Autonomous celestial orbit determination using Bayesian bootstrap filtering and EKF

In this study, an extended Kalman filter (EKF) for estimation of spacecraft's position and velocity by single station antenna tracking data in the presence of singularities is proposed. The designed EKF estimates the position and velocity of the spacecraft on direct nonlinear range-azimuth-elevation measurements. The proposed EKF is examined through the geostationary satellite orbital motion simulations. The corruption in the results by EKF emerges from singularities caused by the highly complex elements of the Jacobian measurement matrix. The recommendations to prevent the mentioned problem are given.

A method of autonomous orbit determination for a satellite constellation using a star sensor combined with inter satellite links (ISLs) is studied. Two types of simulated observation data, Three-Satellite Constellation ISLs and background stellar observations by a CCD star sensor, are first produced. Based on these data, an observation equation is built for the constellation joint autonomous orbit determination, in which the simulations are run. The accuracy of this method with different orbital determination models are analyzed and compared with regard to the effect of potential measurement errors. The results show that autonomous satellite constellation orbit determination using star sensor measurement and ISLs data is feasible. Finally, this paper arrives at several conclusions which contribute to extending this method to a more general satellite constellation.

BeiDou Navigation Satellite System (BDS) is composed of satellites in geostationary Earth orbit (GEO), medium Earth orbit (MEO) and inclined geosynchronous orbit (IGSO). However, the orbit determination of geostationary Earth orbits and of geosynchronous orbits (GSO) with small inclination angle and small eccentricity is a challenging task that is addressed in this paper using Extended Kalman Filter (EKF). The satellite positions were predicted in Earth-centred inertial (ECI) reference frame when propagated through Keplerian model and perturbation force model for different values of right ascension of ascending node (RAAN). Root mean square (RMS) errors of 9.61 cm, 6.73 cm and 11.46 cm were observed in ECI X, Y and Z satellite position coordinates of GSO respectively, whereas, the RMS errors for GEO satellite were 8.89 cm, 7.92 cm, and 0.93 cm respectively in ECI X, Y and Z coordinates; for perturbation force model with maximum value of RAAN when compared with dynamic orbit determination model. Kolmogorov-Smirnov test for EKF reported a p-value > 0.05, indicating a good fit of perturbation force model for orbit propagation. Orbit determination using EKF with perturbation force model were compared with that using EKF with Kepler's model. Wilcoxon Rank Sum test was used to compare the residuals from EKF algorithm through Kepler's model and perturbation force model. EKF with Perturbation force model showed improvement in predicting the satellite positions as compared to Kepler's model. EKF with Perturbation force model was further applied to International GNSS Service (IGS) station data and kilometre level accuracy was achieved. RMS errors of 0.75 km, 2.53 km and 1.91 km were observed in ECI X, Y and Z satellite position coordinates of GSO, respectively, whereas, the RMS errors for GEO satellite were 3.89 km, 4.20 km and 6.66 km respectively in ECI X, Y and Z coordinates for perturbation force model.

Autonomous orbit and attitude determination for Earth satellites using images of regular-shaped ground objects

This paper presents an innovative application of the particle filtering techniques to the vertical gyro problem, which is a highly nonlinear and non Gaussian recursive state estimation problem. The classical approach to recursive state estimation problem of nonlinear and/or non Gaussian systems is based on the extended Kalman filter (EKF), which is a heuristic method based on the linearization of the state dynamics and observations near a nominal path. Depending on the amount of nonlinearities and non Gaussian noise, the EKF often provides a solution far from acceptable. The vertical gyro is an instrument adopted to measure the tilt angles (pitch and roll) of an aircraft with respect to local vertical. It is composed by three orthogonal gyros that are used as process sensors and by three orthogonal accelerometers that are used as aiding sensors. The output of accelerometers is filtered using a proper low-pass filter to allow for the estimation of the local direction of the gravity vector that is assumed the same of the local vertical. In the application to the vertical gyro, Gordon's version of the particle filter was used. The relevant dynamical model is based on non-linear attitude rate equation using Euler angles rather than quaternions. The algorithm, developed in Matlab environment, was first calibrated and tested in simulations, obtaining very appealing performances. Subsequently, it was implemented using real data, acquired by means of an inertial unit produced by Crossbow <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">TM</sup> (model DMU-HDX <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">TM</sup> ), and its results were compared to those provided by the proprietary EKF embedded in the unit. First of all, stationary tests were performed. Sensor data were input to the particle filter that outputs the tilt angles (roll and pitch) with respect to the local geodetic reference. The results were compared to those provided by the internal EKF. Subsequently, the same operation was done using data that were acquired with moving platform. The accuracy of the filter was tested also for degraded operating conditions (lower data rates) and large initial errors. The main advantage of the methodology is that, while the internal filter works with 7 states (quaternions, biases and temperature), the particle filter ensures the convergence with 3 states, and provides acceptable performances with 1000 particles only, appearing promising for a real time application.

A novel autonomous real-time orbit determination method for deep space probe based on filter coordinate is proposed in this paper. This method is a variant of the traditional autonomous orbit determination based on extended Kalman filter. The stability of filter process is enhanced by adjusting the reference frame, termed as filter coordinate frame (FCF) in this paper, in each filtering cycle. The key of this method is to find a proper FCF, so that the expansion point of state equation and observation equation can be mapped to fit position, which improves the linearization and dicretization process of traditional EKF. In the simulation, this novel method is applied to cruise phase of lunar probe, the result shows its advantage in stability compared with the traditional method based on EKF.

