## MAP estimator: Laplacian error

Hello,

suppose we have N noisy versions of the parameter x. The (additive) noise is Laplacian distributed and the parameter x is known a priori to have a gaussian distribution. What is required is to estimate x given the N noisy measurements, using the MAP estimator.

Since the absolute function is non-differentiable it's approximated with a hyperbola. However, finding the (approximate) MAP solution requires evaluating the following finite series, first:

f(x) = sum { (y_k - x)/del * 1/sqrt(1+ ((y_k - x)/del)^2) } , k=1:N, (y_k is the k-th measurement).

Did any of the members here come across a similar problem?

Thanks.