This paper analyzes the real-time relative pose estimation and attitude prediction of a tumbling target spacecraft through a high-order numerical extended Kalman filter based on differential algebra. In particular, linear and nonlinear algorithms are developed and implemented on a BeagleBone Black platform, as representative of the limited computational capability available on onboard processors. The performance are assessed varying measurement acquisition frequency and processor clock frequency, and considering various levels of uncertainties. Moreover, a comparison among the different orders of the filter is carried out