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At least 19 records

Geometric dilution of precision in Global Positioning System navigation

The evaluation of the GPS navigation performance is essentially equivalent to the computation of the diagonal terms of the geometric dilution of precision (GDOP) matrix. Certain theoretical results concerning the general properties of the GDOP matrix are obtained. An efficient algorithm for the computation of the GDOP matrix and the navigation performance index is given; and applications of the results are illustrated by numerical examples.

Fang, B. T.↗

Dilution-of-Precision-Based Lunar Surface Navigation System Analysis Utilizing Lunar Orbiters

The NASA Vision for Space Exploration is focused on the return of astronauts to the Moon. Although navigation systems have already been proven in the Apollo missions to the Moon, the current exploration campaign will involve more extensive and extended missions requiring new concepts for lunar navigation. In contrast to Apollo missions, which were limited to the near-side equatorial region of the Moon, those under the Exploration Systems Initiative will require navigation on the Moon's limb and far side. Since these regions have poor Earth visibility, a navigation system comprised solely of Earth-based tracking stations will not provide adequate navigation solutions in these areas. In this report, a dilution-of-precision (DoP)-based analysis of the performance of a network of Moon orbiting satellites is provided. This analysis extends a previous analysis of a lunar network (LN) of navigation satellites by providing an assessment of the capability associated with a variety of assumptions. These assumptions pertain to the minimum surface user elevation angle and a total single satellite failure in the lunar network. The assessment is accomplished by making appropriately formed estimates of DoP. Different adaptations of DoP, such as geometric DoP and positional DoP (GDoP and PDoP), are associated with a different set of assumptions regarding augmentations to the navigation receiver or transceiver.

Welch, Bryan W.↗

Parameter Analysis of Lunar Surface Navigation Utilizing Dilution-of-Precision Methodology With Lunar Orbiters

With the NASA Vision for Space Exploration focusing on the return of astronauts to the Moon and eventually to Mars, architectures for new navigation concepts must be derived and analyzed. One such concept, developed by the Space Communications Architecture Working Group (SCAWG), is to place a constellation of satellites around the Moon. Previously completed analyses examined the performance of multiple satellite constellations and recommended a constellation oriented as a Walker polar 6/2/1 with a semimajor axis (SMA) of 9250 km. One requirement of the constellations that were examined was that they have continuous access to any location on the lunar surface. In this report, the polar 6/2/1 and polar 8/2/1, with equal SMAs, are examined in greater detail. The dilution-of-precision (DoP) methodology is utilized to examine the effects of longitude surface points, latitude surface points, elevation requirements, and modified failure modes for these two constellations with regard to system availability. Longitude study results show that points along a meridian closely approximate the results of a global set of data points. Latitude study results show that previous assumptions with regard to latitude spacing are adequate to simulate global system availability. Elevation study results show that global system availability curves follow a reverse sigmoid function. Modified failure mode study results show that the benefits of reorienting a failure mode constellation depend on the type of navigation system and the length of the integration period being used.

Welch, Bryan W.↗

Dilution-of-Precision-Based Lunar Surface Navigation System Analysis Utilizing Earth-Based Assets

The NASA Vision for Space Exploration is focused on the return of astronauts to the Moon. Although navigation systems have already been proven in the Apollo missions to the Moon, the current exploration campaign will involve more extensive and extended missions requiring new concepts for lunar navigation. In contrast to Apollo missions, which were limited to the near-side equatorial region of the Moon, those under the Exploration Systems Initiative will require navigation on the Moon's limb and far side. These regions are known to have poor Earth visibility, but unknown is the extent to which a navigation system comprised solely of Earth-based tracking stations will provide adequate navigation solutions in these areas. This report presents a dilution-of-precision (DoP)-based analysis of the performance of a network of Earth-based assets. This analysis extends a previous analysis of a lunar network (LN) of navigation satellites by providing an assessment of the capability associated with a variety of assumptions. These assumptions pertain to the minimum provider elevation angle, nadir and zenith beam widths, and a total single failure in one of the Earth-based assets. The assessment is accomplished by making appropriately formed estimates of DoP. Different adaptations of DoP, such as geometrical DoP and positional DoP (GDoP and PDoP), are associated with a different set of assumptions regarding augmentations to the navigation receiver or transceiver.

