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)}.sup.T(l) s+v(l); applying RMMSE estimation to each successive N samples to obtain initial impulse response estimates [{circumflex over (x)}.sub.1{-(M-1)(N-1)}, . . . , {circumflex over (x)}.sub.1{-1}, {circumflex over (x)}.sub.1 {0}, . . . , {circumflex over (x)}.sub.1{L-1}, . . . , {circumflex over (x)}.sub.1{L}, {circumflex over (x)}.sub.1{-1 +(M-1)(N-1)}]; computing power estimates {circumflex over (.rho.)}.sub.1(l)=|{circumflex over (x)}.sub.1(l)|.sup..alpha. for l=-(M-1)(N-1), . . . , L-1+(M-1)(N-1) and 0<.alpha..ltoreq.2; computing MMSE filters according to w(l)=.rho.(l) (C(l)+R).sup.-1s, where .rho.(l)=E[|x(l)|.sup..alpha.] is the power of x(l), for 0<.alpha..ltoreq.2, and R=E[v(l) v.sup.H(l)] is the noise covariance matrix; applying the MMSE filters to y to obtain [{circumflex over (x)}.sub.2{-(M-2)(N-1)}, . . . , {circumflex over (x)}.sub.2{-1}, {circumflex over (x)}.sub.2{0}, . . . , {circumflex over (x)}.sub.2{L-1}, {circumflex over (x)}.sub.2{L}, . . . , {circumflex over (x)}.sub.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.