Integrated Manoeuvre Detection and Estimation Using Nonlinear Kalman Filters During Orbit Determination of Satellites

Kurzfassung

We present our approach to automatically detect and characterize satellite manoeuvres during the orbit de termination (OD) process, based on passive-optical measurements of several geostationary (GEO) satellites from the SMARTnet telescope network [4]. Our technique employs a nonlinear Kalman filter (either an Extended Kalman Filter (EKF) or an Unscented Kalman Filter (UKF)) to detect unexpected deviations from the predicted states of a satellite during the OD process, and subsequently estimates the manoeuvre epoch and respective ∆v-components. An immediate benefit of using nonlinear Kalman filters is that the analysis is performed directly on the angle measurements (right ascension and declination) of an object, which are derived from passive-optical observations with a telescope, as an integral part of the object identification and orbit determination / improvement processes. This mitigates the need to first calculate a new orbit, as is the case for more traditional post-orbit-determination techniques that work with time-series of orbital elements. Once a manoeuvre is detected, its epoch is estimated by means of conjunction analysis. This way we can incorporate the covariance information of the object’s state estimates. More specifically, we propagate two state vectors bracketing the manoeuvre forward and backward in time, respectively. The interval between the two epochs is sampled and the encounter probability is calculated for each step. We then identify the manoeuvre epoch as the time at which the encounter probability takes on its maximum value. Once the manoeuvre epoch is known, the ∆v-components of the manoeuvre can be determined by direct comparison of the two propagated states at that epoch, which also yields information about the type of manoeuvre that has occurred. For the analysis in this study we use passive-optical measurements of two GEO satellites (ASTRA-1KR and ASTRA-1L), for which we had access to operator data including manoeuvre information. Observations were taken with the SMARTnet telescope network station near Sutherland, South Africa. We present our results of using a UKF and an EKF. For each filter, several manoeuvre indicators are employed, namely the squared and normalized residuals, the Log-Likelihood, and the Mahalanobis distance. We demonstrate the ability to determine manoeuvre epochs accurate to within less than a minute and ∆v components to the cm/s-level. Eventually, this automated manoeuvre detection and estimation will be applied to all measurements taken with the SMARTnet telescope network.