Research On Radar Coincidence Imaging With Model Mismatch

Radar coincidence imaging(RCI)is a novel staring/forward-looking imaging technique.By modulating the wavefront of transmissions and constructing a time-space independent radiation field,the target image can be reconstructed by coincidence processing between the reference matrix and the received signals.Generally,the reference matrix needs to be computed precisely,but several kinds of model errors will interfere the computing,cause model mismatch and degrade the imaging qualities accordingly.In this thesis,we mainly focus on the RCI with model mismatch.The effect of model mismatch to imaging is analyzed and imaging methods for RCI with model mismatch are proposed.This work can ensure the high-quality imaging results of RCI under the perturbations of several kinds of model errors,as well as benefiting the RCI in practical imaging conditions.In RCI,a precise model of the imaging process is required to calculate the reference signal.However,several kinds of model errors will cause model mismatch.In this paper,the signal expression of RCI with model errors are derived and by adopting a perturbation matrix to represent the effect of model errors to reference matrix,the imaging model of RCI with model mismatch are established.By utilizing the probability theory and random signal processing theory,the conclusion that the elements of perturbation matrix are independently and identically complex Gaussian distributed is drawn,which is validated by further numerical simulations.The constrained Cramér-Rao bound(CCRB)of imaging error is also obtained by theoretical derivation.Currently,most existing works of RCI are aiming at the simple point-sparse target and the existing methods possess high imaging performances which will unfortunately be degraded by model mismatch.In this paper,the model-mismatched problem of point-sparse target imaging is generalized into a sparse total least squares(S-TLS)problem.When the variance of the elements of perturbation matrix is known,by adopting the generalized Gaussian distribution to describe the sparse prior information of scatterers,the objective function of scattering coefficients is obtained based on its maximum a posterior estimation(MAP)and the TLS-FOCUSS algorithm is derived.When the variance of the elements of perturbation matrix is unknown,after regarding the perturbation matrix as an unknown variable,the regularized objective function is obtained based on the MAP of scattering coefficients and perturbation matrix.And after proposing a norm-ratio method to determine suitable regularization parameters,the regularization-FOCUSS(R-FOCUSS)algorithm is derived.Furthermore,the matrix uncertainty-sparse Bayesian learning(MU-SBL)algorithm is derived by using the SBL framework to update the mean values of scattering coefficients,the variance of scattering coefficients and the variance of perturbation matrix iteratively where the scattering coefficients are modeled by Gaussian distribution and its variance could be obtained by expectation maximization(EM)algorithm.The validities of the proposed algorithms are verified and their performances in different system parameters and imaging conditions are analyzed by numerical simulations.In RCI,the imaging area is meshed into grids during imaging process.The scatters of actual target may be blocky rather than disperse distributed in the grids.Hence,this kind of target belongs to block-sparse target.Aiming at the RCI with model mismatch for block-sparse target,the sparseness is defined to evaluate the sparsities of different target and the effects of block-sparse target to conventional sparse reconstruction method are analyzed.Based on the edge-preserving quality of total variation(TV)regularization,the objective function of RCI with model mismatch for block-sparse target is obtained by using TV regularization as the constraint item.And the TV-TLS algorithm is derived based on the augmented Lagrangian multiplier method and alternating direction method.Results of numerical experiments demonstrate that,for uniform block-sparse target,point-sparse target and complex block-sparse target,the TV-TLS algorithm can achieve preferable imaging performance in both suppressing noise and adapting to model mismatch.And the performances of TV-TLS in different system parameters and imaging conditions are also analyzed.Finally,the main contents of this thesis are summarized and some key points about RCI that need to be investigated further are discussed.