Galileo Earth approach navigation using connected-element interferometer phase-delay tracking

The application of a Connected-Element Interferometer (CEI) to the navigation of the Galileo spacecraft during its encounter with Earth in December 1990 is investigated. A CEI tracking demonstration is planned for the week of November 11 through 18, 1990, from 27 days to 20 days prior to Earth encounter on December 8. During this period, the spacecraft will be tracked daily with Deep Space Network Stations 13 and 15 at Goldstone. The purpose of this work is twofold: first, to establish and define the navigation performance expected during the tracking demonstration and, second, to study, in a more general sense, the sensitivity of orbit demonstration results obtained with CEI to the data density within CEI tracking passes and to important system parameters, such as baseline orientation errors and the phase-delay measurement accuracy. Computer simulation results indicate that the use of CEI data, coupled with conventional range and Doppler data, may reduce the uncertainty in the declination of the spacecraft's incoming trajectory by 15 to 66 percent compared with the operational solution using range and Doppler data only. The level of improvement depends upon the quantity and quality of the CEI data

Information content of a single pass of phase-delay data from a short baseline connected element interferometer

An analytic development of the information array obtained with a single tracking pass of phase-delay measurements made from a short baseline interferometer is presented. Phase-delay observations can be made with great precision from two antennas using a single, common distributed frequency standard, hence the name connected element. With the information array, closed-form expressions are developed for the error covariance in declination and right ascension. These equations serve as useful tools for analyzing the relative merits of candidate station locations for connected element interferometry (CEI). The navigation performance of a short baseline interferometer located at the Deep Space Network's (DSN's) Goldstone intracomplex is compared with that which is presently achievable using Very Long Baseline Interferometry (VLBI) over intercontinental baselines. The performance of an intracomplex pair of short baselines formed by three stations is also investigated, along with the use of a single baseline in conjunction with conventional two-way Doppler data. The phase-delay measurement accuracy and data rate used in the analysis are based on the expected performance of an experimental connected element system presently under construction at Goldstone. The results indicate that the VLBI system that will be used during the Galileo mission can determine the declination and right ascension of a distant spacecraft to an accuracy of 20 to 25 nrad, while the CEI triad system and the combination of CEI-Doppler system are both capable of 30 to 70 nrad performance

Applications of different design methodologies in navigation systems and development at JPL

The NASA/JPL deep space navigation system consists of a complex array of measurement systems, data processing systems, and support facilities, with components located both on the ground and on-board interplanetary spacecraft. From its beginings nearly 30 years ago, this system has steadily evolved and grown to meet the demands for ever-increasing navigation accuracy placed on it by a succession of unmanned planetary missions. Principal characteristics of this system are its capabilities and great complexity. Three examples in the design and development of interplanetary space navigation systems are examined in order to make a brief assessment of the usefulness of three basic design theories, known as normative, rational, and heuristic. Evaluation of the examples indicates that a heuristic approach, coupled with rational-based mathematical and computational analysis methods, is used most often in problems such as orbit determination strategy development and mission navigation system design, while normative methods have seen only limited use is such applications as the development of large software systems and in the design of certain operational navigation subsystems

Deep-space navigation with differenced data types. Part 3: An expanded information content and sensitivity analysis

An approximate six-parameter analytic model for Earth-based differential range measurements is presented and is used to derive a representative analytic approximation for differenced Doppler measurements. The analytical models are tasked to investigate the ability of these data types to estimate spacecraft geocentric angular motion, Deep Space Network station oscillator (clock/frequency) offsets, and signal-path calibration errors over a period of a few days, in the presence of systematic station location and transmission media calibration errors. Quantitative results indicate that a few differenced Doppler plus ranging passes yield angular position estimates with a precision on the order of 0.1 to 0.4 micro-rad, and angular rate precision on the order of 10 to 25 x 10(exp -12) rad/sec, assuming no a priori information on the coordinate parameters. Sensitivity analyses suggest that troposphere zenith delay calibration error is the dominant systematic error source in most of the tracking scenarios investigated; as expected, the differenced Doppler data were found to be much more sensitive to troposphere calibration errors than differenced range. By comparison, results computed using wideband and narrowband (delta) VLBI under similar circumstances yielded angular precisions of 0.07 to 0.4 micro-rad, and angular rate precisions of 0.5 to 1.0 x 10(exp -12) rad/sec

Orbit-determination performance of Doppler data for interplanetary cruise trajectories. Part 1: Error analysis methodology

An error covariance analysis methodology is used to investigate different weighting schemes for two-way (coherent) Doppler data in the presence of transmission-media and observing-platform calibration errors. The analysis focuses on orbit-determination performance in the interplanetary cruise phase of deep-space missions. Analytical models for the Doppler observable and for transmission-media and observing-platform calibration errors are presented, drawn primarily from previous work. Previously published analytical models were improved upon by the following: (1) considering the effects of errors in the calibration of radio signal propagation through the troposphere and ionosphere as well as station-location errors; (2) modelling the spacecraft state transition matrix using a more accurate piecewise-linear approximation to represent the evolution of the spacecraft trajectory; and (3) incorporating Doppler data weighting functions that are functions of elevation angle, which reduce the sensitivity of the estimated spacecraft trajectory to troposphere and ionosphere calibration errors. The analysis is motivated by the need to develop suitable weighting functions for two-way Doppler data acquired at 8.4 GHz (X-band) and 32 GHz (Ka-band). This weighting is likely to be different from that in the weighting functions currently in use; the current functions were constructed originally for use with 2.3 GHz (S-band) Doppler data, which are affected much more strongly by the ionosphere than are the higher frequency data

