\contentsline {chapter}{\numberline {第1章}序論}{1}{chapter.1}
\contentsline {section}{\numberline {1.1}はじめに}{1}{section.1.1}
\contentsline {section}{\numberline {1.2}仕様および検討}{2}{section.1.2}
\contentsline {section}{\numberline {1.3}INS/GPS}{5}{section.1.3}
\contentsline {chapter}{\numberline {第2章}Kalman Filter}{6}{chapter.2}
\contentsline {section}{\numberline {2.1}最小二乗法}{6}{section.2.1}
\contentsline {section}{\numberline {2.2}重み付き最小二乗法}{8}{section.2.2}
\contentsline {section}{\numberline {2.3}再帰的重み付き最小二乗法}{9}{section.2.3}
\contentsline {section}{\numberline {2.4}離散系 Kalman Filter}{10}{section.2.4}
\contentsline {section}{\numberline {2.5}離散系 Kalman Filterの連続系への適用}{13}{section.2.5}
\contentsline {section}{\numberline {2.6}UD分解 Kalman Filter}{13}{section.2.6}
\contentsline {subsection}{\numberline {2.6.1}UD分解}{13}{subsection.2.6.1}
\contentsline {chapter}{\numberline {第3章}System Design}{14}{chapter.3}
\contentsline {section}{\numberline {3.1}運動方程式}{14}{section.3.1}
\contentsline {subsection}{\numberline {3.1.1}速度の運動方程式}{14}{subsection.3.1.1}
\contentsline {subsection}{\numberline {3.1.2}位置の運動方程式}{19}{subsection.3.1.2}
\contentsline {subsection}{\numberline {3.1.3}姿勢の運動方程式}{19}{subsection.3.1.3}
\contentsline {section}{\numberline {3.2}運動方程式の線形化}{20}{section.3.2}
\contentsline {subsection}{\numberline {3.2.1}速度の運動方程式の線形化}{20}{subsection.3.2.1}
\contentsline {subsection}{\numberline {3.2.2}位置の運動方程式の線形化}{22}{subsection.3.2.2}
\contentsline {subsection}{\numberline {3.2.3}姿勢の運動方程式の線形化}{22}{subsection.3.2.3}
\contentsline {subsection}{\numberline {3.2.4}線形化された運動方程式}{23}{subsection.3.2.4}
\contentsline {section}{\numberline {3.3}観測方程式}{26}{section.3.3}
\contentsline {section}{\numberline {3.4}INS/GPS アルゴリズム}{27}{section.3.4}
\contentsline {subsection}{\numberline {3.4.1}Initialize状態}{27}{subsection.3.4.1}
\contentsline {subsection}{\numberline {3.4.2}Flight状態:Update時}{27}{subsection.3.4.2}
\contentsline {subsection}{\numberline {3.4.3}Flight状態:Correct時}{28}{subsection.3.4.3}
\contentsline {chapter}{\numberline {第4章}数値シミュレーション}{30}{chapter.4}
\contentsline {section}{\numberline {4.1}方法}{30}{section.4.1}
\contentsline {subsection}{\numberline {4.1.1}慣性センサモデル1: 単純なホワイトノイズのみの場合}{31}{subsection.4.1.1}
\contentsline {subsection}{\numberline {4.1.2}慣性センサモデル2: ジャイロのランダムドリフトまで考慮した場合}{32}{subsection.4.1.2}
\contentsline {section}{\numberline {4.2}結果}{33}{section.4.2}
\contentsline {subsection}{\numberline {4.2.1}位置履歴}{35}{subsection.4.2.1}
\contentsline {subsection}{\numberline {4.2.2}速度履歴}{35}{subsection.4.2.2}
\contentsline {subsection}{\numberline {4.2.3}姿勢履歴}{38}{subsection.4.2.3}
\contentsline {section}{\numberline {4.3}考察}{38}{section.4.3}
\contentsline {subsection}{\numberline {4.3.1}センサモデルについて}{38}{subsection.4.3.1}
\contentsline {subsection}{\numberline {4.3.2}収束性について}{40}{subsection.4.3.2}
\contentsline {chapter}{\numberline {第5章}実機試験}{42}{chapter.5}
\contentsline {section}{\numberline {5.1}機材}{42}{section.5.1}
