥t st❛t❡✲♦❢✲t❤❡✲❛rt ♠❡t❤♦❞ ✐♥ ❞❡t❡r♠✐♥✐♥❣ t❤❡ ♣♦s❡ ♦❢ ❛ ❯❆❱ ✐♥ ✢✐❣❤t ✐s t♦ ✉s❡ ❛♥ ✐♥❞♦♦r ♠♦t✐♦♥ tr❛❝❦✐♥❣ s②st❡♠✱ s✉❝❤ ❛s ❛ ❱✐❝♦♥✶ s②st❡♠ ✇❤✐❝❤ ✉s❡s ❛ s❡t ♦❢ ✐♥❢r❛r❡❞ ❝❛♠❡r❛s t♦ tr❛❝❦ ♠❛r❦❡rs ♣❧❛❝❡❞ ♦♥ ❛♥ ♦❜❥❡❝t✳ ❍♦✇❡✈❡r✱ s✉❝❤ s②st❡♠s ❝❛♥♥♦t ❜❡ ✉s❡❞ ✐♥ t❤✐s ❝❛s❡ s✐♥❝❡ t❤❡ ❯❆❱s ♦❢ ✐♥t❡r❡st t♦ t❤✐s ♣r♦❥❡❝t r❡q✉✐r❡ ❛❝❝❡ss t♦ t❤❡✐r ●P❙ ❝♦♦r❞✐♥❛t❡s✳ ❚❤❡ ●P❙s ✉s❡❞ ✐♥ t❤✐s ♣r♦❥❡❝t r❡q✉✐r❡ ❛ str♦♥❣ ❝♦♥♥❡❝t✐♦♥ ✇✐t❤ ❛ r❡❛s♦♥❛❜❧② ❝❧❡❛r ❧✐♥❡ ♦❢ s✐t❡ t♦ ❛t ❧❡❛st ✻ ❞✐✛❡r❡♥t ●P❙ s❛t❡❧❧✐t❡s t♦ ♣r♦❞✉❝❡ ❛❝❝✉r❛t❡ ♣♦s✐t✐♦♥ ❞❛t❛✳ ❚❤❡s❡ ●P❙s ❛r❡ ❛❧s♦ ❧♦✇✲♣♦✇❡r❡❞ ❛♥❞ s♠❛❧❧ ❛♥❞ t❤❡r❡❢♦r❡ str✉❣❣❧❡ t♦ ♠❛❦❡ ❣♦♦❞ ❝♦♥♥❡❝t✐♦♥s t♦ s❛t❡❧❧✐t❡s ✇❤❡♥ ✐♥❞♦♦rs✳ ❚❤❡✐r ❧✐♥❡ ♦❢ s✐❣❤t t♦ t❤❡ s❛t❡❧❧✐t❡s ✇✐❧❧ ❛❧s♦ ❜❡ ❛✛❡❝t❡❞✱ ❢✉rt❤❡r r❡❞✉❝✐♥❣ t❤❡ ●P❙✬s ❛❝❝✉r❛❝②✳ ■t ✇❛s t❤❡r❡❢♦r❡ ❞❡❝✐❞❡❞ t❤❛t t❤❡ q✉❛❞❝♦♣t❡rs ✇♦✉❧❞ ❜❡ ✢♦✇♥ ✐♥ t❤❡ ♦✉t❞♦♦rs ❢♦r t❤✐s ♣r♦❥❡❝t✳ ❚❤✐s ✐♠♣❧✐❡s t❤❛t ❛♥ ♦✉t❞♦♦r ♣♦s❡ ♠❡❛s✉r❡♠❡♥t s②st❡♠ ✐s r❡q✉✐r❡❞✳ ❖✉t❞♦♦r ♣♦s❡ ♠❡❛s✉r❡♠❡♥t s②st❡♠s✱ s✉❝❤ ❛s r❛❞❛r✲ ♦r ❧❛s❡r✲❜❛s❡❞ s②st❡♠s✱ ❝❛♥ ❛❧s♦ ❜❡ ✉s❡❞ t♦ ♣❡r❢♦r♠ ♣♦s❡ ♠❡❛s✉r❡♠❡♥ts ♦❢ ❛ ❯❆❱✳ ❍♦✇❡✈❡r✱ t❤❡s❡ s②st❡♠s ♥♦r♠❛❧❧② ❝♦♠❡ ❛t ❛ ♣r❡♠✐✉♠ ❝♦st✳ ■t ✇❛s t❤❡r❡❢♦r❡ ❞❡❝✐❞❡❞ t♦ ✐♥✲ ✈❡st✐❣❛t❡ ❛♥❞ ✐♠♣❧❡♠❡♥t ❛♥♦t❤❡r ♣♦s❡ ♠❡❛s✉r❡♠❡♥t ♠❡t❤♦❞ t❤❛t ✐s ❝❤❡❛♣✱ ❛❝❝✉r❛t❡✱ r❡♣❡❛t❛❜❧❡ ❛♥❞ ❡❛s② t♦ ✉s❡✳ ❚❤❡ ♣r♦♣♦s❡❞ ♦✉t❞♦♦r ❯❆❱ ♣♦s❡ ♠❡❛s✉r❡♠❡♥t s②st❡♠ ✐s ❜❛s❡❞ ♦♥ ❝♦♠♣✉t❡r ✈✐s✐♦♥ t❡❝❤♥✐q✉❡s ✇❤❡r❡ t❤❡ ♣♦s❡ ❞❛t❛ ♦❢ ❛♥ ♦❜❥❡❝t ❝❛♥ ❜❡ ❡①tr❛❝t❡❞ ❢r♦♠ ✐♠❛❣❡ ♦r ✈✐❞❡♦ ❞❛t❛ ❝♦♥t❛✐♥✐♥❣ t❤❡ ♦❜❥❡❝t✳ ❚❤❡ s②st❡♠ ❝♦♥s✐sts ♦❢ ❛ ❝❛♠❡r❛ t♦ ❝❛♣t✉r❡ t❤❡ ✐♠❛❣❡ ❞❛t❛ ❛♥❞ ❛ ❝♦♠♣✉t❡r t♦ ♣❡r❢♦r♠ t❤❡ ♣♦s❡ ❞❛t❛ ❡①tr❛❝t✐♦♥✳

