1、第第1414讲讲 条件平差的精度评定条件平差的精度评定主讲人：刘春阁主讲人：刘春阁v 提纲：v 一、单位权中误差的计算v 二、平差值函数的中误差v 三、非线性函数的权倒数一、一、0TpvvV PVntr2221 122TnnV PVpvvp vp vp v1()iiaibiriva kbkrkp一、一、aabbrrpvvw kw kw k 1 12 21 12 21 12 2000an nan nbbn nrravwav avavwbv bvbvwbvwrv rvrvwrvw 11111222221()1()1()abrabrnn an bn rnabrvakbkrkpva kbkrkpva
2、kbkrkppvvav kbv krv k一、一、1()TTTTTTTV PVV PPA KV A KAVKW K 110TTTTaaAVWVP A KQA KNAP AAQATT1T1TT11T1V PVA KA KK AA KTTTaaPP PPPPKAPAKK NK二、二、设平差值线性函数的一般形式112200nniiFf Lf Lf LffLf其中，为平差值的系数，为不包含误差的常数项将F化为独立观测值的函数，上式代入iiiLLv0TTFf Lf Vf1212,TTnnffffLL LL12nvvVv 二、二、1TTVPA KQA K0TTFfLf Vf10TTTFf Lf P A K
3、f1aaKN W 0WALA110TTTaaFf Lf P A N Wf1100()TTTaaFfLfPANA LAf二、二、10aaNqAPf1111001111001111111 1()TTTTTaaaaTTTTTaaaan nn rrnn nn rnnnr rr rrFfLfPA NALfPA NAfffPA NA LfPA NAf1111TTTaaaaqf P A NN AP f二、二、1111001111TTTTTaaaaTTTaaaaFfLfPA NALfPA NAfqfPA NNAPf 0000()()TTTTTTFfq A Lq AffA qLq Af111111()()()(
4、)TTTTTTFFLLFTTTTTTQfA qQfA qfA qPfA qPf Pff PA qq APfq APA q111()TTFf P fAP fqP二、二、220iip202FFp01FFP二、二、ABh1h4h2h3Ch5D二、二、123145011100100110hhhAhhhABh1h4h2h3Ch5D30 0 1 0 0TDAFHHhf11iiiiiCpSSkmSpC1令，则 1(42442)QPdiag二、二、14112101 110010441010011410401401TaaNAP A14020111004411001104040APf 二、二、1104400410
5、00aaabqN qAPfq 即40200.47610010041402.100.1904040DHP 0.4760.190abqq三、三、对上式求全微分得：),(21nLLLfF1212nnL LL LL LfffdFdLdLdLLLL1212,TnnL LL LL LfffffffLLL三、三、TFFLLQf Qf12112212,nnnnTdLdLdFf dLf dLf dLfffdLdFf dL即 三、三、1101100TTTTaar raar raar rLL VLL QA KVP A KQA KLL QANAL AKN WKNAL AWAL A110TTaaaaLLEQA N A
6、LQA N A将 展开，合并同类项得：三、三、11 1111111112TTTaaLLaaLLTTaaaaTTTTaaaaaaaaTTTaaaaaaQEQA NA QEQA NAEQA NA Q EA NAQQQA NAQQA NAQQA NAQA NAQQQA NAQQA NAQQQA NAQ三、三、111TTFFaaTTTaaTTaaQfQQA NAQffQffQA NAQffQfAQfNAQf111(A)TTFfPfPfqP111=aaaaqN AP fN AQf又 三、三、04.8CD1456B23A12345645 30 46,67 22 1067 07 14,69 031452 3
7、2 22,58 24 18LLLLLL三、三、12345618001110000001111800LLLALLLCD1456B23A1435sinsinsinsinCDABLLSSLL4513sinsinsinsinCDBDBDABLSSLLSSL三、三、114433551345dFcotcotcotcot0.980.420.380.77CDCDdSL dLL dLL dLL dLSdLdLdLdL1411144435135433551414353355sinsincossinsincossinsinsinsinsinsincoscossinsinsinsinsinsinsinsinsinsi
8、nCDABABABABLLL dLLLL dLdSSSLLLLLLL dLL dLLLLLSSLLLLLL35141435cotLcotLcotLcotLCDCDCDCDCDdLdLdLdLdSSSSS 即 三、三、1010111000103000011101030101TTaaNAQAAAPQE0.9800.420.380.770Tf 三、三、10.9801110000.420.560001110.380.390.770APfAf300.560030.390abqq 0.190.13abqq 三、三、1111(A)(A)TTTTFf P fP fqf fP fqP0.9800.420.1910.9800.420.380.7700.560.39=1.710.380.130.770FP6.28120626533000CDSFCDSdFCDCDdSS014.8 1.716.28FFPv谢 谢！
