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. Nonlinear 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 leastsquares 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 leastsquares 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 nonestimable 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 nonestimable 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 ndimensional 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 pointvalues 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 pointvalues 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
