ON THE RELATION BETWEEN FILTER MAPS AND CORRECTION FACTORS IN LIKELIHOOD RATIOS

The robust form of the likelihood ratio for a signal in the presence o f white noise has an additional term in the exponent called the correc tion factor which corresponds to the trace of the conditional covarian ce of the signal given the observations. In this correspondence we sho w that this correction term is nothing but the trace of the symmetrize d Frechet derivative of the nonlinear filter map and hence the likelih ood ratio can be completely represented in terms of the observations a nd the filter map.