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■♥tr♦❞✉❝t✐♦♥ ▼♦❞❡❧❧✐♥❣ ■❞❡♥t✐✜❛❜✐❧✐t② ❊st✐♠❛t✐♦♥ ❆♣♣❧✐❝❛t✐♦♥ ❈♦♥❝❧✉s✐♦♥s ❛♥❞ ♣❡rs♣❡❝t✐✈❡s ❇❛②❡s✐❛♥ ❛♣♣r♦❛❝❤ ♦❢ str✉❝t✉r❛❧ ❡q✉❛t✐♦♥ ♠♦❞❡❧s ❙✳❉❡♠❡②❡r ✶ , ✷ ◆✳❋✐s❝❤❡r ✶ ●✳❙❛♣♦rt❛ ✷ ✶ ▲◆❊✱ ▲❛❜♦r❛t♦✐r❡ ◆❛t✐♦♥❛❧ ❞❡ ▼étr♦❧♦❣✐❡ ❡t ❞✬❊ss❛✐s ✷ ❈❤❛✐r❡ ❞❡ ❙t❛t✐st✐q✉❡ ❆♣♣❧✐q✉é❡ ✫ ❈❡❞r✐❝✱ ❈◆❆▼ ❆✉❣✉st ✷✸r❞ ✷✵✶✵ ✶✴✷✹ ❉❡♠❡②❡r✱ ❋✐s❝❤❡r✱ ❙❛♣♦rt❛ ❇❛②❡s✐❛♥ ❛♣♣r♦❛❝❤ ♦❢ str✉❝t✉r❛❧ ❡q✉❛t✐♦♥ ♠♦❞❡❧s

■♥tr♦❞✉❝t✐♦♥ ▼♦❞❡❧❧✐♥❣ ■❞❡♥t✐✜❛❜✐❧✐t② ❊st✐♠❛t✐♦♥ ❆♣♣❧✐❝❛t✐♦♥ ❈♦♥❝❧✉s✐♦♥s ❛♥❞ ♣❡rs♣❡❝t✐✈❡s P▲❆◆ ✶ ■♥tr♦❞✉❝t✐♦♥ ✷ ▼♦❞❡❧❧✐♥❣ ✸ ■❞❡♥t✐✜❛❜✐❧✐t② ✹ ❊st✐♠❛t✐♦♥ ✺ ❆♣♣❧✐❝❛t✐♦♥ ✻ ❈♦♥❝❧✉s✐♦♥s ❛♥❞ ♣❡rs♣❡❝t✐✈❡s ✷✴✷✹ ❉❡♠❡②❡r✱ ❋✐s❝❤❡r✱ ❙❛♣♦rt❛ ❇❛②❡s✐❛♥ ❛♣♣r♦❛❝❤ ♦❢ str✉❝t✉r❛❧ ❡q✉❛t✐♦♥ ♠♦❞❡❧s

■♥tr♦❞✉❝t✐♦♥ ▼♦❞❡❧❧✐♥❣ ■❞❡♥t✐✜❛❜✐❧✐t② ❊st✐♠❛t✐♦♥ ❆♣♣❧✐❝❛t✐♦♥ ❈♦♥❝❧✉s✐♦♥s ❛♥❞ ♣❡rs♣❡❝t✐✈❡s ❊①❛♠♣❧❡ ❙✐t✉❛t✐♦♥ ❚❤❡ ♠❛r❦❡t✐♥❣ ❞❡♣❛rt♠❡♥t ♦❢ ❛ ❝♦♠♣❛♥② ♥❡❡❞s t♦ ✉♥❞❡rst❛♥❞ t❤❡ ❧♦②❛❧t② ♦❢ ✐ts ❝❧✐❡♥ts t♦ ✐♠♣r♦✈❡ ✐ts ♠❛r❦❡t✐♥❣ str❛t❡❣②✳ ❆ q✉❡st✐♦♥♥❛✐r❡ ✐s s❡♥t t♦ ❝❧✐❡♥ts✳ ❉✐r❡❝t q✉❡st✐♦♥ ✿ ✧❆r❡ ②♦✉ ❧♦②❛❧ t♦ ♦✉r ❝♦♠♣❛♥② ❄✧ ❨❊❙ ♦r ◆❖ ▼♦r❡ ✐♥❢♦r♠❛t✐✈❡ ✿ ✧❲♦✉❧❞ ②♦✉ r❡❝♦♠♠❡♥❞ ♦✉r ❝♦♠♣❛♥② t♦ ❛ ❢r✐❡♥❞ ❄✧ ❙❚❘❖◆●▲❨✲▼❆❨❇❊✲◆❖❚ ❆❚ ❆▲▲ ■♥❞✐r❡❝t q✉❡st✐♦♥ ✿ ✧❆r❡ ②♦✉ s❡♥s✐t✐✈❡ t♦ ♦✉r ❧❛t❡st ❛❞ ❄✧ ♦r ✧❆r❡ ②♦✉ s❛t✐s✜❡❞ ✇✐t❤ ♦✉r ♦♥✲❧✐♥❡ s❡r✈✐❝❡s ❄✧ ▲♦②❛❧t② ✐s ❝❧♦s❡❧② r❡❧❛t❡❞ t♦ s❛t✐s❢❛❝t✐♦♥ ❛♥❞ ✐♠❛❣❡ ✳ ✸✴✷✹ ❉❡♠❡②❡r✱ ❋✐s❝❤❡r✱ ❙❛♣♦rt❛ ❇❛②❡s✐❛♥ ❛♣♣r♦❛❝❤ ♦❢ str✉❝t✉r❛❧ ❡q✉❛t✐♦♥ ♠♦❞❡❧s

