Doppler Tracking Of Spacecraft Research Articles

Precision of Spacecraft Doppler Tracking at Low Signal‐To‐Noise Ratios

AbstractThe signal‐to‐noise ratio received at Earth is typically larger than 10 dB‐Hz for radio tracking of a spacecraft in deep space, allowing a phase‐locked loop to execute reliable carrier tracking. Recently, missions have been proposed to utilize low‐gain antennas for Doppler tracking where the signal‐to‐noise ratio may be at the single‐digit (dB‐Hz) level. In this work, we discuss spacecraft Doppler tracking at these low signal‐to‐noise ratios through an analysis of thermal noise on the radio link, results from ground testing with the Deep Space Network, and demonstrations with an active spacecraft. We show that by utilizing an open‐loop receiver to capture the carrier signal and by applying post‐processing techniques, radio data with the signal‐to‐noise ratio as low as 4 dB‐Hz can be used to derive Doppler data with precision sufficient for tracking a spacecraft in deep space.

High spectral resolution multi-tone Spacecraft Doppler tracking software: Algorithms and implementations

AbstractWe present a software package for single-dish data processing of spacecraft signals observed with VLBI-equipped radio telescopes. The Spacecraft Doppler tracking (SDtracker) software allows one to obtain topocentric frequency detections with a sub-Hz precision and reconstructed and residual phases of the carrier signal of any spacecraft or landing vehicle at any location in the Solar System. These data products are estimated using the ground-based telescope’s highly stable oscillator as a reference, without requiring an a priori model of the spacecraft dynamics nor the downlink transmission carrier frequency. The software has been extensively validated in multiple observing campaigns of various deep space missions and is compatible with the raw sample data acquired by any standard VLBI radio telescope worldwide. In this paper, we report the numerical methodology of SDtracker, the technical operations for deployment and usage, and a summary of use cases and scientific results produced since its initial release.

A possible flyby anomaly for Juno at Jupiter

In the last decades there have been an increasing interest in improving the accuracy of spacecraft navigation and trajectory data. In the course of this plan some anomalies have been found that cannot, in principle, be explained in the context of the most accurate orbital models including all known effects from classical dynamics and general relativity. Of particular interest for its puzzling nature, and the lack of any accepted explanation for the moment, is the flyby anomaly discovered in some spacecraft flybys of the Earth over the course of twenty years. This anomaly manifest itself as the impossibility of matching the pre and post-encounter Doppler tracking and ranging data within a single orbit but, on the contrary, a difference of a few mm/s in the asymptotic velocities is required to perform the fitting.Nevertheless, no dedicated missions have been carried out to elucidate the origin of this phenomenon with the objective either of revising our understanding of gravity or to improve the accuracy of spacecraft Doppler tracking by revealing a conventional origin.With the occasion of the Juno mission arrival at Jupiter and the close flybys of this planet, that are currently been performed, we have developed an orbital model suited to the time window close to the perijove. This model shows that an anomalous acceleration of a few mm/s2 is also present in this case. The chance for overlooked conventional or possible unconventional explanations is discussed.

Spacecraft Doppler tracking with possible violations of LLI and LPI: upper bounds from one-way measurements on MEX

We analyze the post-fit residuals of one-way Doppler tracking data from the Mars Express (MEX) spacecraft to test possible violations of local Lorentz invariance (LLI) and local position invariance (LPI). These one-way Doppler observations were carried out on 2011 August 7 for about 20 minutes at Sheshan Station of Shanghai Astronomical Observatory in China. These downlink signals were sent by MEX for telemetry at X-band. Because we are not able to decode the data in the form of telemetry and separate them from the carrier frequency, this makes the post-fit residuals of the Doppler data degrade to the level of 0.1 m s−1. Even so, the residuals can still impose upper bounds on LLI and LPI at 10−1, which is consistent with the prediction based on our analysis of the detectability. Although the upper bounds given by three-way Doppler tracking of MEX are better than those obtained in the present work, one-way Doppler measurements still provide a unique chance to test possible violations of LLI and LPI far from the ground stations.

