A method for processing a received, modulated pulse (i.e. waveform) that requires predictive deconvolution to resolve a scatterer from noise and other scatterers includes receiving a return signal; obtaining L+(2M-1)(N-1) samples y of the return signal, where y(l)={tilde over (x)}^T(l)s+v(l); applying RMMSE estimation to each successive N samples to obtain initial impulse response estimates [{circumflex over (x)}₁{-(M-1)(N-1)}, . . . , {circumflex over (x)}₁{-1}, {circumflex over (x)}₁{0}, . . . , {circumflex over (x)}₁{L-1}, {circumflex over (x)}₁{L}, . . . , {circumflex over (x)}₁{L-1+(M-1)(N-1)}]; computing power estimates {circumflex over ()}₁(l)=|{circumflex over (x)}₁(l)|² for l=-(M-1)(N-1), . . . , L-1+(M-1)(N-1); computing MMSE filters according to w(l)=(l)(C(l)+R)^-1s, where (l)=|x(l)|² is the power of x(l), and R=E[v(l)v^H(l)] is the noise covariance matrix; applying the MMSE filters to y to obtain [{circumflex over (x)}₂{-(M-2)(N-1)}, . . . , {circumflex over (x)}₂{-1}, {circumflex over (x)}₂{0}, . . . , {circumflex over (x)}₂{L-1}, {circumflex over (x)}₂{L}, . . . , {circumflex over (x)}₂{L-1+(M-2)(N-1)}]; and repeating (d)-(f) for subsequent reiterative stages until a desired length-L range window is reached, thereby resolving the scatterer from noise and other scatterers. The RMMSE predictive deconvolution approach provides high-fidelity impulse response estimation. The RMMSE estimator can reiteratively estimate the MMSE filter for each specific impulse response coefficient by mitigating the interference from neighboring coefficients that is a result of the temporal (i.e. spatial) extent of the transmitted waveform. The result is a robust estimator that adaptively eliminates the spatial ambiguities that occur when a fixed receiver filter is used.