■♥tr♦❞✉❝t✐♦♥ ▼♦❞❡❧❧✐♥❣ ■❞❡♥t✐✜❛❜✐❧✐t② ❊st✐♠❛t✐♦♥ ❆♣♣❧✐❝❛t✐♦♥ ❈♦♥❝❧✉s✐♦♥s ❛♥❞ ♣❡rs♣❡❝t✐✈❡s ❙tr✉❝t✉r❛❧ ❊q✉❛t✐♦♥ ▼♦❞❡❧❧✐♥❣ ❆♥s✇❡r ❯♥❞❡rst❛♥❞✐♥❣ r❡❧❛t✐♦♥s ❜❡t✇❡❡♥ ❧♦②❛❧t② ✱ s❛t✐s❢❛❝t✐♦♥ ❛♥❞ ✐♠❛❣❡ r❡q✉✐r❡s ❙tr✉❝t✉r❡❧ ❊q✉❛t✐♦♥ ▼♦❞❡❧✐♥❣✳ ✹✴✷✹ ❉❡♠❡②❡r✱ ❋✐s❝❤❡r✱ ❙❛♣♦rt❛ ❇❛②❡s✐❛♥ ❛♣♣r♦❛❝❤ ♦❢ str✉❝t✉r❛❧ ❡q✉❛t✐♦♥ ♠♦❞❡❧s

■♥tr♦❞✉❝t✐♦♥ ▼♦❞❡❧❧✐♥❣ ■❞❡♥t✐✜❛❜✐❧✐t② ❊st✐♠❛t✐♦♥ ❆♣♣❧✐❝❛t✐♦♥ ❈♦♥❝❧✉s✐♦♥s ❛♥❞ ♣❡rs♣❡❝t✐✈❡s ❋❡❛t✉r❡s ♦❢ ❙tr✉❝t✉r❛❧ ❊q✉❛t✐♦♥ ▼♦❞❡❧s P✉r♣♦s❡ ❚♦ ❝❛♣t✉r❡ ❧❛t❡♥t ❝❛✉s❛❧✐t② ❧✐♥❦s ✐♥ ❞❛t❛ ❜❛s❡❞ ♦♥ ❡①♣❡rt ❦♥♦✇❧❡❞❣❡✳ ❋❡❛t✉r❡s ♠✉❧t✐✈❛r✐❛t❡ ♠♦❞❡❧s ❧❛t❡♥t ✈❛r✐❛❜❧❡ ♠♦❞❡❧s ❞✐✛❡r❡♥t t②♣❡s ♦❢ ♠❛♥✐❢❡st ✈❛r✐❛❜❧❡s ✿ ❝♦♥t✐♥✉♦✉s✱ ❜✐♥❛r② ❛♥❞ ♦r❞❡r❡❞ ❝❛t❡❣♦r✐❝❛❧ ✺✴✷✹ ❉❡♠❡②❡r✱ ❋✐s❝❤❡r✱ ❙❛♣♦rt❛ ❇❛②❡s✐❛♥ ❛♣♣r♦❛❝❤ ♦❢ str✉❝t✉r❛❧ ❡q✉❛t✐♦♥ ♠♦❞❡❧s