\contentsline {section}{\numberline {5.2}方法}{42}{section.5.2}
\contentsline {section}{\numberline {5.3}結果}{42}{section.5.3}
\contentsline {chapter}{\numberline {第6章}まとめ}{43}{chapter.6}
\contentsline {chapter}{\numberline {付録A}Quaternion Algebra}{44}{appendix.A}
\contentsline {section}{\numberline {A.1}Quaternionの定義}{45}{section.A.1}
\contentsline {section}{\numberline {A.2}共役Quaternionの定義}{45}{section.A.2}
\contentsline {section}{\numberline {A.3}Quaternionのスカラー積}{46}{section.A.3}
\contentsline {section}{\numberline {A.4}Quaternion間の加算}{46}{section.A.4}
\contentsline {section}{\numberline {A.5}Quaternion間の乗算}{46}{section.A.5}
\contentsline {section}{\numberline {A.6}Quaternionによる3次元ベクトルの回転}{47}{section.A.6}
\contentsline {section}{\numberline {A.7}Quaternionによる回転の合成}{49}{section.A.7}
\contentsline {section}{\numberline {A.8}Quaternionの時間微分}{50}{section.A.8}
\contentsline {section}{\numberline {A.9}回転QuaternionとDirection Cosine Matrixの関係}{50}{section.A.9}
\contentsline {chapter}{\numberline {付録B}Coordinate Systems}{51}{appendix.B}
\contentsline {section}{\numberline {B.1}Earth-Centered Inertial Frame (\textit {i-Frame})}{51}{section.B.1}
\contentsline {section}{\numberline {B.2}Earth-Centered, Earth-Fixed Frame (\textit {e-Frame})}{51}{section.B.2}
\contentsline {section}{\numberline {B.3}Local Geodetic Frame (\textit {g-Frame})}{51}{section.B.3}
\contentsline {section}{\numberline {B.4}Navigation Frame (Wander Azimuth Frame) (\textit {n-Frame})}{52}{section.B.4}
\contentsline {section}{\numberline {B.5}Body Frame (\textit {b-Frame})}{52}{section.B.5}
\contentsline {section}{\numberline {B.6}座標変換の表記}{53}{section.B.6}
\contentsline {section}{\numberline {B.7}\textit {i-Frame}と\textit {e-Frame}の関係}{54}{section.B.7}
\contentsline {section}{\numberline {B.8}\textit {e-Frame}と\textit {g-Frame}の関係}{54}{section.B.8}
\contentsline {section}{\numberline {B.9}\textit {g-Frame}と\textit {n-Frame}の関係}{55}{section.B.9}
\contentsline {section}{\numberline {B.10}\textit {e-Frame}と\textit {n-Frame}の関係}{56}{section.B.10}
\contentsline {section}{\numberline {B.11}\textit {n-Frame}と\textit {b-Frame}の関係}{58}{section.B.11}
\contentsline {chapter}{\numberline {付録C}Earth Model(WGS-84)}{59}{appendix.C}
\contentsline {section}{\numberline {C.1}楕円モデル}{59}{section.C.1}
\contentsline {section}{\numberline {C.2}南北方向ならびに東西方向の曲率半径}{60}{section.C.2}
\contentsline {section}{\numberline {C.3}重力}{61}{section.C.3}
\contentsline {section}{\numberline {C.4}WGS-84}{61}{section.C.4}
\contentsline {chapter}{\numberline {付録D}Allan Variance}{63}{appendix.D}
\contentsline {section}{\numberline {D.1}Allan Variance}{63}{section.D.1}
\contentsline {chapter}{\numberline {付録E}ソースコード}{64}{appendix.E}
\contentsline {chapter}{\numberline {付録F}実機試験基板}{65}{appendix.F}
\contentsline {section}{\numberline {F.1}回路図}{65}{section.F.1}
\contentsline {section}{\numberline {F.2}ガーバ}{65}{section.F.2}
\contentsline {section}{\numberline {F.3}参考文献}{65}{section.F.3}
\contentsline {chapter}{参考文献}{66}{appendix*.8}