CE 597 Adjustment of Geospatial Observations Notes, Fall 2013

• matlab command summary
• solve 2x2 linear system of equations
• listing of matlab function
• tutorial on constrained minimization
• scatter plot, conf. ellipse, conf. circle
• how a singular matrix produces small residuals (12-14)
• statistical tables from OLS
• lecture 01 intro, course mechanics, errors, math model, redundancy
• lecture 02 counting, observation, residual, std. dev., weight, ref. var.
• lecture 03 manual LS, IO, line fit, 1D netw, angle figure
• lecture_04 linear dep., indep., constr. min., Lagr. Mult., OO
• lecture 05 O/O scalar LS, level netw., curve fit
• lecture 06 diff. wrt vect., derive mat LS I/O, ex, wts
• lecture 07 wts, regr. O/O, mat LS O/O, summary mat LS
• lecture 08 coord. tranf., rot. mat. 2D&3D, orth. mat.
• lecture 09 rot. mat., 2D coord. tranf., L&NL, affine, 3D c.t.
• lecture 10 L vs NL, newton iter., overview
• lecture 11 NL I/O & O/O, range eqn.
• lecture 12 2D range prob., convergence alg., NL debug, NL O/O
• lecture 13 deriv. num. apprx., wts & units, lin. azm, ang, range
• lecture 14 minimal constraints
• lecture 15 prob. density func., expectation, var, cov, corr., RV, EP
• lecture 16 EP 1,2-step, Qdd for I/O, prob. distr., N, MVN, X2
• exam 1 (session 17) and solution
• lecture 18 prob. distr. M,MVN,t,Chi2,F,z Qvv,Qlhlh
• lecture 19 global test, 1,2-sided, EP, conf. interval
• lecture 20 c.i., EP after GT, conf. region, v^TWv ~ Chi2_r
• lecture 21 conf. ell, eig. val. for 2x2, theta, chi^2,F, plotting, GLS
• lecture 22 GLS, counting
• lecture 23 GLS exmpl, circle, 7-par,linearize, sm angle rotation mx
• lecture 24 conf. circle, parameter constraints
• lecture 25 constr eqns, by determinant, solve LSE elimination, general
• lecture 26 solve LSE N full rank & not, added par, seq. LS, summations
• lecture 27 inversion by part, SMWS inv. lemma, seq LS, rows & cols, KF
• lecture 28 KF, conventional notation, STM navigation, unified LS
• lecture 29 ULS, l/nl, redundancy num., blunder det., IRLS, DS, L1
• listing of matlab code using symbolic tools
• example showing scatter diagram, error ellipse, and error circle + code