This paper presents an estimation scheme of mass property and momentum actuator alignment of the rigid-body spacecraft with considering external torque. In many previous researches, it is assumed that external torque acts on a spacecraft is negligible. This assumption makes it feasible to build an estimator based on constant angular momentum vector of rigid-body spacecraft in inertial frame. However, the influence of external torque increases dramatically in low orbit Earth observation mission because of gravity-gradient torque. This paper develops a novel estimator that formulates gravity-gradient torque to get exact system dynamics equation. The performance of an estimator is verified by high-fidelity simulator. Nomenclature= Direction cosine matrix from inertial frame (N) to body frame at time (k) = Transpose of matrix A 1 = m-by-m identity matrix = Inertial parameters = [ ] [ ] = Body-fixed inertial matrix ω = Body rate of spacecraft in body frame , = Inertial of th reaction-wheel n = Number of reaction-wheels = Rotational rate of th reaction-wheel = Alignment vector of th reaction-wheel in body frame , , , = Extended Kalman filter system dynamics relevant components (system dynamics, state, control input, and process noise respectively) , ℋ, = Extended Kalman filter measurement equation relevant components (system measurement: means measurement for variable x, measurement equation, and measurement noise respectively) h = Total angular momentum of spacecraft in inertial frame T = Rotational kinetic energy P = Actuator misalignment parameters = [ 11 12 21 22 ⋯ 2] ∆ = Error value of variable x ̂ = Best knowledge of variable x = Position vector from spacecraft to center of the Earth in body frame = Standard deviation of random variable , ℎ = Additional linearization errors of rotational kinetic energy and angular momentum respectively = Gravity constant (3.986012 × 10 6 3 2 ⁄ ) = Gravity-gradient torque at time time

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In this paper, we present a Model-Free Stochastic Inverse Optimal Control (IOC) algorithm for the discrete-time infinite-horizon stochastic linear quadratic regulator (LQR). Our proposed algorithm exploits the richness of the available system trajectories to recover the control gain K and cost function parameters (Q, R) in a low (space, sample, and computational) complexity manner. By leveraging insights on the stochastic LQR, we guarantee well-posedness of the Model-Free Stochastic IOC LQR via satisfaction of the Certainty Equivalence optimality conditions. The exact solution of the control gain K is recovered via a deterministic, low complexity Least Squares approach. Using K, we solve a completely model-free noniterative SemiDefinite Programming (SDP) problem to obtain a unique (up to a scalar ambiguity) (Q, R), in which optimality and feasibility are jointly ensured. Via derivation of the sample complexity bounds, we show that the non-asymptotic performance of the Model-Free Stochastic IOC LQR can be characterized by the signal-to-noise (SNR) ratio of the finite set of system state and input signals. We present a model-based version of the algorithm for the special case where (A, B) is available, and we, further, provide the extension to the Stochastic Model-Free IOC linear quadratic tracking (LQT) case.

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