TABLE OF CONTENTS In some applications the signal has to be estimated in the presence of a disturbance signal. Two approaches are discussed and compared.
The received signal vector z[ N, 1] is composed of a target signal and Gaussian noise. The original signal s[ M, 1], dependent on unknown parameters, is transformed by a known matrix C[ N, M] to the measurable target signal Cs and we have for the measured or received signal z:
We want an estimate for s. For a Gaussian distributed noise n with covariance matrix Q the probability density function according to equation 3.49 is:
Following the discussion in section 3.4 we look for the maximum of p dependent on s. That is, we have to minimise a = ( z ? Cs)* Q ?1( z ? Cs) by taking the derivative with respect to s:
or
and finally resolving for s:
? is the estimate of the signal vector s with maximum probability or a maximum-likelihood estimate.
The received and measured signal is again z = Cs + n. But now s is unknown with random components and the noise may be nonGaussian distributed. A linear estimate which minimises the mean-squared error for s shall be derived with a filter matrix W by:
By...