Welch, Bryan W.↗

Dilution of precision-based lunar navigation assessment for dynamic position fixing

The NASA vision of exploration is focused on the return of astronauts to the Moon [1]. While navigation systems have already been proven in the Apollo missions to the moon, the current exploration campaign will involve more extensive and extended missions requiring new concepts for lunar navigation. In contrast to Apollo missions, which were limited to the near-side equatorial region of the moon, missions under the Exploration Systems Initiative will require navigation on the moon’s limb and far-side. As these regions have poor Earth visibility, a navigation system comprised solely of Earth-based tracking stations will not provide adequate navigation solutions in these areas. In this paper, a Dilution of Precision (DoP) based analysis of the performance of a network of Moon orbiting satellites is provided. The analysis extends previous analysis of a Lunar Network (LN) of navigation satellites by providing an assessment of the capability associated with a variety of assumptions regarding the navigation receiver and satellite visibility. The assessment is accomplished by making appropriately formed estimates of DoP, with different adaptations of DoP (i.e. GDoP, PDoP, etc.) being associated with a different set of assumptions regarding augmentations to the navigation receiver or transceiver A significant innovation described in this paper is the “Generalized” Dilution of Precision. In the same sense that the various versions of DoP can be represented as a functional of the observability grammian, Generalized DoP is defined as a functional of the sum of observability grammians associated with a batch of radiometric measurements. Generalized DoP extends the DoP concept to cases in which radiometric range and range-rate measurements are integrated over time to develop an estimate of user position (referred to here as a ‘dynamic’ solution.) Generalized DoP allows for the inclusion of cases in which the receiver location is underdetermined when assessed in the usual ‘kinematic’ sense. The Generalized DoP concept is thereby a method to assess the navigation capability associated with constellations with sparse coverage without the burden of performing a full “covariance analysis” for each point on the surface of the Moon.

Berry, Kevin↗

Dilution of Precision-Based Lunar Navigation Assessment for Dynamic Position Fixing

The NASA Vision for Space Exploration is focused on the return of astronauts to the Moon. While navigation systems have already been proven in the Apollo missions to the moon, the current exploration campaign will involve more extensive and extended missions requiring new concepts for lunar navigation. In contrast to Apollo missions, which were limited to the near-side equatorial region of the moon, missions under the Exploration Systems Initiative will require navigation on the moon's limb and far-side. As these regions have poor Earth visibility, a navigation system comprised solely of Earth-based tracking stations will not provide adequate navigation solutions in these areas. In this paper, a Dilution of Precision (DoP) based analysis of the performance of a network of Moon orbiting satellites is provided. The analysis extends previous analysis of a Lunar Network (LN) of navigation satellites by providing an assessment of the capability associated with a variety of assumptions. These assumptions are with regard to the navigation receiver and satellite visibility. The assessment is accomplished by making appropriately formed estimates of DoP. Different adaptations of DoP (i.e. GDoP, PDoP, etc.) are associated with a different set of assumptions regarding augmentations to the navigation receiver or transceiver. A significant innovation described in this paper is the "Generalized" Dilution of Precision. In the same sense that the various versions of DoP can be represented as a functional of the observability grammian, Generalized DoP is defined as a functional of the sum of observability grammians associated with a batch of radiometric measurements. Generalized DoP extends the DoP concept to cases in which radiometric range and range-rate measurements are integrated over time to develop an estimate of user position (referred to here as a 'dynamic' solution.) Generalized DoP allows for the inclusion of cases in which the receiver location is underdetermined when assessed in the usual 'kinematic' sense. The Generalized DoP concept is thereby a method to assess the navigation capability associated with constellations with sparse coverage. This alleviates the burden of performing a full "covariance analysis" for each point on the surface of the Moon.