✶✳✺ Pr♦❥❡❝t ❖❜❥❡❝t✐✈❡s

❚❤❡ ♦❜❥❡❝t✐✈❡s ♦❢ t❤✐s r❡s❡❛r❝❤ ♣r♦❥❡❝t ❛r❡ ❛s ❢♦❧❧♦✇s✳ ❼ ❉❡s✐❣♥ ❛♥❞ ✐♠♣❧❡♠❡♥t ❛ r❡❧❛t✐✈❡❧② ❝❤❡❛♣ ❝♦♠♣✉t❡r ✈✐s✐♦♥ ♣♦s❡ ♠❡❛s✉r❡✲ ♠❡♥t s②st❡♠✳ ✶✇✇✇✳✈✐❝♦♥✳❝♦♠✴

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❈❍❆P❚❊❘ ✶✳ ■◆❚❘❖❉❯❈❚■❖◆ ✻ ❼ ❉❡t❡r♠✐♥❡ t❤❡ ♠❡❛s✉r❡♠❡♥t ❛❝❝✉r❛❝② ♦❢ t❤❡ ❝♦♠♣✉t❡r ✈✐s✐♦♥ s②st❡♠✳ ❼ ❯s❡ t❤❡ ❝♦♠♣✉t❡r ✈✐s✐♦♥ s②st❡♠ t♦ ❞❡t❡r♠✐♥❡ t❤❡ ♣♦s❡ ❡st✐♠❛t✐♦♥ ❛❝❝✉✲ r❛❝② ♦❢ ❛ ❞❡♠♦♥str❛t✐♦♥ q✉❛❞❝♦♣t❡r ✐♥ ✢✐❣❤t✳

