Deren Gong

Huber-based divided difference filter with application to relative navigation

In this article, a simplified divided difference filter based on the model structure with linear output equations and the assumption of additive Gaussian noise is introduced. By making use of the Huber technique to modify the measurement update equations of the simplified divided difference filter, the new filter exhibits robustness with respect to deviations from the common assumption of Gaussian distributed random measurement errors, for which the simplified divided difference filter exhibits mild degradation in estimation accuracy. In addition, in contrast to standard extended Kalman filter, more accurate estimation and fast convergence are achieved from the poor initial conditions. The proposed Huber-based simplified divided difference filter algorithm has been tested in relative navigation using global position system for spacecraft formation flying in low Earth orbits with real orbit perturbations and non-Gaussian random measurement errors in flight simulations. Simulations results indicate that the proposed filter provides better performance in relative navigation accuracy and robustness when compared to extended Kalman filter and simplified divided difference filter in the presence of non-Gaussian measurement noise.

Optimal linear attitude estimator and its recursive algorithm via geometric analysis

A new optimal linear attitude estimator is proposed for single-point attitude estimation using geometric approach, and a recursive optimal linear attitude estimator is developed through filtering noisy measurements. Dot and cross products are taken in order to eliminate the unknown parameters of relationships between measurements and Gibbs vector. The optimality criterion, which does not coincide with Wahba’s constrained criterion, yields linear attitude estimate. A prior rotation is adopted to avoid singularity which occurs when the principal angle is close to π. The recursive algorithm is achieved for the purpose of improving attitude accuracy using all past measurements. For long-term space missions, memory fading concept is introduced into recursive optimal linear attitude estimator. The optimal relative weighting is obtained through minimizing error propagation, and an efficient modification is proposed to significantly reduce the sudden increase of attitude error of recursive optimal linear attitude estimator in special cases. Numerical simulations show that the estimate of optimal linear attitude estimator is almost identical with that of the famous QUaternion ESTimator, and the accuracy provided by recursive optimal linear attitude estimator is over an order magnitude higher than that of optimal linear attitude estimator or QUaternion ESTimator in most cases.

Adaptive Kalman Filtering for Spacecraft Attitude Estimation

An adaptive Kalman filter (AKF) algorithm is proposed to model and approximation errors in this work. The adaptive algorithm for model and approximation errors is attained by using an upper bound for the state error prediction covariance matrix. The proposed adaptive filter algorithm has been tested in attitude estimation using gyroscope and star tracker sensors for single spacecraft in flight simulations. Simulation results demonstrate the superior performance of the proposed filter as compared to the standard Kalman filter.

Radio/VISNAV integrated navigation system for autonomous spacecraft rendezvous using two-order filter

A new relative navigation and attitude determination approach was developed for autonomous spacecraft rendezvous in this paper. The approach uses multiple optical line-of-sight vectors observations from spacecraft to another combined with radio measurements. A two order kalman filter was designed to determine relative attitude and position information. The modified rodrigues parameter was used to describe the relative attitude kinematics and relative attitude dynamics were also introduced. General relative orbit equations were adopted to describe the positional dynamics. To resolve the problem of highly sensitivity with large initial errors inherent in filter, a nonlinear iteration initialization was introduced in detail. Simulation results indicate that the accurate relative attitude and position estimates can be achieved by proposed sensor/estimator approach.

Relative semimajor axis estimation using augmented GPS navigation for HEO formation

This paper deals with the investigation of the impact of relative navigation error on relative semimajor axis (SMA) estimation for formation flying of spacecraft in high earth orbit (HEO). The use of carrier-phase/code-phase differential Global Positioning System(GPS) measurements in relative navigation filters is analyzed, with a particular augmentation of crosslink range measurement when no visible GPS satellites occurs in HEO. Two types of relative navigation filter design are proposed for relative SMA estimation analysis: one uses relative position and velocity information and chief radius/true anomaly knowledge while the other one uses reduced states. Although relative semimajor axis error is dependent on all of the coplanar position and velocity uncertainties in highly eccentric orbits, analytical methods and numerical simulations show that the typical HEO Kalman filter seldom satisfies correlation and balance requirements. Moreover, relative SMA uncertainty for HEO formation was more sensitive to radial position and intrack velocity error than that of the near-circular reference orbit according to numerical analysis. Orbit eccentricity has a large impact on the relative SMA estimation error. Kalman filters using reduced states have little effect on relative SMA uncertainty. A HEO formation with real orbit perturbations was analyzed and adaptive two-sensor tracking algorithm was proposed for integrated GPS/crosslink measurement. The combination of these simulations and analysis provides new insights concerning the relative navigation performance in determining relative SMA knowledge for HEO formation missions.