Athanasios Dermanis

Adjustment of Observations and Estimation Theory, Volume 2

Editions Ziti, Thessaloniki, 1987 (in Greek)


 
CONTENTS
 
7. The method of observation equations
1. The problem of parameter estimation and the adjustment of the observations - 2. The observation equations - 3. Linearization of the Observation equations - 4. The Method of Least Squares - 5. The stochastic model of observation equations - 6. Unbiased linear estimation of minimum variance - 7. Determination of the reference variance - 8. Estimation with the maximum likelihood method - 9. Non-linear least squares and successive approximations
 
8. Special cases of observation equations
1. Addition of normal equations - 2. Observation equations with prior estimates of the parameters - 3. Observation equations with parameter constraints - 4. Intermediate quantities, synthetic observations and repeated measurements - 5. Sequential adjustment and the Kalman form - 6. Biased estimation
 
9. The method of condition equations
1. The condition equations - 2. Linearization of the condition equations - 3. Application of the least-squares method - 4. The stochastic model of condition equations - 5. Determination of the reference variance - 6. Relation between condition and observation equations - 7. Condition equations with random parameters
 
10. The method of mixed equations
1. Mixed observation and condition equations - 2. Application of the least-squares method - 3. The stochastic model of condition equations - 4. Mixed equations with constraints - 5. Mixed equations with prior estimates of the parameters - 6. Mixed equations with random parameters
 
11. Adjustment with non estimable parameters
1. Identifiable and estimable quantities in observation equations without full rank - 2. General characteristics of adjustment with non-estimable parameters - 3. Adjustment with minimal constraints - 4. Adjustment with inner constraints - 5. Adjustment with essential constraints - 6. Mixed equations without full rank
 
12. Comparison and Unification of the adjustment methods
1. General aspects - 2. Relation of the adjustment problem with the underlying physical problem - 3. Adjustment with independent estimable parameters - 4. Adjustment with dependent estimable parameters - 5. Adjustment with non-estimable parameters - 6. Reduction of all adjustment methods to a common model
 
13. Best Unbiased linear estimation
1. General aspects - 2. The adjustment methods as derived from the application of Best Unbiased Linear Estimation - 3. Best unbiased estimation - 4. Best unbiased estimation of the reference variance - 5. Biased estimation
 
14. Statistical inference and evaluation of adjustment results
1. General aspects - 2. The distributions of the estimates of the unknown parameters, of the errors and of the reference variance - 3. The General hypothesis q = Hx = z - 4. Special cases of the general hypothesis - 5. Confidence intervals and regions - 6. Statistical hypothesis testing for the other adjustment methods - 7. Statistical hypothesis testing for observation equations without full rank - 8. Statistical hypothesis testing and confidence intervals for the reference variance - 9. Statistical hypothesis testing and confidence intervals when the covariance matrix of the observations is completely known - 10. Testing for blunders and systematic errors
 
15. The geometric interpretation of the adjustment
1. The geometry of n-dimensional linear space - 2. Best approximation - 3. Observation and condition equations - 4. Observation equations with constraints - 5. Observation equations without full rank - 6. The adjustment with generalized inverses
 
16. Least squares interpolation
1. General characteristics of the interpolation problem - 2. Smoothing least squares interpolation - 3. Exact minimum norm interpolation - 4. Hybrid interpolation and interpolation with trend removal - 5. Interpolation with infinite number of base functions
 
17. Prediction and adjustment with stochastic parameters
1. Minimum Mean Square Error prediction - 2. Best linear inhomogeneous prediction - 3. Best linear inhomogeneous prediction - 4. Best prediction for normally distributed random variables - 5. Stochastic processes - 6. Prediction of point-values of a stochastic process -7. The norm choice problem - 8. Stationary, homogeneous, isotropic and ergodic stochastic processes - 9. Interpolation with minimum mean square error - 10. Prediction of point-values of a stochastic process from noisy observations - 11. Prediction with continuous observations - 12. Prediction with unknown parameters - 13. Adjustment with stochastic parameters

 
          Appendix A. Minimal constraints
Appendix B. Summary of observation adjustment and parameter estimation methods
 
References
Index