■♥tr♦❞✉❝t✐♦♥ ▼♦❞❡❧❧✐♥❣ ■❞❡♥t✐✜❛❜✐❧✐t② ▼♦❞❡❧❧✐♥❣ t❤❡ ❡①❛♠♣❧❡ ❊st✐♠❛t✐♦♥ ❙tr✉❝t✉r❛❧ ❡q✉❛t✐♦♥ ♠♦❞❡❧❧✐♥❣ ❆♣♣❧✐❝❛t✐♦♥ ❈♦♥❝❧✉s✐♦♥s ❛♥❞ ♣❡rs♣❡❝t✐✈❡s ▼♦❞❡❧❧✐♥❣ t❤❡ ❡①❛♠♣❧❡ ❊q✉❛t✐♦♥s ♦❢ t❤❡ ♦✉t❡r ♠♦❞❡❧ ❨ ✐ ✶ = θ ✶✶ η ✐ ✶ + ❊ ✐ ✶ ❨ ✐ ✷ = θ ✶✷ η ✐ ✶ + ❊ ✐ ✷ ❨ ✐ ✸ = θ ✷✸ η ✐ ✷ + ❊ ✐ ✸ ❨ ✐ ✹ = θ ✷✹ η ✐ ✷ + ❊ ✐ ✹ ❨ ✐ ✺ = θ ✸✺ ξ ✐ + ❊ ✐ ✺ ❨ ✐ ✻ = θ ✸✻ ξ ✐ + ❊ ✐ ✻ ❊q✉❛t✐♦♥s ♦❢ t❤❡ ✐♥♥❡r ♠♦❞❡❧ η ✐ ✶ = π ✶✷ η ✐ ✷ + λ ✶ ξ ✐ + δ ✐ ✶ η ✐ ✷ = λ ✷ ξ ✐ + δ ✐ ✷ ✻✴✷✹ ❉❡♠❡②❡r✱ ❋✐s❝❤❡r✱ ❙❛♣♦rt❛ ❇❛②❡s✐❛♥ ❛♣♣r♦❛❝❤ ♦❢ str✉❝t✉r❛❧ ❡q✉❛t✐♦♥ ♠♦❞❡❧s

■♥tr♦❞✉❝t✐♦♥ ▼♦❞❡❧❧✐♥❣ ■❞❡♥t✐✜❛❜✐❧✐t② ▼♦❞❡❧❧✐♥❣ t❤❡ ❡①❛♠♣❧❡ ❊st✐♠❛t✐♦♥ ❙tr✉❝t✉r❛❧ ❡q✉❛t✐♦♥ ♠♦❞❡❧❧✐♥❣ ❆♣♣❧✐❝❛t✐♦♥ ❈♦♥❝❧✉s✐♦♥s ❛♥❞ ♣❡rs♣❡❝t✐✈❡s ▼❛tr✐❝✐❛❧ ❡①♣r❡ss✐♦♥ ♦❢ t❤❡ ❡①❛♠♣❧❡ ❩ = ( η ✶ η ✷ ξ ) = ( ❍ Ξ)   ✵ ✵ ✵ ✵ θ ✶✶ θ ✶✷ θ = ✵ ✵ θ ✷✸ θ ✷✹ ✵ ✵   ✵ ✵ ✵ ✵ θ ✸✺ θ ✸✻   ✵ ✵ Λ = π ✶✷ ✵   λ ✶ λ ✷ ( ❨ ✐ ✶ . . . ❨ ✐ ✻ ) = ( ❩ ✐ ✶ . . . ❩ ✐ ✸ ) θ + ❊ ✐ ( ❍ ✐ ✶ ❍ ✐ ✷ ) = ( ❩ ✐ ✶ . . . ❩ ✐ ✸ ) Λ + δ ✐ ✼✴✷✹ ❉❡♠❡②❡r✱ ❋✐s❝❤❡r✱ ❙❛♣♦rt❛ ❇❛②❡s✐❛♥ ❛♣♣r♦❛❝❤ ♦❢ str✉❝t✉r❛❧ ❡q✉❛t✐♦♥ ♠♦❞❡❧s

