A comparison of nonlinear filters for orbit determination

This paper compares the performance of three filters which have been applied to the problem of orbit determination using actual satellite tracking data obtained from ground based radars. The states estimated are the osculating classical orbital elements and the satellite ballistic coefficient. The dynamics used to propagate the state vector forward include the two-body acceleration plus perturbations due to atmospheric drag, zonal harmonics in the geopotential through J_S, and tesseral harmonics in the geopotential through J₄₄. The atmospheric density model used is an exponential model that includes diurnal variations and variations in the decimeter solar flux. The observations used to update the state vector estimates are slant range, azimuth, and elevation relative to a radar site. The three filters investigated in this research are a nonlinear least squares filter, an Extended Kalman filter, and a Gauss second order filter. Data are processed for three different satellites. The first is a high altitude (1000km at perigee), non-circular (e=0.015), orbit. The second satellite orbit is a low altitude (250km at perigee), non-circular (e=0.01), orbit. The final orbit is a low altitude (300km), nearly circular (e=0.0003), orbit. The filters are compared using four criteria: estimation errors, prediction errors, computer time of operation, and computer storage requirements. The Gauss second order filter is shown to provide a substantial improvement in orbit determination accuracy for satellites subject to significant perturbing accelerations.