✶✳✻ ❉♦❝✉♠❡♥t ❙tr✉❝t✉r❡

❚❤✐s ❞♦❝✉♠❡♥t ❜❡❣✐♥s ✇✐t❤ ❛ r❡✈✐❡✇ ♦❢ ❡①✐st✐♥❣ ❧✐t❡r❛t✉r❡ ❛♥❞ ♦❢ ♣r❡✈✐♦✉s r❡✲ s❡❛r❝❤ r❡s✉❧ts ✐♥ t❤❡ ✜❡❧❞s r❡❧❡✈❛♥t t♦ t❤✐s ♣r♦❥❡❝t✱ s✉❝❤ ❛s ❝♦♠♣✉t❡r ✈✐s✐♦♥ t❡❝❤♥✐q✉❡s✱ ❯❆❱ ❝♦♥tr♦❧ str❛t❡❣✐❡s ❛♥❞ ♦t❤❡rs✳ ❆❢t❡r✇❛r❞s✱ t❤❡ ❞❡s✐❣♥ ❛♥❞ ✐♠♣❧❡♠❡♥t❛t✐♦♥✱ ❛s ✇❡❧❧ ❛s t❤❡ ❞❡t❡r♠✐♥❛t✐♦♥ ♦❢ t❤❡ ❛❝❝✉r❛❝② ♦❢ t❤❡ ❝♦♠♣✉t❡r ✈✐s✐♦♥ ♣♦s❡ ❡st✐♠❛t✐♦♥ s②st❡♠ ✐s ❞✐s❝✉ss❡❞✳ ❚❤✐s ✐s ❢♦❧❧♦✇❡❞ ❜② ❛ ❞✐s❝✉ss✐♦♥ ♦♥ ❤♦✇ t❤❡ ♣♦s❡ ♠❡❛s✉r❡♠❡♥t ❡rr♦r ♦❢ t❤❡ ❝♦♠♣✉t❡r ✈✐s✐♦♥ s②st❡♠ ✇❛s ❞❡t❡r♠✐♥❡❞ ❢♦r s✉❜s❡q✉❡♥t ♠❡❛s✉r❡♠❡♥ts ❛♥❞ ✉s❡❞ t♦ ❞❡t❡r♠✐♥❡ t❤❡ ♣♦s❡ ❡st✐♠❛t✐♦♥ ❛❝❝✉✲ r❛❝② ♦❢ ❛ q✉❛❞❝♦♣t❡r ✐♥ ✢✐❣❤t✳ ❋✐♥❛❧❧②✱ ❛ ❝♦♥❝❧✉s✐♦♥ ♦♥ t❤❡ s✐❣♥✐✜❝❛♥t ✜♥❞✐♥❣s ❛♥❞ r❡s✉❧ts✱ ❛s ✇❡❧❧ ❛s s❤♦rt❝♦♠✐♥❣s ❛♥❞ ♣♦t❡♥t✐❛❧ ✐♠♣r♦✈❡♠❡♥ts✱ ❛r❡ ♣r❡s❡♥t❡❞✳

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❈❤❛♣t❡r ✷

▲✐t❡r❛t✉r❡ ❘❡✈✐❡✇

✷✳✶ ■♥tr♦❞✉❝t✐♦♥

■♥ t❤✐s ❝❤❛♣t❡r✱ ♣r❡✈✐♦✉s ✇♦r❦ ❛♥❞ r❡s❡❛r❝❤ ✜♥❞✐♥❣s r❡❧❡✈❛♥t t♦ t❤✐s ♣r♦❥❡❝t ❛r❡ ♠❡♥t✐♦♥❡❞ ❛♥❞ ❞✐s❝✉ss❡❞✳ ❚❤❡s❡ ✜❡❧❞s ✐♥❝❧✉❞❡ t❤❡ q✉❛❞❝♦♣t❡r ♣❧❛t❢♦r♠✱ ❝♦♠✲ ♣✉t❡r ✈✐s✐♦♥ ❛♥❞ ♠❛❝❤✐♥❡ ❧❡❛r♥✐♥❣ t❡❝❤♥✐q✉❡s✳ ❙♦♠❡ ❝♦♥❝❡♣ts ❛♥❞ t❡r♠✐♥♦❧♦❣② ✉s❡❞ ✐♥ ❧❛t❡r ❝❤❛♣t❡rs ♦❢ t❤✐s ❞♦❝✉♠❡♥t ❛r❡ ❛❧s♦ ❡①♣❧❛✐♥❡❞ ❛♥❞ ❡①♣❛♥❞❡❞ ✉♣♦♥✳

