The relative orbit parameters of space targets can provide important information support for on-orbit services and other missions. In traditional Extended Kalman filter (EKF) algorithms needs to invert the high-order matrix, which is difficult to implement independently on the spacecraft with severely limited resources. In this paper, a method using Sequential Extended Kalman Filtering (SEKF) is proposed to address this issue. This method can estimate the relative position of the space target quickly and accurately without inverting the matrix, and realize the lightweight of the algorithm. The computational burden in terms of floating-point operations (FLOPs) of the two algorithms is compared through theoretical analysis. Finally, simulation experiments demonstrate that compared to EKF, SEKF reduces the computational effort and improves the computational efficiency by 28.34%.