David A. Cicci

Analysis of GPS static positioning problems

Global positioning system (GPS) static positioning solution algorithms for solving the receivers position and clock bias using pseudorange measurements are investigated. The nonlinearized iterative version based on the linearized iterative version of Noe et al.s algorithm and the iterative version based on the direct version of Bancrofts algorithm have been derived. Noe et al.s, Bancrofts, and Biton et al.s algorithms were examined to analyze accuracy and efficiency. The errors in the solutions of the algorithms were very small and there was only a small difference between the solution errors of the algorithms. The direct version of Biton et al.s algorithm proved to be more computationally efficient on the basis of the execution times and the number of iterations than the other algorithms. However, the differences between the timing results of the algorithms were not significant. All the solution algorithms were also tested using real GPS data. The nonlinearized iterative version of Noe et al.s algorithm and the iterative version of Bancrofts algorithm give accuracy and efficiency comparable to the other algorithms as well.

Ballistic missile trajectory prediction using a state transition matrix

A method for the determination of the trajectory of a ballistic missile over a rotating, spherical Earth given only the launch position and impact point has been developed. The iterative solution presented uses a state transition matrix to correct the initial conditions of the ballistic missile state vector based upon deviations from a desired set of final conditions. A six-degree-of-freedom simulation of a ballistic missile is developed to calculate the resulting trajectory. Given the initial state vector of the ballistic missile, the trajectory is simulated and the state transition matrix propagated along the trajectory to the impact point. The error in the final state vector is calculated and elements of the initial state vector are corrected using the state transition matrix. The process is repeated until the ballistic missile impacts the target location within a predefined miss distance tolerance. The result of this research is an analysis tool which accurately solves for the initial state vector of the ballistic missile.

Existence of periodic motions of a tether trailing satellite

Tethered satellite systems are becoming more widely used in space explorations. In this analytical study, the dynamics of a satellite trailing a tether are addressed. More precisely, we derive the conditions for existence of periodic motions about the relative equilibrium states of the tethered system. The system is considered to be affected by the atmospheric drag and nonspherical Earth. The mathematical proof of the existence result is based on the Leray-Schauder degree theory. Main conclusions can be easily generalized for any bounded forcing and/or forces with linear growth.

A look at tethered satellite identification using ridge-type estimation methods

Recent studies of ill-conditioned orbit determination problems have demonstrated that ridge-type estimation methods have the capability to provide increased solution accuracy over classical estimation techniques. These advanced estimation methods add a small amount of bias to the solution in order to decrease the total variance of the estimates. Even though the addition of bias to the solution results in a slightly poorer data fit, the overall solution accuracy can be improved in certain types of ill-conditioned problems. One application in which the usefulness of ridge-type estimation methods has been demonstrated is the problem of quick-look orbit determination, i.e., the problem of accurately determining the trajectory of a spacecraft using only a short arc of observational data. One similar type of orbit determination problem which has received renewed interest lately is that of the identification of a satellite to be part of a tethered satellite system without prior knowledge that it is so. A batch filter has recently been developed which has the capability of identifying a satellite to be tethered, however the accuracy of this filter is highly dependent on the amount of observational data being processed. The performance of this filter has indicated that the shorter the data arc, the more ill-conditioned the problem, thereby resulting in inaccurate solutions. This paper applies ridge-type estimation methods to the problem of identifying a tethered satellite using short arcs of observational data. Performance of the ridge-type filter is evaluated for cases of differing tether lengths, tether orientations, levels of observation error, and observation span. Results will be compared to those obtained from classical minimum variance methods with special attention being given to the speed at which the identification of a tethered satellite can take place.

Two-body missile separation dynamics

The dynamics of the separation of a two-body missile has been investigated. This missile consists of an outer boost vehicle and an inner center body vehicle. Upon completion of the boost phase the two bodies separate as a result of differing aerodynamic loads applied to each body and the thrust from a sustainer motor contained within the center body. Through simulation, the separation event was evaluated for interaction between the two bodies as a function of flight-path-angle, interstage pressure, sustainer motor thrusting force, thrust misalignment angles, and radial clearance. The impact and friction forces created by any interaction were evaluated and their effects on the separation event were quantified. The flight characteristics of the center body after the separation event were also calculated for use in determination of the missile flight profile. Finally, recommendations are made regarding the design and performance conditions for the specific two-body missile addressed in this study.