Physical response of light-time gravitational wave detectors

Gravitational wave detectors are typically described as responding to gravitational wave metric perturbations, which are gauge-dependent and --- correspondingly --- unphysical quantities. This is particularly true for ground-based interferometric detectors, like LIGO, space-based detectors, like LISA and its derivatives, spacecraft doppler tracking detectors, and pulsar timing arrays detectors. The description of gravitational waves, and a gravitational wave detector's response, to the unphysical metric perturbation has lead to a proliferation of false analogies and descriptions regarding how these detectors function, and true misunderstandings of the physical character of gravitational waves. Here we provide a fully physical and gauge invariant description of the response of a wide class of gravitational wave detectors in terms of the Riemann curvature, the physical quantity that describes gravitational phenomena in general relativity. In the limit of high frequency gravitational waves, the Riemann curvature separates into two independent gauge invariant quantities: a "background" curvature contribution and a "wave" curvature contribution. In this limit the gravitational wave contribution to the detector response reduces to an integral of the gravitational wave contribution of the curvature along the unperturbed photon path between components of the detector. The description presented here provides an unambiguous physical description of what a gravitational wave detector measures and how it operates, a simple means of computing corrections to a detectors response owing to general detector motion, a straightforward way of connecting the results of numerical relativity simulations to gravitational wave detection, and a basis for a general and fully relativistic pulsar timing formula.

Spacecraft Doppler tracking with possible violations of LLI and LPI: preliminary bounds on LLI from Mars Express

Three-way spacecraft Doppler tracking is currently widely used and it plays an important role in the control and navigation of deep space missions. Using the theory of three-way Doppler tracking, including possible violations of the local Lorentz invariance (LLI) and the local position invariance (LPI), we analyze the post-fit residuals of three-way Doppler tracking data of Mars Express. These Doppler observations were carried out from August 7th to 8th in 2009, with an uplink station administered by the European Space Agency at New Norcia in Australia and three downlink stations at Shanghai, Kunming and Urumqi in China. We find that, although these observations impose preliminary bounds on LLI at the level of 10−2, they are not suitable for testing LPI because of the configuration of these stations and the accuracy of the observations. To our knowledge, this is one of the first attempts in China to apply radio science to the field of fundamental physics.

Spacecraft Doppler tracking with possible violations of LLI and LPI: a theoretical modeling

Currently two-way and three-way spacecraft Doppler tracking techniques are widely used and play important roles in control and navigation of deep space missions. Starting from a one-way Doppler model, we extend the theory to two-way and three-way Doppler models by making them include possible violations of the local Lorentz invariance (LLI) and the local position invariance (LPI) in order to test the Einstein equivalence principle, which is the cornerstone of general relativity and all other metric theories of gravity. After taking the finite speed of light into account, which is the so-called light time solution (LTS), we make these models depend on the time of reception of the signal only for practical convenience. We find that possible violations of LLI and LPI cannot affect two-way Doppler tracking under a linear approximation of LTS, although this approximation is sufficiently good for most cases in the solar system. We also show that, in three-way Doppler tracking, possible violations of LLI and LPI are only associated with two stations, which suggests that it is better to set the stations at places with significant differences in velocities and gravitational potentials to obtain a high level of sensitivity for the tests.

Alternative derivation of the response of interferometric gravitational wave detectors

It has recently been pointed out by Finn that the long-standing derivation of the response of an interferometric gravitational wave detector contains several errors. Here I point out that a contemporaneous derivation of the gravitational wave response for spacecraft doppler tracking and pulsar timing avoids these pitfalls, and when adapted to describe interferometers, recovers a simplified version of Finn's derivation. This simplified derivation may be useful for pedagogical purposes.

Low-Frequency Gravitational Wave Searches Using Spacecraft Doppler Tracking.