■♥tr♦❞✉❝t✐♦♥ ▼♦❞❡❧❧✐♥❣ ■❞❡♥t✐✜❛❜✐❧✐t② ▼♦❞❡❧❧✐♥❣ t❤❡ ❡①❛♠♣❧❡ ❊st✐♠❛t✐♦♥ ❙tr✉❝t✉r❛❧ ❡q✉❛t✐♦♥ ♠♦❞❡❧❧✐♥❣ ❆♣♣❧✐❝❛t✐♦♥ ❈♦♥❝❧✉s✐♦♥s ❛♥❞ ♣❡rs♣❡❝t✐✈❡s ❙tr✉❝t✉r❛❧ ❊q✉❛t✐♦♥ ▼♦❞❡❧ ❖✉t❡r ♠♦❞❡❧ ✿ ❨ ✐ = ❩ ✐ θ + ❊ ✐ ■♥♥❡r ♠♦❞❡❧ ✿ s✐♠✉❧t❛♥❡♦✉s ❡q✉❛t✐♦♥ ♠♦❞❡❧ ❍ ✐ = ❩ ✐ Λ + ∆ ✐ Π t ✵ ❍ ✐ = Γ t Ξ ✐ + ∆ ✐ Π ✵ = ■❞ − Π ❍②♣♦t❤❡s❡s ❊ ✐ ∼ N ( ✵ , Σ ε ) , ∆ ✐ ∼ N ( ✵ , Σ δ ) ✱ Σ ε ❛♥❞ Σ δ ❛r❡ ❞✐❛❣♦♥❛❧✱ δ ✐ ❛♥❞ Ξ ✐ ❛r❡ ✐♥❞❡♣❡♥❞❛♥t✱ Ξ ✐ ✐s ❞✐str✐❜✉t❡❞ N ( ✵ , Φ) ✳ ✽✴✷✹ ❉❡♠❡②❡r✱ ❋✐s❝❤❡r✱ ❙❛♣♦rt❛ ❇❛②❡s✐❛♥ ❛♣♣r♦❛❝❤ ♦❢ str✉❝t✉r❛❧ ❡q✉❛t✐♦♥ ♠♦❞❡❧s

■♥tr♦❞✉❝t✐♦♥ ▼♦❞❡❧❧✐♥❣ ■❞❡♥t✐✜❛❜✐❧✐t② ▼♦❞❡❧❧✐♥❣ t❤❡ ❡①❛♠♣❧❡ ❊st✐♠❛t✐♦♥ ❙tr✉❝t✉r❛❧ ❡q✉❛t✐♦♥ ♠♦❞❡❧❧✐♥❣ ❆♣♣❧✐❝❛t✐♦♥ ❈♦♥❝❧✉s✐♦♥s ❛♥❞ ♣❡rs♣❡❝t✐✈❡s ❈♦✈❛r✐❛♥❝❡ ♠❛tr✐① ♦❢ ❧❛t❡♥t ✈❛r✐❛❜❧❡s ▲❡t Σ ❩ = ❝♦✈ ( ❩ ) ✳ ❚❤❡♥ Σ ❩ = Σ ❩ ( π ✶✷ , λ ✶ , λ ✷ , δ ✶ , δ ✷ , φ ) ✳ ❈♦✈❛r✐❛♥❝❡ ♠❛tr✐① ♦❢ ❧❛t❡♥t ✈❛r✐❛❜❧❡s ✐♥ t❤❡ ❡①❛♠♣❧❡ ❱❛r ( η ✶ ) = ( π ✶✷ λ ✷ + λ ✶ ) ✷ φ + ❱❛r ( δ ✶ ) + π ✷ ✶✷ ❱❛r ( δ ✷ ) ❱❛r ( η ✷ ) = λ ✷ ✷ φ + ❱❛r ( δ ✷ ) ❱❛r ( ξ ) = φ � � λ ✶ λ ✷ + π ✶✷ λ ✷ ❈♦✈ ( η ✶ , η ✷ ) = φ + π ✶✷ ❱❛r ( δ ✷ ) ✷ ❈♦✈ ( η ✶ , ξ ) = ( π ✶✷ λ ✷ + λ ✶ ) φ ❈♦✈ ( η ✷ , ξ ) = λ ✷ φ ❋♦r♠✉❧❛ ✐♥ t❡r♠s ♦❢ t❤❡ ✐♥♥❡r ♣❛r❛♠❡t❡rs ✵ ) − ✶ (Γ t ΦΓ + Σ δ ) Π − ✶ ✵ ) − ✶ Γ t Φ � � (Π t (Π t Σ ❩ = ✵ ΦΓΠ − ✶ Φ ✵ ✾✴✷✹ ❉❡♠❡②❡r✱ ❋✐s❝❤❡r✱ ❙❛♣♦rt❛ ❇❛②❡s✐❛♥ ❛♣♣r♦❛❝❤ ♦❢ str✉❝t✉r❛❧ ❡q✉❛t✐♦♥ ♠♦❞❡❧s