Spacecraft Attitude & Rate Estimation by an Adaptive Unscented Kalman Filter Manasi Das, Smita Sadhu, Tapan Kumar Ghoshal Dept. of Electrical Engg. Jadavpur University Kolkata – 700032, India. Abstract—This paper presents a scheme for spacecraft attitude and rate estimation based on an Adaptive Unscented Kalman Filter (AUKF). The integrated attitude determination system here consists of rate gyros and attitude sensors as the measurement units. The process equations are formed combining the information from the rotational dynamics and kinematics of the spacecraft. As the measurement noise statistics of the rate gyros and the attitude sensors are often unknown, so an adaptive filter is employed here, which determines the measurement noise covariance (R) adaptively. Further, the choice of UKF facilitates with its high accuracy and derivative-free implementation. Two versions of the AUKF algorithm are shown here depending on the residual sequences and the innovation sequences. The residual based proposed AUKF comprises of two phase of measurement update. Further, a provision to regulate the speed of adaptation through a modulating factor, is also incorporated in the presented adaptive schemes. Positive definiteness and the diagonal structure of the adapted measurement noise covariance (R) is also ensured here. Simulation results show the superiority of the AUKF based attitude estimation scheme compared to the nonadaptive filter based schemes in terms of the estimation errors. Keywords—Adaptive filter; Integrated attitude determination system; Spacecraft rotational dynamics; Unscented Kalman filter I. INTRODUCTION This paper has presented a spacecraft attitude and rate estimation technique based on a novel Adaptive Unscented Kalman Filter (AUKF). Unfortunately, the most widely used Extended Kalman Filtering (EKF) scheme for nonlinear system is based on a sub-optimal implementation [1]. This may sometime degrade the estimation performance or even may lead to divergence. Whereas, Unscented Kalman Filter (UKF) use a carefully selected set of sample points known as sigma points to map the probability distribution, providing better accuracy and faster convergence [2] compared to the EKF especially in strongly nonlinear systems with large initial errors. Calculation burden of the UKF is also less as it doesn’t require complex Jacobian calculations like the EKF. On the other hand, nonadaptive filters may it be EKF or UKF require a priori knowledge of process and measurement noise covariances. If, the prior knowledge of the noise covariances used in the filter model does not correspond to the actual one, estimation accuracy may be seriously affected. To obviate this difficulty here in our work adaptive filtering framework is utilized. The idea of employing AUKF for state estimation is relatively new which is found in few recent works. Most of the existing AUKF algorithms have utilized scaling factors [3]-[9] to make the UKF adaptive. In [3] an AUKF is employed to estimate the attitudes of a pico satellite, where the process noise covariance (Q) is adapted by a scaling factor only when faulty condition is detected depending on the residual sequences. In [4] the same authors have used another AUKF for the same purpose, where instead of the process noise covariance (Q), the measurement noise covariance (R) is scaled by a scaling matrix, at the presence of measurement malfunction. But, the positive definiteness is not guaranteed in this proposed scaling method. To ensure the positive definiteness another type of R scaling method is shown in [5]. But this scaling method fails to adapt R when the filter R is initialized with a higher value than the true one. In [6], both Q and R scaling, as presented in [3] and [5] respectively, are executed depending on the type of the fault (whether process fault or measurement fault). Another Q and R scaling methods are shown in [7], where the scaling factors are determined by an optimal Downhill Simplex search technique. In [8] another type of AUKF is involved, where the scaling of predicted error covariance (P - ) and the Kalman gain (K) is implemented by utilizing two different scaling factors. This method also fails to adapt when the filter R is initialized with a higher value than the true one. In [9] only the predicted error covariance (P - ) is scaled to make the UKF adaptive. Both [8] and [9] are unable to estimate the noise covariances and rely on the prior knowledge about them. AUKF based on complex MIT adaptation rule may be found in [10]. But the implementation of this method is often unrealistic due to its huge partial derivative calculations. Among the all existing AUKF techniques the simplest technique is to adapt the Q or R directly from the innovation sequences or the residual sequences. In [11] an AUKF for GPS based position estimation problem is presented where, Q is estimated directly from the innovation sequences. In [12] a residual based R adaptive AUKF algorithm is shown. Although, the defining formula ((14) in [12]) rebels with the corresponding R-adaptive Kalman filter relation. Another innovation based AUKF algorithm with both Q and R adaptation and a forgetting factor is shown in [13]. However in this algorithm only the innovation sequence of the k th instant is utilized. The first author acknowledges the financial support of Council of Scientific & Industrial Research (CSIR), India. 2014 International Conference on Control, Instrumentation, Energy & Communication(CIEC) 978-1-4799-2044-0/14/$31.00©2014IEEE 96