Firstly, a complete mathematical description of target missile relative motion problem, which consider the slope error of seeker radome is established,including nonlinear state equation and measurement equation.Secondly,the simplified mathematical model of target missile relative motion considering radome error slope in the elevation channel isgiven,and the mathematical model of joint estimation of line-of-sight rate and radome error slope in the elevation channel is derived.The observability of the joint observation system of line-of-sight rate and radome error slope corresponding to the above mathematical model is proved.Finally,an extended Kalman filter is designed to estimate the line-of-sight rate and radome error slope in the elevation loop and azimuth loop,respectively.The filters are applied in the simulation experiments and compared with the Kalman filter of line-of-sight rate estimation without considering the error slope of radome.The simulation results show that the extended Kalman filter with joint estimation of line-of-sight rate and radome error slope is effective,since it can significantly improve the guidance accuracy of a guidance system with radome error slope.