Sands, Obed S.↗

Dilution of Precision-Based Lunar Navigation Assessment for Dynamic Position Fixing

The NASA Vision for Space Exploration is focused on the return of astronauts to the Moon. While navigation systems have already been proven in the Apollo missions to the moon, the current exploration campaign will involve more extensive and extended missions requiring new concepts for lunar navigation. In contrast to Apollo missions, which were limited to the near-side equatorial region of the moon, missions under the Exploration Systems Initiative will require navigation on the moon's limb and far-side. As these regions have poor Earth visibility, a navigation system comprised solely of Earth-based tracking stations will not provide adequate navigation solutions in these areas. In this paper, a Dilution of Precision (DoP) based analysis of the performance of a network of Moon orbiting satellites is provided. The analysis extends previous analysis of a Lunar Network (LN) of navigation satellites by providing an assessment of the capability associated with a variety of assumptions. These assumptions are with regard to the navigation receiver and satellite visibility. The assessment is accomplished by making appropriately formed estimates of DoP. Different adaptations of DoP (i.e., GDoP, PDoP, etc.) are associated with a different set of assumptions regarding augmentations to the navigation receiver or transceiver.

Sands, Obed S.↗

Quantifying Uncertainties in Navigation and Orbit Propagation Analyses

A tool used to calculate dilution of precision (DOP) was created in order to assist the Space Communications and Navigation (SCaN) program to analyze current and future user missions. The SCaN Center for Engineering, Networks, Integration, and Communication (SCENIC) is developing a new user interface (UI) to augment and replace the capabilities of currently used commercial software, such as Systems Tool Kit (STK). The DOP tool will be integrated in the SCENIC UI and will be used to analyze the accuracy of navigation solutions. This tool was developed using MATLAB and free and open-source tools to save cost and to use already existing orbital software libraries. GPS DOP data was collected and used for validation purposes. The similarities between the DOP tool results and GPS data show that the DOP tool is performing correctly. Additional improvements can be made in the DOP tool to improve its accuracy and performance in analyzing navigation solutions.

dilution of precision↗

GPS vertical axis performance enhancement for helicopter precision landing approach

Several areas were investigated for improving vertical accuracy for a rotorcraft using the differential Global Positioning System (GPS) during a landing approach. Continuous deltaranging was studied and the potential improvement achieved by estimating acceleration was studied by comparing the performance on a constant acceleration turn and a rough landing profile of several filters: a position-velocity (PV) filter, a position-velocity-constant acceleration (PVAC) filter, and a position-velocity-turning acceleration (PVAT) filter. In overall statistics, the PVAC filter was found to be most efficient with the more complex PVAT performing equally well. Vertical performance was not significantly different among the filters. Satellite selection algorithms based on vertical errors only (vertical dilution of precision or VDOP) and even-weighted cross-track and vertical errors (XVDOP) were tested. The inclusion of an altimeter was studied by modifying the PVAC filter to include a baro bias estimate. Improved vertical accuracy during degraded DOP conditions resulted. Flight test results for raw differential results excluding filter effects indicated that the differential performance significantly improved overall navigation accuracy. A landing glidepath steering algorithm was devised which exploits the flexibility of GPS in determining precise relative position. A method for propagating the steering command over the GPS update interval was implemented.

