<title>Estimation of time-varying range-direction target density functions in nonstationary environments</title>

Abstract

Two different solutions are given to the problem of estimation of time-varying target density functions in arbitrary nonstationary environments via use of one transmitted signal and a distributed sensor (or an array of point sensors). The first one utilizes a wideband signal with a certain bandlimitedness condition on the time variation of the target density function at each point in space. By choosing small successive processing time intervals, bandlimitedness of the time-variation becomes much more realistic than assuming no time-variation or a specific time-variation. The second one does not have this assumption and utilizes a narrowband signal with a continuous spectral content. These provide a general methodology for imaging of nonstationary environments. In addition to nonstationarity, time-varying density functions can also describe nonlinearity of a medium where each point distorts the transmitted wave by multiplying it with a time-varying function during reflection.