Estimation of the Average Density of a Nonuniform Poisson Process

The average densitylambda (t)of a Poisson process is estimated by a nonstationary shot noise processs(t). The processs(t)is generated by a time-varying system whose impulse responseh (t, alpha)is so determined as to minimize the mean-square (ms) estimation error. It is shown that, under realistic assumptions,h (t, alpha )is a truncated parabola in the variable α . The analysis is extended to two-dimensional processes. The resulting smoothing kernel is an elliptic paraboloid.