Preliminary Orbit Determination of a Tethered Satellite Using the f and g Series

A renewed interest in the deployment of tethered satellites has led to a need for a preliminary orbit determination method which is capable of distinguishing tethered satellites from untethered ones. Several of the classical preliminary orbit determination methods, which are used for Keplerian satellites, generally require two or more position vectors along with their respective observation times in order to determine a preliminary orbital element set. These conventional methods, however, are unable to distinguish between Keplerian and tethered satellites, whose motion is modified due to the presence of a tether force. The use of these conventional methods will result in the calculation of inaccurate orbital elements if the observed satellite is part of a tethered satellite system. Modifications have been made to the f and g series preliminary orbit determination method in order to allow for the identification of tethered satellites. These modifications allow for the calculation of a gravitational parameter, in addition to a set of orbital elements, which can be used to distinguish between a tethered satellite and an untethered one. This paper applies this modified f and g series method to the problem of the quick identification of a tethered satellite. The performance of this method is evaluated through scenarios of differing tether lengths, levels of observation error, and orbital eccentricities. Due to the desire for the preliminary orbit determination to be achieved quickly, only short time intervals between observations were considered. A description of how this preliminary orbit information can be used to obtain tether parameters for the subsequent differential correction process is also provided.

Preliminary orbit determination of a tethered satellite

Interest in the deployment of tethered satellites has led to a need for preliminary orbit determination methods which are capable of distinguishing tethered satellites from untethered ones. Classical preliminary orbit determination methods, which are used for Keplerian satellites, generally require two or more position vectors along with their respective observation times in order to determine a preliminary orbital element set. These conventional methods, however, are unable to distinguish between Keplerian and tethered satellites, whose motion is modified due to the presence of a tether force. The use of conventional methods result in the calculation of inaccurate orbital elements if the observed satellite is part of a tethered satellite system. Modifications have been made to four classical preliminary orbit determination methods in order to allow for the identification of tethered satellites. These modifications provide the ability to distinguish between a tethered satellite and an untethered one. This paper applies these modified preliminary orbit determination methods to the problem of the identification of a tethered satellite. The performance of these methods is evaluated through scenarios of differing tether lengths and levels of observation error, and results are compared in order to determine the most accurate method.

Sensitivity of ridge-type estimation methods to condition number

An analysis of ridge-type estimation methods and their performance in response to different levels of ill-conditioning is presented. By adjusting the observation accuracy and the sampling rate, the amount of ill-conditioning in a linear estimation problem is altered. The effectiveness of the ridge-type methods in response to these changes is evaluated by comparing the solution accuracy with those of the standard minimum variance techniques. Results show the improved performance of the ridge-type estimation method for various levels of ill-conditioning. In addition, the amount of improvement increases as the level of ill-conditioning present in the problem is increased.

Filter performance in target tracking using space-based observers

The objective of this research was to evaluate the performance of an extended Kalman filter (EKF) and an adaptive EKF in tracking a target vehicle using various measurement types from space-based observers. The adaptive EKF incorporates ridge-type estimation methods to improve the accuracy obtained by the standard EKF. The dynamical model developed for the target vehicle includes the effects of the spherical and non-spherical earth, launch vehicle thrust, and atmospheric drag. Possible observation types considered are azimuth and elevation angles, range, and range-rate data from up to three space-based observers. Comparative studies were made to evaluate the estimation accuracy as a function of observation type, number of observers, and observation rate for an observation time of up to 2 min after target vehicle burnout. In addition, comparisons were made with and without the use of initial orbit determination techniques. Results show that the performance of the adaptive EKF exceeds that of the EKF in a number of scenarios studied.

Filter sensitivity in exoatmospheric target vehicle tracking

Abstract An analysis of the orbit determination capabilities of the miniature seeker technology integration (MSTI) program was conducted. In the analysis an extended Kalman filter and an adaptive extended Kalman filter were used to estimate the position and velocity of an exoatmospheric target vehicle. A number of cases were investigated, including measurements from up to three spaced-based observers using angles-only measurements; angles plus range measurements; and angles, range, and range-rate measurements at each observation time. The target was tracked from the burnout point at 59 sec after launch through 180 sec after launch and final estimates for position and velocity were computed at 180 sec. Both the extended Kalman filter and the adaptive extended Kalman filter were found to be unsuitable for estimates using one satellite and angles-only measurements. The estimates were greatly improved when adding range measurements or a second observation satellite. The addition of a third observation satellite did not greatly improve the estimation results. It was also found that adding range-rate measurements improved the velocity results, but degraded the position estimates. In addition, the extended Kalman filter was determined to give good overall results, while the adaptive extended Kalman filter produced excellent results in certain cases and poor results in other. The results are graphically presented and conclusions are provided concerning use of the filters.