TRUNCATED ESTIMATION 
Kurt Kubik 
Anton Schenk r 
Department of Geodetic Science and Surveying 
Ohio State University 
1958 Neil Avenue 
Columbus, Ohio 43220 
1. INTRODUCTION 
In this paper, we formulate the method of truncated estimation and relate it 
to other well-known estimation methods. We show that truncated estimation 
may be regarded as robust Maximum Likelihood Method, also yielding a 
theoretical foundation for the Danish Method of estimation. 
2. CLASSICAL TRUNCATED ESTIMATION 
Classical truncated estimation is only applied to mean estimation: Consider 
a sample of (uncorrelated and equally accurate) measurements Z;. In order 
to estimate their mean, the «X largest and smallest measurements are 
rejected and the arithmetic mean is computed from the remaining (l-«)% 
measurements. For the case of Z, =: N(E(Z), e), the estimator has =a 
variance, which is a% larger than the minimal attainable variance. In the 
presence of outlyer in the measurements, the estimator is by far superior 
to the least squares estimator (Andrews et al, 1972). In the following 
sections, we generalize this idea to the least squares adjustment problem. 
3. THEORETICAL FOUNDATION OF THE METHOD 
Consider the model: 
EZ) - B . u 
B coefficient matrix’ 
u vector of unknown coefficients 
E(Z) expectation of Z 
and a set of uncorrelated measurements Z, for E(Z), possibly containing 
outliers. We assume a truncated normal distribution: 
^ 
m 
c. exp ( - gl, (X-E(x))T (X-E(x))} for (X - EGO) 
Na(x) = 
(1) 
0 
with P (IX -EB(x)) « 2) 21-4«- 
else 
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