✷✳✷ ◗✉❛❞❝♦♣t❡rs

❆ q✉❛❞❝♦♣t❡r ✐s ❛♥ ❛✉t♦♥♦♠♦✉s ❛❡r✐❛❧ ✈❡❤✐❝❧❡ ✭❯❆❱✮ ✐♥ ❛ ❢♦✉r✲❛r♠ ❢r❛♠❡ ❝♦♥✜❣✉r❛t✐♦♥✳ ❚❤❡ ❢r❛♠❡s t②♣✐❝❛❧❧② ❝♦♠❡ ✐♥ ❛♥ ❳ ♦r ♣❧✉s ✭✰✮ s❤❛♣❡ ✇✐t❤ t❤❡ ❝♦♥tr♦❧ ❡q✉✐♣♠❡♥t ❛♥❞ s❡♥s♦rs ❧♦❝❛t❡❞ ❛t t❤❡ ❝❡♥tr❡ ♦❢ t❤❡ ❢r❛♠❡✳ ❘❡❢❡r t♦ ❋✐❣✉r❡ ✷✳✶ ❢♦r ❛ ♣✐❝t✉r❡ ♦❢ t❤❡ ❙♦❧❛r ❚❤❡r♠❛❧ ❊♥❡r❣② ❘❡s❡❛r❝❤ ●r♦✉♣✬s ✭❙❚❊❘●✮ ❙✉♥❝♦♣t❡r r❡s❡❛r❝❤ ♣❧❛t❢♦r♠ ✇❤✐❝❤ ❤❛s ❛♥ ❳ ❝♦♥✜❣✉r❛t✐♦♥✳ ❚❤❡② ❝❛♥ ❛❧s♦ ❝♦♠❡ ❡q✉✐♣♣❡❞ ✇✐t❤ ❡✐t❤❡r ❢♦✉r ♦r ❡✐❣❤t ♠♦t♦rs ❛♥❞ ♣r♦♣s✱ t❤♦✉❣❤ t❤❡ ❢♦✉r✲r♦t♦r ✈❛r✐❛♥t ✐s ❝♦♠♠♦♥❧② ✉s❡❞ ❛♥❞ ✐s ✉s❡❞ ✐♥ t❤✐s ♣r♦❥❡❝t✳ ❋✐❣✉r❡ ✷✳✶✿ ❆ ♣✐❝t✉r❡ ♦❢ t❤❡ ❙✉♥❝♦♣t❡r ✉s❡❞ ❜② ❙❚❊❘●✳ ✼

