To achieve required system performance under difficult propagation and reverbaration conditions, signal processing systems must be environmentally adaptive. This paper uses results from statistical signal processing and wavelet transform theory to develop an estimator-correlator (EC) approach to environmental adaptivity. The EC is an optimum (in the maximum likelihood sense) detector and estimator that incorporates propagation and interference (reverberation and ambient noise) models as an essential part of its formulation. It is a doubly adaptive processor because it uses propagation models and on-line adaptation to determine conditional mean estimates of the full-field replicas that it correlates with optimally/adaptively filtered received data. The EC concept is applicable to both active and passive sonar. This paper concentrates on wavelet transform domain implementation of active EC that achieves recombination of multipath and multihighlight signals. This paper reviews the underlying wavelet transform concepts, basic EC theory and medium characterization by wideband spreading and scattering functions. Some computer simulation results are presented. [This work was supported by ONR under Grant No. N000149510965, Code ONR 313.]