Denaro, Robert P.↗

GPS World, Innovation: Autonomous Navigation at High Earth Orbits

Calculating a spacecraft's precise location at high orbital altitudes-22,000 miles (35,800 km) and beyond-is an important and challenging problem. New and exciting opportunities become possible if satellites are able to autonomously determine their own orbits. First, the repetitive task of periodically collecting range measurements from terrestrial antennas to high altitude spacecraft becomes less important-this lessens competition for control facilities and saves money by reducing operational costs. Also, autonomous navigation at high orbital altitudes introduces the possibility of autonomous station keeping. For example, if a geostationary satellite begins to drift outside of its designated slot it can make orbit adjustments without requiring commands from the ground. Finally, precise onboard orbit determination opens the door to satellites flying in formation-an emerging concept for many scientific space applications. The realization of these benefits is not a trivial task. While the navigation signals broadcast by GPS satellites are well suited for orbit and attitude determination at lower altitudes, acquiring and using these signals at geostationary (GEO) and highly elliptical orbits is much more difficult. The light blue trace describes the GPS orbit at approximately 12,550 miles (20,200 km) altitude. GPS satellites were designed to provide navigation signals to terrestrial users-consequently the antenna array points directly toward the earth. GEO and HE0 orbits, however, are well above the operational GPS constellation, making signal reception at these altitudes more challenging. The nominal beamwidth of a Block II/IIA GPS satellite antenna array is approximately 42.6 degrees. At GEO and HE0 altitudes, most of these primary beam transmissions are blocked by the Earth, leaving only a narrow region of nominal signal visibility near opposing limbs of the earth. This region is highlighted in gray. If GPS receivers at GEO and HE0 orbits were designed to use these higher power signals only, precise orbit determination would not be practical. Fortunately, the GPS satellite antenna array also produces side lobe signals at much lower power levels. NASA has designed and tested the Navigator, a new GPS receiver that can acquire and track these weaker signals, thereby dramatically increasing the signal visibility at these altitudes. While using much weaker signals is a fundamental requirement for a high orbital altitude GPS receiver, it is certainly not the only challenge. There are other unique characteristics of this application that must also be considered. For example, Position Dilution of Precision (PDOP) figures are much higher at GEO and HE0 altitudes because visible GPS satellites are concentrated in a much smaller area with respect to the spacecraft antenna. These poor PDOP values contribute considerable error to the point solutions calculated by the spacecraft GPS receiver. Finally, spacecraft GPS receivers must be designed to withstand a variety of extreme environmental conditions. Variations in acceleration between launch and booster separation are extreme. Temperature gradients in the space environment are also severe. Furthermore, radiation effects are a major concern-spacecraft-borne GPS receivers must be designed with radiation-hardened electronics to guard against this phenomenon, otherwise they simply will not work. Perhaps most importantly, there are no opportunities to repair or modify any space-borne GPS receiver after it has been launched. Great care must be taken to ensure all performance characteristics have been analyzed prior to liftoff.

Bamford, William↗

NAVSTAR/GPS satellite selection for sequential receivers

Derivation of a satellite in-view procedure and two satellite selection procedures are obtained and comparisons to previous procedures are presented. Two suboptimal satellite selection procedures - Quadrature System (QS) and Flexible Orthogonal System (FOS) - are compared to a suboptimal and optimum procedures, taking into account the execution time and Geometric Dilution of Precision (GDOP) of each.

Noe, P. S.↗

An analysis of GDOP in global positioning system navigation

The accuracy of user navigation fix based on the NAVSTAR global positioning system is described. The trace of this matrix serves as a convenient navigation performance index and the square root of the trace is called geometric dilution of precision (GDOP). Certain theoretical results concerning the general properties of the navigation performance are derived. An efficient algorithm for the computation of GDOP is given. Applications of the results are illustrated by numerical examples.

Fang, B. T.↗

Ridge regression processing

Current navigation requirements depend on a geometric dilution of precision (GDOP) criterion. As long as the GDOP stays below a specific value, navigation requirements are met. The GDOP will exceed the specified value when the measurement geometry becomes too collinear. A new signal processing technique, called Ridge Regression Processing, can reduce the effects of nearly collinear measurement geometry; thereby reducing the inflation of the measurement errors. It is shown that the Ridge signal processor gives a consistently better mean squared error (MSE) in position than the Ordinary Least Mean Squares (OLS) estimator. The applicability of this technique is currently being investigated to improve the following areas: receiver autonomous integrity monitoring (RAIM), coverage requirements, availability requirements, and precision approaches.

