Maneuvering Spacecraft Tracking via State-Dependent Adaptive Estimation

Abstract

In this study, an adaptive estimation algorithm is developed to estimate the state of a spacecraft that performs impulsive maneuvers. The accurate tracking of a maneuvering spacecraft with impulsive burns is a challenging problem since the magnitude and the time of occurrence of impulsive maneuvers are usually unknown a priori. To deal with this problem, an adaptive state estimation algorithm is developed in this study using a bank of extended Kalman filters along with interacting multiple models that account for spacecraft motion with and without impulsive maneuvers. Motivated by the fact that impulsive maneuvers usually occur when certain conditions on the spacecraft state are satisfied, the multiple extended Kalman filters are systematically blended using a state-dependent transition probability. Since the information about the conditions based on which impulsive maneuvers occur is explicitly used in the state-dependent transition probability, the proposed algorithm can predict the impulsive maneuvers more accurately and thus produce more accurate state estimates. The proposed algorithm is demonstrated with two illustrative examples: 1) tracking of a geostationary satellite performing station-keeping maneuvers and 2) tracking of a spacecraft performing orbital transfers. Nomenclature B, G = disturbance and control matrix, respectively inc d = maximum allowed inclination error for geostationary satellite k = discrete-time index m i = mode probability for ith mode m ijj = mixing probability from ith mode to jth mode P = state covariance matrix Q, R = covariance matrix of w and v, respectively q = discrete mode index u = control input vector w, v = process and measurement noise, respectively x, y = state and measurement vector, respectivelŷ x = state estimatê x i , P i = ith mode-conditioned state estimate and covariance matrix, respectively y d = maximum allowed along-track error for geostationary satellite ΔT = sampling time πx = state-dependent jump probability π ij x = state-dependent mode transition probability from ith mode to jth mode

Navigation and Control Scheme for Space Rendezvous and Docking With Maneuvering Noncooperative Target Based on Dynamic Compensation

“…In this paper, variable state dimension estimator (VSDE) [17] [28] is applied to make a comparative test for the case that the target has unknown maneuvers. When the noncooperative target maneuver is detected, the state vector is augmented to X aug k ,…”

“…When the noncooperative targets maneuver, the difficulties of state estimation lie in the inability to establish the accurate dynamic model. The traditional Kalman filter (KF) and extended Kalman filter (EKF) may diverge if the state transition equation is inaccurate [17] [18]. In order to demolish the existing obstacle, some methods have been proposed.…”

Tracklet-to-object Matching for Climbing Starlink Satellites through Recursive Orbit Determination and Prediction

“…Essentially, the filter is adaptive to observations through the inflation of state covariance such that the state estimates are converged to the real-time tracking observations. An adaptive state estimation algorithm based on multiple EKF filters along with the IMM was developed to perform the orbit determination and prediction of spacecraft with and without impulsive maneuvers (Lee et al 2016). The ability to predict impulsive maneuvers more accurately was shown such that more accurate state estimations were achieved.…”

Adaptive Tracking Method for Non-Cooperative Continuously Thrusting Spacecraft

“…Goff et al [21] combined the IMM algorithm with the variable-state dimension filters and proposed an adaptive variable dimension estimation algorithm. Lee et al [34] modeled the unknown maneuvering information as a state change problem under specific conditions, so that the transition probability of the IMM algorithm changes adaptively. In this paper, three RCSJF algorithms with different levels of maneuvering parameters are used to form the IMM algorithm model set, each of which is matched to a maneuver level so that the adaptability of the algorithm to maneuvering conditions can be further improved.…”