CE 597 Adjustment of Geospatial Observations Notes, Fall 2015

• matlab command summary
• solve 2x2 linear system of equations
• listing of matlab function
• tutorial on constrained minimization
• how a singular matrix produces small residuals (12-14)
• statistical tables from OLS
• listing of matlab code using symbolic tools
• multivariate normal distribution
• example showing scatter diagram, error ellipse, and error circle + code
• listing of words & phrases useful in discussing adjustment computations
• motivation for the sphere fit problem
• matlab code for an indirect observation problem
• matlab code for an observations only problem
• plot of sigma0_sqr_hat / sigma_0_sqr for different df
• example for confidence ellipse, confidence circle & code
• derive seq. LS from seq. formation of normal equations
• samples of exam 2 from prior years (topics & emphasis may differ)
• lecture 01: introduction, errors, residuals
• lecture 02: mathematical model, counting, weight, sigma nought
• lecture 03: sigma nought, global test, acc. & prec.,obj. func., line fit I/O
• lecture 04: finish line fit by ind. obs., start same prob. by obs. only
• lecture 05: scalar LS obs. only 2 ways, begin matrix derivation I/O
• lecture 06: derivation MATRIX LS for indirect observations
• lecture 07: steps for matrix I/O solution, derive matrix O/O
• lecture 08: derive 2D rotation matrix, also 3D
• lecture 09: small angle rotations, 2D coord. transformations
• lecture 10: review 4-par, level netw., nonlinear eqns & newton
• lecture 11: multivar. newton, num. example, LS in m/v newton framewk.
• lecture 12: I/O linearization, O/O linearization, convergence chk.
• lecture 13: discussion of HW1, example nonlinear I/O 2D range problem
• lecture 14: finish 2D range, alt. conv. test, 7-par linearization
• lecture 15: numerical example, observations only, nonlinear
• lecture 16: finish O/O example, numerical derivatives
• lecture 17: more weights, azimuth, angle obs., plane coords.
• lecture 18: linearization angle eqn., lg. networks, min. constr.
• lecture 19: min. constr., E.P., randn & rng - matlab functions
• lecture 20: comments on HW2, probability & statistics
• lecture 21: pdf,cdf,icdf,expect.,moments,cov. mx., EP
• lecture 22: HW4 hints, EP, SIGMA vs. Q, derive EP
• lecture 23: exam 1 review, EP corr/uncorr, ncc, EP 1 step
• lecture 24: discussion of HW3 and HW4
• session 25: exam I and solution
• lecture 26: EP 2 step, nonlinear EP example, EP I/O
• lecture 27: discuss exam 1, EP I/O Qdd, norm distr., MVN, chi2
• lecture 28: gamma func., z, t, F, pdf, cdf, icdf, global test
• lecture 29: test stat. limit r->inf., EP: y=Ax+By, 1,2-sided GT
• lecture 30: global test, outcomes & consequence, ident., conf. intvl.
• lecture 31: disc. HW6, conf. intvl. with t distr., 2D conf. regions
• lecture 32: derive 2D conf. region, eigenval., vect., conf. ellipse
• lecture 33: hw4 disc., hw6 hints, conf. regions, interpretation
• lecture 34: eval.,evect. by hand, conf. circle, Qlhlh, Qvv
• lecture 35: Qvv, Qlhlh I/O, O/O, GLS counting, line fit 3 meth.
• lecture 36: GLS, derive LS solution, full NE, elim., EP
• lecture 37: constraints, intro, objective function
• lecture 38: constr & O/O, derive LS for par. constr., N sing./nonsing.
• lecture 39: constr. w/N full rank & singular, seq. formation of NE
• lecture 40: seq. formation of NE, seq. LS, kalman filter
• lecture 41: seq. LS, intro. unified LS
• lecture 42: discuss HW7, review for exam 2
• lecture 43: disc. HW7, HW6, seq. form. NE, cond. no., ex. 2, red. no.