Studies On Several Mathematical Problems Of SAR

Studies Oll several mathematical problems of SARIn this paper,several mathematical problems about SAR aJ'e discussed In the firstthree chapters,the one dimensional and three dimensional models axe introduced,and atthe end of Chapter 2,a numerical experiment is implemented In Chapter 4,w-e discusserror estimate on the matched filter,which is of great importance in radar imaging Themain w-ork is completed in space H。(R)In Chapter 5,w-e discuss the inverse problemabout matched filter,which iS to W'Ork out the"best"w-aveforln in some senseAs is seen above,matched filter is implemented in both one dimensional and threedimensional modelsDenote the received signal bywhere s(t)is the w-aveform,n(t)the noise Our aim is for the distribution p(f)We apply a filter to Srec(f)in order to improve the signal-to-nose ration(SNR)Wedenote the filter'S convolution kernel by h(t),and write for the filter outputwhereTomaximizethewe get Theorem 1．The quotient(3)is maximized when h is chosen as h(t)=s(一t)for sighalSrec(f)as(1)Witll this choice,the filter(3)can be writtenWaveform CW pulse and chirp aJ'e widely used in engineering,the main resultsare asfollows:Theorem 3．The autocorrelation ofnormalized CWpulse isx(t)and Using Hermite polynomials we can solve the problem in finite subspacesspanEventually it is transformed into a nonlinear programming problem:Find a= such thatNonlinear programming problem:(7),(8)can be reduced to the problem of In this process,we use the dichotomy to the implementation the^,and the problemis transformed into solving a linear algebraic equations Numerical experiments showthe algorithm is effectiveInthe end,we getBy using Cosine Fourier inversion formula,we cangetwaveform SnIn addition,we discuss a special cases:Letandwe can get...