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❈❍❆P❚❊❘ ✷✳ ▲■❚❊❘❆❚❯❘❊ ❘❊❱■❊❲ ✽ ❋✐❣✉r❡ ✷✳✷✿ ❆ ❞✐❛❣r❛♠ ♣r❡s❡♥t✐♥❣ t❤❡ ♦♣♣♦s✐♥❣ ❛①✐s r♦t❛t✐♦♥ ❞✐r❡❝t✐♦♥s✳ ❚❤❡ t❤✐❝❦♥❡ss ♦❢ t❤❡ ❛rr♦✇s r❡♣r❡s❡♥t t❤❡ ♣♦✇❡r ♦✉t♣✉t ♦❢ t❤❡ ♠♦t♦r ✭▼❛❥✉♠❞❡r✱ ✷✵✶✹✮✳ ◗✉❛❞❝♦♣t❡rs ♠♦✈❡ ❢r❡❡❧② ✐♥ t❤r❡❡✲❞✐♠❡♥s✐♦♥❛❧ s♣❛❝❡ ❛♥❞ ❤❛✈❡ s✐① ❞❡❣r❡❡s ♦❢ ❢r❡❡❞♦♠✿ t❤r❡❡ ✐♥ ♣♦s✐t✐♦♥ s♣❛❝❡ ✭x, y, z✮ ❛♥❞ t❤r❡❡ ✐♥ ♦r✐❡♥t❛t✐♦♥ s♣❛❝❡ ✭θ, φ, ψ✮✱ ✇❤❡r❡ t❤❡ ♦r✐❡♥t❛t✐♦♥ ✐s ❞❡✜♥❡❞ ❜② t❤❡ ❊✉❧❡r✐❛♥ ❛❡r♦♣❧❛♥❡ ❛♥❣❧❡ s❝❤❡♠❡✱ ✐✳❡✳ r♦❧❧✱ ♣✐t❝❤ ❛♥❞ ②❛✇ ❛♥❣❧❡s✳ ❚❤❡ r♦t♦rs ♦♥ ❡❛❝❤ ❛①✐s ♦❢ t❤❡ ❢r❛♠❡ r♦t❛t❡ ✐♥ t❤❡ s❛♠❡ ❞✐r❡❝t✐♦♥ ❛♥❞ ❡❛❝❤ ❛①✐s✬ r♦t♦rs s♣✐♥ ✐♥ ♦♣♣♦s✐t❡ ❞✐r❡❝t✐♦♥s r❡❧❛t✐✈❡ t♦ ♦♥❡ ❛♥♦t❤❡r✳ ❘❡❢❡r t♦ ❋✐❣✉r❡ ✷✳✷ ❢♦r ❛ ❞✐❛❣r❛♠ ❞❡♠♦♥str❛t✐♥❣ t❤✐s✳ ▼♦✈❡♠❡♥t ✐♥ ❡❛❝❤ ♦❢ t❤❡ s✐① ❞✐♠❡♥s✐♦♥s ✐s ❞❡s❝r✐❜❡❞ ❜❡❧♦✇✳ ❼ ❋♦r✇❛r❞✴❜❛❝❦✇❛r❞ ♦r ❧❡❢t✴r✐❣❤t ♠♦✈❡♠❡♥t✿ ❑❡❡♣ ♦♥❡ ❛①✐s✬ r♦t♦r s♣❡❡❞ ❝♦♥st❛♥t✱ ✇❤✐❧❡ r❛✐s✐♥❣ ♦r ❧♦✇❡r✐♥❣ t❤❡ s♣❡❡❞ ♦❢ t❤❡ r♦t♦rs ♦♥ t❤❡ ♦t❤❡r ❛①✐s ✭s❤♦✇♥ ✐♥ ❋✐❣✉r❡ ✷✳✷✮✳ ❼ ❍✐❣❤❡r✴❧♦✇❡r✿ ■♥❝r❡❛s❡ ♦r ❞❡❝r❡❛s❡ ❛❧❧ ♦❢ t❤❡ r♦t♦r s♣❡❡❞s✳ ❼ ❘♦❧❧✴♣✐t❝❤✿ ▲✐♥❡❛r ♠♦✈❡♠❡♥t ✐s ❛❝❤✐❡✈❡❞ ❜② t✐❧t✐♥❣ t❤❡ q✉❛❞❝♦♣t❡r✱ t❤❡r❡✲ ❢♦r❡ ♠♦✈❡♠❡♥t ✐♥ t❤❡ r♦❧❧ ❛♥❞ ♣✐t❝❤ ❞✐♠❡♥s✐♦♥s ✐s ❛❝❤✐❡✈❡❞ ✇✐t❤ t❤❡ s❛♠❡ ♣r♦❝❡ss ❛s ❞❡s❝r✐❜❡❞ ✐♥ t❤❡ ✜rst ♣♦✐♥t✳ ❼ ❨❛✇✿ ■♥❝r❡❛s❡ ♦r ❞❡❝r❡❛s❡ t❤❡ r♦t♦r s♣❡❡❞ ♦❢ ♦♥❡ ❛①✐s r❡❧❛t✐✈❡ t♦ t❤❡ ♦t❤❡r✳ ❆s ❞❡s❝r✐❜❡❞ ✐♥ ❈❤❛♣t❡r ✶✱ t❤❡ ❣♦❛❧ ♦❢ t❤✐s ♣r♦❥❡❝t ✐s t♦ ❞❡t❡r♠✐♥❡ ❛ q✉❛❞✲ ❝♦♣t❡r✬s ♣♦s❡ ❡st✐♠❛t✐♦♥ ❡rr♦r✱ ✐✳❡✳ t❤❡ ❞✐✛❡r❡♥❝❡ ❜❡t✇❡❡♥ ❛ q✉❛❞❝♦♣t❡r✬s tr✉❡ ♣♦s❡ ❛♥❞ ✐ts ❡st✐♠❛t❡❞ ♣♦s❡✳ ❚♦ ❜❡ ❛❜❧❡ t♦ ❞♦ t❤✐s✱ ✐t ✐s ✐♠♣♦rt❛♥t t❤❛t t❤❡ ❞②♥❛♠✐❝s ❛♥❞ ❝♦♥tr♦❧ str❛t❡❣✐❡s ♦❢ ❛ t②♣✐❝❛❧ q✉❛❞❝♦♣t❡r ❛r❡ ✇❡❧❧ ❞❡✜♥❡❞ ❛♥❞ ✉♥❞❡rst♦♦❞✳ ❚❤✐s s❡❝t✐♦♥ s❡ts ♦✉t t♦ ❞✐s❝✉ss t❤❡ ✇♦r❦ t❤❛t ❤❛s ❣♦♥❡ ✐♥t♦ t❤❡