Kuhl, Mark R.↗

Availability of positioning and receiver autonomous integrity monitoring for the global positioning system

Receiver-autonomous integrity monitoring (RAIM) of GPS data is examined by means of a simulation of the availability of a RAIM system that can provide both a GPS coverage model and a Markov reliability model. State probabilities of GPS failure scenarios are assigned with the Markov model with a maximum of 6 simultaneous satellite failures. The parametric analysis of the failures on GPS RAIM availability includes the maximum allowable value of the horizontal dilution of precision (HDOP), the mean time to repair, and the efficacy of incorporating altimeter measurements. When the HDOP requirement is relaxed the number of RAIM outages is minimized, and poor satellite geometry can lead to a large HDOP. The use of an altimeter can also reduce outages, and RAIM availability increases with optimistic values for the mean time to repair.

Kline, Paul A.↗

REE and other trace lithophiles in MAC88177, LEW88280 and LEW88763

In order to investigate the petrogenesis of primitive achondrites, we have carried out precise isotope dilution analyses of REE, Sr, Ba, Rb, K, Li, Ca, Mg, and Fe for three new meteorites: (Lodranites) MAC88177, LEW88280, (Brachinite) LEW88763, together with analyses for Acapulco. Present results are compared with those of other primitive achondrites previously reported by us and others.

Nakamura, N.↗

A simulation of GPS and differential GPS sensors

The Global Positioning System (GPS) is a revolutionary advance in navigation. Users can determine latitude, longitude, and altitude by receiving range information from at least four satellites. The statistical accuracy of the user's position is directly proportional to the statistical accuracy of the range measurement. Range errors are caused by clock errors, ephemeris errors, atmospheric delays, multipath errors, and receiver noise. Selective Availability, which the military uses to intentionally degrade accuracy for non-authorized users, is a major error source. The proportionality constant relating position errors to range errors is the Dilution of Precision (DOP) which is a function of the satellite geometry. Receivers separated by relatively short distances have the same satellite and atmospheric errors. Differential GPS (DGPS) removes these errors by transmitting pseudorange corrections from a fixed receiver to a mobile receiver. The corrected pseudorange at the moving receiver is now corrupted only by errors from the receiver clock, multipath, and measurement noise. This paper describes a software package that models position errors for various GPS and DGPS systems. The error model is used in the Real-Time Simulator and Cockpit Technology workstation simulations at NASA-LaRC. The GPS/DGPS sensor can simulate enroute navigation, instrument approaches, or on-airport navigation.

Rankin, James M.↗

Performance analysis of an integrated GPS/inertial attitude determination system

The performance of an integrated GPS/inertial attitude determination system is investigated using a linear covariance analysis. The principles of GPS interferometry are reviewed, and the major error sources of both interferometers and gyroscopes are discussed and modeled. A new figure of merit, attitude dilution of precision (ADOP), is defined for two possible GPS attitude determination methods, namely single difference and double difference interferometry. Based on this figure of merit, a satellite selection scheme is proposed. The performance of the integrated GPS/inertial attitude determination system is determined using a linear covariance analysis. Based on this analysis, it is concluded that the baseline errors (i.e., knowledge of the GPS interferometer baseline relative to the vehicle coordinate system) are the limiting factor in system performance. By reducing baseline errors, it should be possible to use lower quality gyroscopes without significantly reducing performance. For the cases considered, single difference interferometry is only marginally better than double difference interferometry. Finally, the performance of the system is found to be relatively insensitive to the satellite selection technique.

Sullivan, Wendy I.↗