This paper discusses spacecraft Doppler tracking, the current-generation detector technology used in the low-frequency (∼millihertz) gravitational wave band. In the Doppler method the earth and a distant spacecraft act as free test masses with a ground-based precision Doppler tracking system continuously monitoring the earth-spacecraft relative dimensionless velocity 2Δv/c = Δν/ν0, where Δν is the Doppler shift and ν0 is the radio link carrier frequency. A gravitational wave having strain amplitude h incident on the earth-spacecraft system causes perturbations of order h in the time series of Δν/ν0. Unlike other detectors, the ∼ 1–10 AU earth-spacecraft separation makes the detector large compared with millihertz-band gravitational wavelengths, and thus times-of-flight of signals and radio waves through the apparatus are important. A burst signal, for example, is time-resolved into a characteristic signature: three discrete events in the Doppler time series. I discuss here the principles of operation of this detector (emphasizing transfer functions of gravitational wave signals and the principal noises to the Doppler time series), some data analysis techniques, experiments to date, and illustrations of sensitivity and current detector performance. I conclude with a discussion of how gravitational wave sensitivity can be improved in the low-frequency band.

Spacecraft Doppler tracking: Noise budget and accuracy achievable in precision radio science observations

We discuss noise in Doppler tracking of deep space probes and provide a detailed noise model for Doppler radio science experiments. The most sensitive current experiments achieve fractional frequency fluctuation noise of about 3 × 10−15 at 1000‐s integration time, corresponding to better than 1 micron per second velocity noise. Our noise model focuses primarily on the Fourier range ≈10−4–1 Hz, but we briefly discuss noise in lower‐frequency observations. We indicate applications of the noise model to experiment planning, identify phenomena limiting current Doppler sensitivity, and discuss the prospects for significant sensitivity improvements.

ASTROD, ASTROD I and their gravitational-wave sensitivities

Astrodynamical space test of relativity using optical devices (ASTROD) is a mission concept with three spacecraft—one near the L1/L2 point, one with an inner solar orbit and one with an outer solar orbit, ranging coherently with one another using lasers to test relativistic gravity, measure the solar system and detect gravitational waves. ASTROD I with one spacecraft ranging optically with ground stations is the first step towards the ASTROD mission. In this paper, we present the ASTROD I payload and accelerometer requirements, discuss the gravitational-wave sensitivities for ASTROD and ASTROD I, and compare them with LISA and radio-wave Doppler tracking of spacecraft.

Modification of the Doppler effect due to the helicity–rotation coupling

The helicity–rotation coupling and its current empirical basis are examined. The modification of the Doppler effect due to the coupling of photon spin with the rotation of the observer is considered in detail in connection with its applications in the Doppler tracking of spacecraft. Further implications of this coupling and the possibility of searching for it in the intensity response of a rotating detector are briefly discussed.

A two-way, noncoherent method for precise Doppler tracking of spacecraft

This paper describes a method of obtaining precise Doppler measurements of the velocity of a spacecraft without the use of a coherent transponder. Transceiver systems in which the uplink and downlink carriers are not phase locked have the advantage of being simpler and offering a wider range of design and packaging options than transponder systems. The disadvantage of a simple transceiver approach is that the downlink carrier frequency observed by a ground station is dependent upon the spacecraft frequency reference as well as on the Doppler velocity. A method of removing the effects of drift in the spacecraft frequency reference from the Doppler measurement has been developed and successfully tested in the laboratory and at the NASA Deep Space Network Test Facility. This paper will describe the two-way, noncoherent navigation method, its advantages for future spacecraft design, and a simplified error analysis. Transponder-level Doppler precision of 0.1 mm/s over a 60-second interval is supported. The impact of such a system on the normal methods of sequential tone ranging and the application of the method for spin stabilized spacecraft are also described.

