This article presents a novel method for satellite attitude determination, using two electrostatically suspended gyroscopes (ESGs). In this method, two superconducting rings (like gimbals) rotated around each suspended spherical rotor, which causes a variable flux in the rings. A voltage will be induced in the rings according to Faraday’s law of induction. Satellite attitude is determined by integrating of the induced voltages and strap-down rate gyros using the extended Kalman filter. This gyroscope works precisely when the rotor is maintained at the center of the gyroscope cavity, between three pairs of the circular electrodes, and then a backstepping control algorithm is designed for this purpose. The performance of attitude determination using such sensor and designed control algorithm is evaluated by six-degree-of-freedom simulation of a satellite in the MATLAB software. The simulations show the proposed algorithm works in an excellent manner and has lower than a few hundred arc second errors. The accurately aligning of rotors in the known direction to space is essential and is another problem that we do not address here.

A new robust quaternion Kalman filter is developed for accurate alignment of stationary strapdown inertial navigation system. Most fine alignment algorithms have tried to estimate the biases of gyroscopes and accelerometers to reduce the errors of the alignment process. In stationary platforms, due to fixed inputs for sensors, the summation of various errors such as fixed bias, misalignment, scale factor, and nonlinear errors acts like one bias error, and then the identification of each error will be impossible. The observability of gyros and accelerometers’ biases has also been studied. But, nowadays, we know that all of these unknown parameters are not observable. Then this problem can increase the complication of the alignment algorithm. The accelerometers’ errors mainly affect the errors of the roll and pitch angles, but a big portion of the heading’s error results from the gyroscopes’ errors. Modeling of all errors as additional states without considering the observability parameters has no benefits, but will increase the filter’s dimension, so the filter’s performance will decrease. In this study, due to the observability problem, a new robust multiplicative quaternion Kalman filter is designed for the alignment of a stationary platform. The presented algorithm does not estimate the sensors’ errors, but it is robust to uncertainty in the sensors’ errors. In the proposed scheme, the bounds of parameters’ errors are introduced to filter, and the filter tries to remain robust with respect to these uncertainties. The method uses the benefits of quaternions in attitude modeling, and then the robust filter is adapted to work with quaternions. The ability of the new algorithm is evaluated with MATLAB simulations. The outcomes show that the presented algorithm is more accurate than other traditional methods. The extended Kalman filter with accelerometers’ outputs and the horizontal velocities as the measurement equations and additive quaternion Kalman filter are used for comparisons.

No abstract

No abstract

This article considers the minimum variance state estimation of linear dynamic systems with linear state equality constraints. The proposed method uses singular value decomposition to divide the constrained system states into deterministic and stochastic parts. The deterministic part can be independently determined through the constraint equations. The stochastic part consists of random variables which have to be determined through a filtering process. The measurement and dynamic equations of the system are also divided into stochastic and deterministic parts. In order to update the mean and covariance of the state vector's stochastic part, the measurement updating phase of the unconstrained Kalman Filter is used. Then, the deterministic part of the dynamic equation is used as a noisy measurement for the proposed method. Finally, the stochastic part of the dynamic equation is used to predict the mean and covariance of state vector's stochastic part. Simulations show that the proposed method provides superior performance compared to other methods in the literature especially for estimating the constrained unobservable states.