It is of great importance to develop a robust and fast tracking algorithm in passive localization and tracking system because of its inherent disadvantages such as weak observability and large initial errors. In this correspondence, a new algorithm referred to as the iterated unscented Kalman filter (IUKF) is proposed based on the analysis and comparison of conventional nonlinear tracking problem. The algorithm is developed from UKF but it can obtain more accurate state and covariance estimation. Compared with the traditional approaches (e.g., extended Kalman filter (EKF) and UKF) used in passive localization, the proposed method has potential advantages in robustness, convergence speed, and tracking accuracy. The correctness as well as validity of the algorithm is demonstrated through numerical simulation and experiment results.

We propose a Point Mass Filter (PMF) with a grid adaptation algorithm suitable for Terrain Referenced Navigation (TRN) systems having linear system models and highly nonlinear measurement models. The TRN systems are once again attracting attention, with the development of related hardware and sensors that can replace the Global Positioning System (GPS) in GPS denied environments. However, conventional TRN systems implemented by the Extended Kalman Filter (EKF) have some limitations, when operated in a featureless terrain area. A global nonlinear Bayesian estimation method referred to as a PMF has been applied, to overcome these drawbacks. This method, however, also has some limitations and unclear steps. Thus, we propose an adaptive PMF method for TRN systems. This algorithm can overcome the divergence problem, when a vehicle having large initial position error flies over flat or repetitive terrain for a long time. The effectiveness and the performance improvement of the proposed PMF are verified through computer simulation for TRN, compared to the EKF and two conventional PMF methods.

PurposeAutonomous orbit determination using geomagnetic measurements is an important backup technique for safe spacecraft navigation with a mere magnetometer. The geomagnetic model is used for the state estimation of orbit elements, but this model is highly nonlinear. Therefore, many efforts have been paid to developing nonlinear filters based on extended Kalman filter (EKF) and unscented Kalman filter (UKF). This paper aims to analyze whether to use UKF or EKF in solving the geomagnetic orbit determination problem and try to give a general conclusion.Design/methodology/approachThis paper revisits the problem and from both the theoretical and engineering results, the authors show that the EKF and UKF show identical estimation performances in the presence of nonlinearity in the geomagnetic model.FindingsWhile EKF consumes less computational time, the UKF is computationally inefficient but owns better accuracy for most nonlinear models. It is also noted that some other navigation techniques are also very similar with the geomagnetic orbit determination.Practical implicationsThe intrinsic reason of such equivalence is because of the orthogonality of the spherical harmonics which has not been discovered in previous studies. Thus, the applicability of the presented findings are not limited only to the major problem in this paper but can be extended to all those schemes with spherical harmonic models.Originality/valueThe results of this paper provide a fact that there is no need to choose UKF as a preferred candidate in orbit determination. As UKF achieves almost the same accuracy as that of EKF, its loss in computational efficiency will be a significant obstacle in real-time implementation.

X-ray pulsars navigation is a newly developed celestial navigation method, but the filter cycle time is long, and it cannot provide continuous navigation information. COMPASS can provide all-weather and continuous navigation information, but it has poor dynamic performance, and is susceptible to electromagnetic interference and the satellite signal is easy to be blocked. A X-ray pulsars/COMPASS integrated navigation method was proposed in order to improve the autonomous navigation capability of spacecraft. In this case, an autonomous orbit determination method of spacecraft is proposed through federal filtering that combines COMPASS navigation with X-ray pulsar navigation system. The extended Kalman filter (EKF), unscented Kalman filter (UKF) and the square root unscented Kalman filter (SR_UKF) algorithm are applied as the sub-filter. Simulation shows that the integration of the two systems can provide a higher accuracy of orbit determination, and SR_UKF performs better than EKF and UKF in filtering precision and stability.

In this paper, Rauch-Tung-Striebel(RTS) optimal smoothing algorithm is applied to improving off-line satellite attitude determination accuracy. The measurements are first processed by the forward filter, and then, a separate backward smoothing pass is used for obtaining the smoothing solution. The performances between RTS and extended Kalman filter(EKF) in gyro/star-sensor integrated system are compared. RTS smoother exhibits better accuracy and robustness than EKF under the situation of lower sensors precision, different length of data and larger initial attitude error. The results verify the effectiveness and practicability of RTS smoothing algorithm in satellite attitude determination.

Performance evaluation of Cubature Kalman filter in a GPS/IMU tightly-coupled navigation system

For a given device, the rapidity and accuracy of device error coefficient calibration and attitude alignment of the rotational inertial navigation system mainly depend on the convergence rate of the nonlinear filtering algorithm. The traditional extended Kalman filter method has no theoretical convergence guarantee for nonlinear systems and requires a long time in the actual calibration process. Since the attitude is subject to the 3-D rotation transformation group, the error transfer equation can be better linearized by defining the error on the lie group to use the new observation information fully. This article proposes a primary method of using the invariant extended Kalman filter to carry out an inertial navigation system. In the continuous rotation of the framework, the accelerometer, gyroscope, and framework angle are used to calibrate the error coefficient of the accelerometer and gyroscope and estimate the base alignment error angle. Simulation and experiment results show that the proposed method can accomplish alignment and calibration in 10 min under a large initial attitude error.

This paper presents a novel satellite autonomous navigation and orbit determination method in spatial data chains and network, using wireless measurements of the. distances from each other. The satellite position and velocity in ECEF Cartesian coordinates, as a function of the six Keplerian elements, are used to estimate the instantaneous orbital elements by the extended Kalman filter algorithm. The problems confronted in the spatial network are simply analyzed, such as high data transmission between satellites, accurate wireless distance measurement and network management. In the case of the low Earth orbit satellite (LEO), the estimated position error was controlled to around ten meters. Two important problems to be studied further are discussed.

Earth shadow time/accelerometer/GNSS-based geosynchronous transfer orbit determination method for electric propulsion satellite