Complex Kalman Filter Algorithm Based On Gaussian Entropy

The conventional complex Kalman Filter is based on the well-known mean square error criterion,which is optimal under the circular Gaussian assumption.When a realworld complex signal is involved,the state noise and the observation noise often present non-circular properties to some degree,and thus the conventional complex Kalman Filter does not perform well under these circumstances.The thesis discusses the influence of non-circular signal on complex Kalman Filter algorithm.The specific work is as follows:Firstly,this thesis introduces the basic model of the Kalman Filter algorithm and the basic knowledge of complex signal.Meanwhile,the thesis discusses the complex Kalman Filter algorithm model,and derive two kinds of Kalman Filter algorithms in detail,namely,the Conventional Complex Kalman Filter(CCKF)algorithm and the Augmented Complex Kalman Filter(ACKF)algorithm.Then,based on the complex Kalman Filter algorithm,the thesis obtained a new complex Kalman Filter in which the Gaussian entropy is adopted as the optimality criterion in place of the mean square error.In the end,the Kalman Filter algorithm based on Gaussian entropy is analyzed in detail through theoretical analysis and numerical simulation.In the theoretical analysis,when the state noise and observation noise are circular,the solution based on the Mean Square Error criterion and the solution based on the Gaussian entropy criterion has the same performance.When the non-circular coefficient of state noise and observation noise increases to 0.99,the steady-state mean square deviation of the proposed solution based on Gaussian entropy is-295 db,while the steady-state mean square deviation of the solution based on the Mean Square Error criterion is-25.7db.Briefly,with the increase of noncircular coefficient,the algorithm performance will be better.In the numerical simulation,when the non-circular coefficient of the noise is 0.99,the Kalman Filter algorithm based on Gaussian entropy has a lower steady-state mean square deviation,followed by ACKF,and finally CCKF.In the simulation verification of signal reduction,the Kalman Filter algorithm based on Gaussian entropy can basically reproduce the original signal,while both CCKF and ACKF have some degree of distortion.