DATA SNOOPING USING OBSERVATIONS AND 
PARAMETERS WITH CONSTRAINTS 
Dr. K. Jeyapalan, Professor of Civil Engineering 
Iowa State University 
Ames, Iowa 50011 
U.S.A 
Commission III 
Introduction 
Least squares methods are widely used in photogrammetric 
and geodetic computations. One problem in least squares methods 
is assigning a priori weights to different observations and 
parameters. Another is the detection of noises that are the 
size of the random errors. The author has developed a method 
of detecting noises and compensating for them in a recursive 
adjustment method. This method was successfully used in the 
detection of movement in an Electronic Distance Measurement 
Instrument (EDMI) calibration. This method has both photo- 
grammetric and geodetic applications. The objective of this 
paper is to present the theoretical account of this method. 
Theoretical Background 
  
The optimum estimate X of some value x will be defined 
as the value of x estimated if it minimizes the function 
E{(x - 237 Q(x - )9iz!i where x - X is a column matrix, 
sil. > ; ; : 
(x - x) is the transpose of x - X, Q is a symmetric, posi- 
; Ld ; T ai 
tive definitive matrix, and E{|z E denotes the conditional 
mean operator given the available data vector ze defined 
: th . ; 
at time t or at the t iteration. 
The optimal estimator, which is the conditional mean, is 
given by 
€ fx p(x/Z,)dx (1) 
Q t 
where 
Q 
space of all x 
p(x/Z,) - conditional probability density function of 
x given the data vector Z, 
Extending the function to include a functions in terms of 
a joint probability we will have 
x= [=p (x,a/Z, )dadx 
QA 
where À = space of all a. 
Now p(x,a/z,) = p(x/a,Z,) . p(a/24). Then