Modeling of the Eros gravity field as an ellipsoidal harmonic expansion from the NEAR Doppler tracking data

The gravity field for asteroid 433 Eros has been determined in terms of ellipsoidal harmonic functions by processing the Doppler tracking data of the NEAR spacecraft while it was in orbit about the asteroid. Using the same set of NEAR spacecraft Doppler tracking data, comparative descriptions of the Eros gravity field are provided for both the ellipsoidal and the traditional spherical harmonic models. It is shown that for elongated bodies, like the asteroid Eros, the ellipsoidal harmonics model permits a better representation of the gravity signature than does the spherical harmonics model. Eros has a nearly uniform density but there are negative gravity anomalies near the ends of Eros and positive gravity anomalies near the Psyche crater and the Himeros depression.

Highly accurate, noncoherent technique for spacecraft Doppler tracking

A two-way, noncoherent spacecraft navigation technique has been developed to provide velocity accuracy comparable to that available from a deep space coherent transponder (0.1 mm/s). The technique is compatible with the normal tracking procedures of the Deep Space Network (DSN) ground stations and does not require the use of a highly stable oscillator on-board the spacecraft. The measurement technique, potential error sources, and test results obtained with prototype hardware are described.

Gravitational waves from coalescing binaries and Doppler experiments

Doppler tracking of interplanetary spacecraft provides the only method presently available for broad-band searches of low frequency gravitational waves. The instruments have a peak sensitivity around the reciprocal of the round-trip light-time T of the radio link connecting the Earth to the space-probe and therefore are particularly suitable to search for coalescing binaries containing massive black holes in galactic nuclei. A number of Doppler experiments -- the most recent involving the probes ULYSSES, GALILEO and MARS OBSERVER -- have been carried out so far; moreover, in 2002-2004 the CASSINI spacecraft will perform three 40 days data acquisition runs with expected sensitivity about twenty times better than that achieved so far. Central aims of this paper are: (i) to explore, as a function of the relevant instrumental and astrophysical parameters, the Doppler output produced by in-spiral signals -- sinusoids of increasing frequency and amplitude (the so-called chirp); (ii) to identify the most important parameter regions where to concentrate intense and dedicated data analysis; (iii) to analyze the all-sky and all-frequency sensitivity of the CASSINI's experiments, with particular emphasis on possible astrophysical targets, such as our Galactic Centre and the Virgo Cluster.

Spacecraft Doppler tracking as a narrow-band detector of gravitational radiation

We discuss a filtering technique for reducing the frequency fluctuations due to the troposphere, ionosphere, and mechanical vibrations of the ground antenna in spacecraft Doppler tracking searches for gravitational radiation. This method takes advantage of the sinusoidal behavior of the transfer function to the Doppler observable of these noise sources, which displays sharp nulls at selected Fourier components. The non-zero gravitational wave signal remaining at these frequencies makes this Doppler tracking technique the equivalent of a series of narrow-band detectors of gravitational radiation distributed across the low-frequency band. Estimates for the sensitivities achievable with the future Cassini Doppler tracking experiments are presented in the context of gravitational wave bursts, monochromatic signals, and a stochastic background of gravitational radiation.

Theory of spacecraft Doppler tracking

We present a review of the spacecraft Doppler tracking technique used in broad band searches for gravitational waves in the millihertz frequency band. After deriving the transfer functions of a gravitational wave pulse and of the noise sources entering in

A xylophone detector in space

We discuss spacecraft Doppler tracking for detecting gravitational waves in which Doppler data recorded on the ground are linearly combined with Doppler measurements made on board a spacecraft. By using the four-link radio system first proposed by Vessot

Spacecraft Doppler tracking as a xylophone detector of gravitational radiation.

Spacecraft Doppler tracking is discussed for detecting gravitational waves in which Doppler data recorded on the ground are linearly combined with Doppler measurements made on board a spacecraft. A new method is derived for removing from combined data the frequency fluctuations due to the Earth troposphere, ionosphere, and mechanical vibrations of the antenna on the ground. The remaining non-zero gravitational wave signal could be used for detecting gravitational waves.