測量誤差の処理法目第１章

次

観測の誤差 ········································································ 7

１･１ 観測の種類 ······································································· 7
１． 独立観測 ····································································· 7２.

条件つき観測 ································································· 7３． 直接観測 ····································································· 8４.

間接観測 ····································································· 8１･２ 誤差の種類 ······································································· 9１． 定 誤 差 ····································································· 9２.

不定誤差 ···································································· 12１･３ 定誤差を取り除く方法 ···························································· 12１． 個人的定誤差を取り除く方法 ·················································· 12２． 器械的定誤差を取り除く方法 ·················································· 13３． 物理的定誤差を取り除く方法 ·················································· 15

１･４ 過失とその防止注意 ······························································ 17
１． 過失の起りやすい例 ·························································· 17２.

過失を防ぐ注意 ······························································ 17

例題 ·········································································· 18

第１章の問題 ····································································· 25

第２章

誤差の確率 ······································································· 29

２･１ 誤差の現われかた ································································ 29
１． アメリカ兵器局の実験例 ······················································ 29
２.

日本の三角測量に現われた誤差 ················································ 31

３． 数学的に現われる誤差の分布状態 ·············································· 35

２･２ 確率曲線（誤差曲線）の外観 ······················································ 38
１． 精度と誤差で表わす確率式 ···················································· 38
２.

２つの確率式の精度の比較 ···················································· 38

３． 最小二乗法の原理 ···························································· 40

1第３章

独立観測の最確値とその精度 ···················································· 42

３･１ 真値と最確値はどう違うか ························································ 42
１． 真値の意味 ·································································· 42
２.

最確値の意味 ································································ 42

３． 真誤差，残差および補正値の意味 ·············································· 42

３･２ 観測値の重量（重み・軽重） ······················································ 43
３･３ 最確値の求めかた ································································ 46
１． 算術平均値の求めかた ························································ 46２.

重量平均値の求めかた ························································ 48

３･４ 独立観測値の精度の表わしかた···················································· 51
１． 真誤差で表わす３種の誤差 ···················································· 51
２.

残差で表わす１観測値の誤差 ·················································· 55

３． 残差で表わす最確値の誤差 ···················································· 59
例

題 ·········································································· 61

第３章の問題 ····································································· 70

第４章

誤差および重量の拡張 ··························································· 74

４･１ 誤差拡張に必要な予備知識 ························································ 74
１． 三角関数の定め ······························································ 74
２.

微分法とその予備知識 ························································ 76

３． 本書に用いる主な数学公式 ···················································· 86

４･２ 誤差の拡張 ······································································ 90
１． 誤差の拡張の意味 ···························································· 90
２.

四則算の基本式 ······························································ 91

３． 誤差拡張の一般式 ···························································· 97

４･３ 重量の拡張 ····································································· 100
例題 ········································································· 102

第４章の問題 ···································································· 121

第５章

独立間接観測の処理法 ·························································· 125

５･１ １つの未知量の求めかた ························································· 125
５･２ ２つの未知量の求めかた ························································· 128
１． 一般形式による解法 ························································· 131２.

標準方程式の解きかたとその点検 ············································· 135

３． 計算上の点検式の証明 ······················································· 135

2５･３ 最確値ｘ,ｙの精度の求めかた ··················································· 139
１． 最確値ｘ,ｙの重量の求めかた ················································· 139
２.

１観測の平均二乗誤差（標準誤差）の求めかた ································· 142

５･４ 未知量Ｘ，Ｙが特別な形の場合の処理法 ·········································· 145
１． 未知量の数値が大きな場合 ··················································· 145
２.

未知量Ｘ，Ｙの形が１次形でない場合 ········································· 146

例

題 ········································································· 149

第５章の問題 ···································································· 156

第６章

条件つき観測の処理法 ·························································· 158

６･１ 条件方程式の作りかた ··························································· 158
１． 直接観測による場合の例 ····················································· 158２.

間接観測による場合の例 ····················································· 164

６･２ １つの条件方程式の解きかた ····················································· 175
１． 直接観測による場合の例 ····················································· 175
２.

間接観測による場合の例 ····················································· 180

６･３ ２つ以上の条件方程式の解きかた ················································ 182
１． ３つの条件方程式の一般解法 ················································· 182
２.

補正された最確値の精度の求めかた ··········································· 185

６･４ 条件式の個数の決めかた ························································· 191
１． 三角網（鎖）の整正に必要な条件式の個数 ····································· 191
２.

多角網の整正に必要な条件式の個数 ··········································· 195

３.

水準網の整正に必要な条件式の個数 ··········································· 196

例題 ········································································· 198

第６章の問題 ···································································· 214

付録 ················································································· 217
第１章の問題のヒント ···························································· 217
第３章の問題のヒント ···························································· 218
第４章の問題のヒント ···························································· 218
第５章の問題のヒント ···························································· 219
第６章の問題のヒント ···························································· 219

ギリシヤ文字の読みかた ·························································· 2203