(23)

❈❍❆P❚❊❘ ✷✳ ▲■❚❊❘❆❚❯❘❊ ❘❊❱■❊❲ ✾ ❋✐❣✉r❡ ✷✳✸✿ ❆ ❞✐❛❣r❛♠ ♦❢ t❤❡ q✉❛❞❝♦♣t❡r ♠♦❞❡❧ ✇❤✐❝❤ ✐♥❝❧✉❞❡s t❤❡ ❜❧❛❞❡ ✢❛♣♣✐♥❣ ❞②♥❛♠✐❝s ❞✐s❝✉ss❡❞ ❜② P♦✉♥❞s ❡t ❛❧✳ ✭✷✵✶✵✮✳ ❞②♥❛♠✐❝ ♠♦❞❡❧❧✐♥❣ ♦❢ ❛ q✉❛❞❝♦♣t❡r✱ ❛s ✇❡❧❧ ❛s t❤❡ ❞✐✛❡r❡♥t ❝♦♥tr♦❧ str❛t❡❣✐❡s t❤❛t ❤❛✈❡ ❜❡❡♥ ❞❡✈❡❧♦♣❡❞ ❛♥❞ ✐♠♣❧❡♠❡♥t❡❞ ✐♥ t❤❡ ♣❛st✳

✷✳✷✳✶ ◗✉❛❞❝♦♣t❡r ▼♦❞❡❧❧✐♥❣

❲❤❡♥ ❞❡s✐❣♥✐♥❣ ❛ ❝♦♥tr♦❧ s②st❡♠✱ ❛r❣✉❛❜❧② t❤❡ ♠♦st ❝r✉❝✐❛❧ ♣❛rt ♦❢ t❤❡ ❞❡s✐❣♥ ♣r♦❝❡ss ✐s t♦ ❞❡r✐✈❡ ❛♥ ❛❝❝✉r❛t❡ ♠❛t❤❡♠❛t✐❝❛❧ ♠♦❞❡❧ ♦❢ t❤❡ ♣❧❛♥t✱ s✐♥❝❡ ❛♥ ❛❝✲ ❝✉r❛t❡ ♣❧❛♥t ♠♦❞❡❧ ✇✐❧❧ ❧❡❛❞ t♦ ♠♦r❡ st❛❜❧❡ r❡s♣♦♥s❡ ❛♥❞ s✉♣❡r✐♦r ♣❡r❢♦r♠❛♥❝❡✳ ❚❤❡ ♣❧❛♥t ✐♥ t❤✐s ❝❛s❡ ✐s ❛ ❯❆❱ ✐♥ ❛ q✉❛❞❝♦♣t❡r ❝♦♥✜❣✉r❛t✐♦♥✳ ❆s ♣❛rt ♦❢ t❤❡✐r ❳✲✹ ❋❧②❡r ♣r♦❥❡❝t✱ ❍❛♠❡❧ ❡t ❛❧✳ ✭✷✵✵✷✮ s❡t ♦✉t t♦ ❞❡r✐✈❡ ❛ s✐♠♣❧❡ ♠♦❞❡❧ ❢♦r t❤❡✐r ♣❧❛♥t ✉s✐♥❣ ♦♥❧② r✐❣✐❞ ❜♦❞② ❞②♥❛♠✐❝s ❛♥❞ ❛❜str❛❝t ❢♦r❝❡ ❛♥❞ t♦rq✉❡ ❛❝t✉❛t♦rs✳ ❆s st❛t❡❞ ❜② P♦✉♥❞s ❡t ❛❧✳ ✭✷✵✶✵✮✱ t❤✐s ♠♦❞❡❧ ✭❧✐❦❡ ♠❛♥② ♦t❤❡rs t❤❛t ✇❡r❡ ❞❡r✐✈❡❞ ❛t t❤❡ t✐♠❡✮ r❡♣r❡s❡♥ts t❤❡ q✉❛❞❝♦♣t❡r ❛s ❛ r✐❣✐❞ ❜♦❞② ♠❛ss ✇✐t❤ ✐♥❡rt✐❛ ❛♥❞ ❛✉t♦❣②r♦s❝♦♣✐❝s✱ ✇❤✐❝❤ ✐s ♦♥❧② ❛✛❡❝t❡❞ ❜② ❣r❛✈✐t② ❛♥❞ ❛❝t✉❛t♦r t♦rq✉❡s✳ P♦✉♥❞s ❡t ❛❧✳ ❢✉rt❤❡r ❛r❣✉❡ t❤❛t t❤❡s❡ s✐♠♣❧❡ q✉❛❞❝♦♣t❡r ♠♦❞❡❧s ❞♦ ♥♦t ❛❝❝✉r❛t❡❧② r❡♣r❡s❡♥t t❤❡ ❝♦♠♣❧❡① ❤❡❧✐❝♦♣t❡r✲❧✐❦❡ ❜❡❤❛✈✐♦✉r ❡①❤✐❜✐t❡❞ ❜② r❡❛❧ q✉❛❞❝♦♣t❡rs ❛t ❤✐❣❤ r♦t♦r s♣❡❡❞s✳ ❚❤❡ ❤✐❣❤✲s♣❡❡❞ r♦t♦r ❡✛❡❝ts ✐♥❝❧✉❞❡ ❜❧❛❞❡ ✢❛♣♣✐♥❣ ❡✛❡❝ts✱ ✇❤✐❝❤ ❛✛❡❝t t❤❡ q✉❛❞❝♦♣t❡r ❢r❛♠❡✬s ♦s❝✐❧❧❛t♦r② ♠♦❞❡s✱ r♦t♦r ✢❛♣♣✐♥❣ ✐♥tr♦❞✉❝❡❞ ❜② ✈❛r②✐♥❣ ❛ q✉❛❞❝♦♣t❡r✬s ②❛✇ ❛♥❣❧❡ ❛♥❞ ✈❛r✐❛❜❧❡ ❛✐r✢♦✇ ✈❡❧♦❝✐t✐❡s ♦✈❡r t❤❡ r♦t♦r ❜❧❛❞❡s ❝❛✉s❡❞ ❜② ❝❤❛♥❣✐♥❣ r♦❧❧ ❛♥❞ ♣✐t❝❤ ❛♥❣❧❡s✳ ■♥ ❛♥ ❛tt❡♠♣t t♦ ❝r❡❛t❡ ❛ ♠♦r❡ ❛❝❝✉r❛t❡ q✉❛❞❝♦♣t❡r ♠♦❞❡❧ t❤❛t ✇✐❧❧ ❛❧❧♦✇ ❛ q✉❛❞❝♦♣t❡r t♦ ❜❡ ♠♦r❡ ❝♦♥tr♦❧❧❛❜❧❡ ❛t ❤✐❣❤ r♦t♦r s♣❡❡❞s✱ P♦✉♥❞s ❡t ❛❧✳ s❡t ♦✉t t♦ ❞❡r✐✈❡ ❛ ♠♦❞❡❧ ✐♥❝♦r♣♦r❛t✐♥❣ r✐❣✐❞ ❜♦❞② ❞②♥❛♠✐❝s ❛s ✇❡❧❧ ❛s t❤❡ ❛❡r♦❞②♥❛♠✐❝ ❡✛❡❝ts ♠❡♥t✐♦♥❡❞ ❡❛r❧✐❡r✳ ❚❤❡✐r ♠♦❞❡❧ ✐s ❜❛s❡❞✱ ✐♥ ♣❛rt✱ ♦♥ t❤❡ ❞✐❛❣r❛♠ ❣✐✈❡♥ ✐♥ ❋✐❣✉r❡ ✷✳✸✳ ❚❤❡✐r r❡s✉❧t✐♥❣ ♠♦❞❡❧ ✇❛s ✉s❡❞ t♦ ❞❡✈❡❧♦♣ ❛ s✐♠♣❧❡ Pr♦♣♦rt✐♦♥❛❧ ■♥t❡❣r❛❧ ❉✐✛❡r❡♥t✐❛❧ ✭P■❉✮ ❛tt✐t✉❞❡ ❛♥❞ ❛❧t✐t✉❞❡ ❝♦♥tr♦❧❧❡r ❢♦r t❤❡ ♣✉r♣♦s❡ ♦❢ ♠♦❞❡❧ ✈❡r✐✜❝❛t✐♦♥✳ ❚❤❡✐r r❡s✉❧ts s❤♦✇ t❤❛t t❤❡ q✉❛❞❝♦♣t❡r st❛❜✐❧✐s❡❞ ✐ts❡❧❢ ✭✐♥ ✐♥❞♦♦r

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