Research On Compressed Sensing ISAR Imaging Based On Kalman Filter

Traditional Inverse Synthetic Aperture Radar?ISAR?imaging uses matching filtering technique..In recent years,ISAR imaging based on Compressive Sensing?CS?has become a research issue.CS ISAR imaging method can reconstruct ISAR image with high contrast image and less sidelobe interference by using a small amount of under-sampled data or incomplete echo data.Kalman Filter?KF?can effectively use the prior information of the signal to obtain good estimation and is not susceptible to noise interference.This paper combines KF with CS ISAR imaging to study CS ISAR imaging method under KF framework.The quality of ISAR imaging can be improved by the excellent estimation performance of KF.Firstly,the CS ISAR imaging algorithm based on direct KF is proposed.Under the assumption that the space of ISAR target scene is sparse,ISAR imaging can be constructed as a convex optimization problem with sparse constraints.In the framework of KF filtering,the Pseudo Measurement?PM?technique is introduced.The l₁ norm of the scattering rate of the target scene to be reconstructed is introduced into image reconstruction as an additional non-linear measurement,so as to minimize the l₁ norm to estimate the optimal sparse solution of the scene to be reconstructed.PM can effectively control the convergence accuracy and speed of the algorithm and ensure the convergence of KF iteration.The ISAR data is used to verify the performance of the algorithm.The experimental results show that the imaging quality of the direct KF algorithm is better than that of traditional Orthogonal Matching Pursuit?OMP?algorithm.Then the CS ISAR imaging algorithm based on sequential KF is proposed.In order to make full use of the excellent performance of KF estimation,the internal iteration based on PM is introduced to improve the imaging quality on the basis of CS ISAR imaging algorithm based on direct KF.The performance of this algorithm is verified by ISAR measured data.The experimental results show that the imaging quality of CS ISAR based on sequential KF is better than that of OMP algorithm and the direct KF algorithm,but the nesting of internal iterations leads to the increase of imaging computation and the decrease of imaging efficiency.Finally,the CS ISAR imaging algorithm based on null space KF is proposed.The null space characteristics in CS are used to decompose the target image to be reconstructed into observable and unobservable parts from the perspective of solving the underdetermined equations.The weighted Lease Square?WLS?method is used to estimate the observable part and the WLS result is taken as the initial image of the target.Then,the l₁ norm of the scattering rate of the target scene to be reconstructed is introduced into image reconstruction as an additional non-linear measurement.KF iteration is used to estimate the solution of the unobservable part in the null space to make the sum of the solutions of the two parts is minimized,and the optimal sparse solution is finally obtained.In addition,the convergence speed of the algorithm is accelerated by dynamically adjusting the weighting factor of pseudo-measurements and reasonably reducing the matrix dimension of zero space.The ISAR measured data validate the effectiveness of the CS ISAR imaging method based on null space KF.The experimental results show the imaging quality of CS ISAR based on null space KF is better than that of OMP algorithm and the direct KF algorithm,slightly lower than that of sequential KF algorithm,but its computational efficiency is much higher than that of sequential KF algorithm.