Integrated manoeuvre detection and estimation using nonlinear Kalman filters during orbit determination of satellites

Bergmann, C.; Zollo, A.; Herzog, J.; Schildknecht, T. (2021). Integrated manoeuvre detection and estimation using nonlinear Kalman filters during orbit determination of satellites. In: 8th European Conference on Space Debris. Darmstadt, Deutschland. 20. April 2021 - 23. April 2021.

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We present our approach to automatically detect andcharacterize satellite manoeuvres during the orbit de-termination (OD) process, based on passive-opticalmeasurements of several geostationary (GEO) satellitesfrom the SMARTnet telescope network [4].Our technique employs a nonlinear Kalman filter (eitheran Extended Kalman Filter (EKF) or an UnscentedKalman Filter (UKF)) to detect unexpected deviationsfrom the predicted states of a satellite during the ODprocess, and subsequently estimates the manoeuvreepoch and respective∆v-components. An immediatebenefit of using nonlinear Kalman filters is that theanalysis is performed directly on the angle measurements(right ascension and declination) of an object, whichare derived from passive-optical observations with atelescope, as an integral part of the object identificationand orbit determination / improvement processes. Thismitigates the need to first calculate a new orbit, as isthe case for more traditional post-orbit-determinationtechniques that work with time-series of orbital elements.Once a manoeuvre is detected, its epoch is estimatedby means of conjunction analysis. This way we canincorporate the covariance information of the object’sstate estimates. More specifically, we propagate twostate vectors bracketing the manoeuvre forward andbackward in time, respectively. The interval between thetwo epochs is sampled and the encounter probability iscalculated for each step. We then identify the manoeuvreepoch as the time at which the encounter probabilitytakes on its maximum value. Once the manoeuvre epochis known, the∆v-components of the manoeuvre can bedetermined by direct comparison of the two propagatedstates at that epoch, which also yields information aboutthe type of manoeuvre that has occurred.For the analysis in this study we use passive-opticalmeasurements of two GEO satellites (ASTRA-1KR andASTRA-1L), for which we had access to operator dataincluding manoeuvre information. Observations weretaken with the SMARTnet telescope network stationnear Sutherland, South Africa. We present our resultsof using a UKF and an EKF. For each filter, severalmanoeuvre indicators are employed, namely the squaredand normalized residuals, the Log-Likelihood, and theMahalanobis distance.We demonstrate the ability to determine manoeuvreepochs accurate to within less than a minute and∆v-components to the cm/s-level.Eventually, this automated manoeuvre detection andestimation will be applied to all measurements takenwith the SMARTnet telescope network.

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