Trajectory and navigation system design for robotic and piloted missions to Mars

Future Mars exploration missions, both robotic and piloted, may utilize Earth to Mars transfer trajectories that are significantly different from one another, depending upon the type of mission being flown and the time period during which the flight takes place. The use of new or emerging technologies for future missions to Mars, such as aerobraking and nuclear rocket propulsion, may yield navigation requirements that are much more stringent than those of past robotic missions, and are very difficult to meet for some trajectories. This article explores the interdependencies between the properties of direct Earth to Mars trajectories and the Mars approach navigation accuracy that can be achieved using different radio metric data types, such as ranging measurements between an approaching spacecraft and Mars orbiting relay satellites, or Earth based measurements such as coherent Doppler and very long baseline interferometry. The trajectory characteristics affecting navigation performance are identified, and the variations in accuracy that might be experienced over the range of different Mars approach trajectories are discussed. The results predict that three sigma periapsis altitude navigation uncertainties of 2 to 10 km can be achieved when a Mars orbiting satellite is used as a navigation aid

Using connected-element interferometer phase-delay data for Magellan navigation in Venus orbit

The pointing accuracy needed to support Magellan's Synthetic Aperture Radar mapping of Venus places stringent requirements on navigation accuracy. This need is met with a combination of two-way Doppler and narrowband delta Very Long Baseline Interferometer (delta VLBI) data, which are capable of determining the spacecraft's orbit to the required level, typically about one-kilometer position uncertainty. Differenced Doppler (two-way Doppler minus three-way Doppler) is also capable of meeting mission navigation requirements, and serves as a backup to narrowband delta VLBI. The Magellan Project specifies that the turn-around time for processing narrowband delta VLBI data must be 12 hours or less, a very difficult requirement to meet operationally. The use of phase-delay data, taken from a Connected-Element Interferometer (CEI) with a 21-km baseline, for Magellan orbit determination was investigated to determine if navigation performance comparable with narrowband delta VLBI and differenced Doppler could be achieved. CEI possesses an operational advantage over delta VLBI data in that the observables are constructed in near-real time, thus greatly reducing the turn-around time needed to process the data, relative to the off-line system used to generate delta VLBI observables. Unfortunately, the results indicate that CEI data are much less powerful than narrowband delta VLBI and differenced Doppler for orbiter navigation, although there was some marginal improvement over the navigation performance obtained when only two-way Doppler data were used

Precision X-band radio Doppler and ranging navigation: Mars Observer interplanetary cruise scenario

This article describes an error covariance analysis based on a Mars Observer mission scenario; the study was performed to establish the navigation performance that can potentially be achieved in a demonstration of precision two-way X-band (8.4-GHz) Doppler and ranging with the Mars Observer spacecraft planned for next year, and to evaluate the sensitivity of the predicted performance to variations in ground system error modeling assumptions. Orbit determination error statistics computed for a 182-day Doppler and ranging data arc predicted Mars approach orbit determination accuracies of about 0.45 micro-rad in an angular sense, using a conservative ground system error model as a baseline. When less-conservative error model assumptions were employed, it was found that orbit determination accuracies of 0.19 to 0.30 micro-rad could be obtained; the level of accuracy of the assumed Mars ephemeris is about 0.11 micro-rad. In comparison, Doppler-only performance with the baseline error model was predicted to be about 1.30 to 1.51 micro-rad, although it was found that when improved station location accuracies and Global Positioning System-based tropospheric calibration accuracies were assumed, accuracies of 0.44 to 0.52 micro-rad were predicted. In the Doppler plus ranging cases, the results were relatively insensitive to variations in ranging system and station delay calibration uncertainties of a few meters and tropospheric zenith delay calibration uncertainties of a few centimeters

Application of high-precision two-way ranging to Galileo Earth-1 encounter navigation

The application of precision two-way ranging to orbit determination with relatively short data arcs is investigated for the Galileo spacecraft's approach to its first Earth encounter (December 8, 1990). Analysis of previous S-band (2.3-GHz) ranging data acquired from Galileo indicated that under good signal conditions submeter precision and 10-m ranging accuracy were achieved. It is shown that ranging data of sufficient accuracy, when acquired from multiple stations, can sense the geocentric angular position of a distant spacecraft. A range data filtering technique, in which explicit modeling of range measurement bias parameters for each station pass is utilized, is shown to largely remove the systematic ground system calibration errors and transmission media effects from the Galileo range measurements, which would otherwise corrupt the angle-finding capabilities of the data. The accuracy of the Galileo orbit solutions obtained with S-band Doppler and precision ranging were found to be consistent with simple theoretical calculations, which predicted that angular accuracies of 0.26-0.34 microrad were achievable. In addition, the navigation accuracy achieved with precision ranging was marginally better than that obtained using delta-differenced one-way range (delta DOR), the principal data type that was previously used to obtain spacecraft angular position measurements operationally

Development of New Heuristics for the Euclidean Traveling SalesmanProblem

Many heuristics have been developed to approximate optimal tours for the Euclidean Traveling Salesman Problem (ETSP). While much progress has been made, there are few quick heuristics which consistently produce tours within 4 percent of the optimal solution. This project examines a few of the well known heuristics and introduces two improvements, Maxdiff and Checks. Most algorithms, during tour constrution, add a city to the subtour because the city best satisfies some criterion. Maxdiff, applied to an algorithm, ranks a city according to its effect (based on the algorithm's criterion) if it is not added to the subtour