By Jan Roskam
Moment Library reproduction. San Diego Air and area Museum.
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Moment Library reproduction- San Diego Air and area Museum
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Additional resources for Airplane flight dynamics and automatic flight controls
This function gives zero penalty if all the components of the estimation error are less than £, and penalty one in the opposite case (one component or more greater than e). t. 167) since an error occurs whenever one or more than one estimated component has an error greater than £. 168) and the first integral equals 1. 169) and to minimise the cost function it is necessary to choose p(6\z) as large as possible. 170) In practice, this estimator tends to maximise the a posteriori probability, and for this reason it is called the MAP estimator; it is also called the conditional mode estimator, because it leads to the maximum value of the PDF p(duc\z), that is the (conditional) mode.
221) Taking the logarithm of eqn. a, can be obtained putting equal to zero the power of the stochastic component of the useful signal in eqns. 218.
The estimate does not depend on the noise variance O2. 144) so that, as is intuitive, the precision of the estimate is improved as TV increases. Let us now find the CRLB for the stated problem. e. 1(0) = — E[L"(x\0)] is used. 145) So we have obtained the important result that this ML estimator is efficient, in the sense that it satisfies the CRLB with the equality sign. 4 Comments on the application of the maximum likelihood estimation with one example^ The examples of the application of ML estimation shown before lead to solutions in closed form, that is 0ML is expressed as a well-defined function of the observations.
Airplane flight dynamics and automatic flight controls by Jan Roskam