Doppler Observations Research Articles

Sensitivity of Global Oscillation Frequencies to Solar Activity on Short Timescales

Sun’s oscillations frequencies vary with the changing magnetic activity and hold a strong positive correlation. While most of the analysis for global modes have been carried out using time series longer than a solar rotation, only a few studies are available showing their variation on shorter timescales. Using Doppler observations from Global Oscillation Network Group during the period 1995–2024, we analyze oscillation frequencies computed on a timescale of nine days and compare them with those obtained from 108 days. We also study their sensitivity in cycles 23 and 24 to the change in solar activity as represented by the 10.7 cm radio flux.

About the improvement in Mars Polar Motion determination from radio tracking of two landers

The polar motion of Mars is defined as the movement of the rotation axis with respect to a body-fixed frame tied to the crust of the planet. It is composed of forced motion at annual and sub-annual frequencies caused by the seasonal mass redistribution, formation of the polar ice caps and angular momentum variations of the atmosphere, and of the free mode called the Chandler wobble.Radio-tracking data from landers offers the most suitable means to measure the rotation of Mars, including its polar motion. The latter, however, has not yet been achieved using lander data alone. In this study, we assess the uncertainties associated with Mars polar motion estimation using Direct-To-Earth Doppler, range and Same-Beam Interferometry (SBI) observables between multiple landers on the surface of Mars. We evaluate the improvement enabled by combining data from multiple landers with respect to one-lander scenarios, and identify the optimal mission architectures for polar motion estimation by considering the influence of respective mission parameters on the estimation uncertainty. In particular, we consider the effects of absolute and relative locations of the landers and of mission scheduling. We re-evaluate the possibility of estimating the polar motion using data from landers in proximity to the equator, and apply our considerations to simulated data consistent in number and accuracy with that collected by past Martian missions. We notice and explain a strong longitude dependence of the formal errors when the polar motion parameters are estimated concurrently with the seasonal spin variation parameters, making it impossible to properly determine all components of polar motion with a single lander regardless of its location. However, the use of two or more landers in optimal locations with respect to each other eliminates those limitations. We evaluate the influence of latitudinal and longitudinal separation on polar motion determination in such cases. In particular, we are able to determine polar motion well even in cases where the longitudes of the two landers make determination from each single lander impossible.

Doppler Positioning with LEO Mega-Constellation: Equation Properties and Improved Algorithm

Doppler positioning, as an early form of positioning, has regained significant research interest in the context of Low Earth Orbit (LEO) satellites.Given the LEO mega-constellation scenario, the objective function of Doppler positioning manifests significant nonlinearity, leading to ill-conditioning challenges for prevalent algorithms like iterative least squares (LS) estimation, especially in cases where inappropriate initial values are selected. In this study, we investigate the causes of ill-posed problems from two perspectives. Firstly, we analyze the linearization errors of the Doppler observation equations in relation to satellite orbital altitude and initial value errors, revealing instances where traditional algorithms may fail to converge. Secondly, from an optimization theory perspective, we demonstrate the occurrence of convergence to locally non-unique solutions for Doppler positioning. Subsequently, to address these ill-conditioning issues, we introduce Tikhonov regularization terms in the objective function to constrain algorithm divergence, with a fitted model for the regularization coefficient. Finally, we conduct comprehensive simulation experiments in both dynamic and static scenarios to validate the performance of the proposed algorithm. On the one hand, when the initial values are set to 0, our algorithm achieves high-precision positioning, whereas the iterative LS fails to converge. On the other hand, in certain simulation scenarios, the iterative LS converges to locally non-unique solutions, resulting in positioning errors exceeding 50 km in the north and east directions, several hundred kilometers in the vertical direction, and velocity errors surpassing 120 m/s. In contrast, our algorithm demonstrates typical errors of a position error of 6.8462 m, velocity error of 0.0137 m/s, and clock drift error of 8.3746 × 10−6 s/s.This work provides an effective solution to the sensitivity issue of initial points in Doppler positioning and can serve as a reference for the algorithm design of Doppler positioning receivers with LEO mega-constellations.

Testing General Relativity with Juno at Jupiter

The Juno spacecraft has been orbiting Jupiter since 2016 July to deepen our comprehension of the solar system by studying the gas giant. The radio science experiment enables the determination of Jupiter’s gravitational field, thus shedding light on its interior structure. The experiment relies on determining the orbit of the spacecraft during its pericenter passages. Previous gravity data analyses assumed the correctness of the general theory of relativity, which was used for trajectory integration and radio signal propagation modeling. In this work, we aim to test general relativity within the unique context of a spacecraft orbiting Jupiter, by employing the parameterized post-Newtonian (PPN) formalism, an established framework for comparing various gravitational theories. Within this framework, we focus our attention toward the PPN parameters γ and β, which offer insights into the curvature of spacetime and the nonlinearity of gravitational effects, respectively. Additionally, we extend our investigation to the Lense–Thirring effect, which models the dragging of spacetime induced by a rotating mass. By measuring the relativistic frequency shift on Doppler observables caused by Jupiter during Juno’s perijove passes, we estimate γ = 1 + (1.5 ± 4.9) × 10−3, consistent with the general theory of relativity. Our estimated γ is primarily influenced by its effect on light-time computation, with a negligible contribution from spacecraft dynamics. Furthermore, we also present a modest level of accuracy for the β parameter, reflecting the minimal dynamical perturbation on Juno from general relativity. This also applies to the Lense–Thirring effect, whose signal is too small to be confidently resolved.

An approach to improve smartphone-based PPP performance in constrained environments using Doppler observations

ABSTRACT The smartphone-based precise point positioning (PPP) technique is usually used in limited satellite visibility environments, resulting in discontinuities in carrier phase observations. This study proposes an approach to improve the smartphone-based PPP performance by predicting the missed carrier phase observations with Doppler observations. Kinematic smartphone-based PPP experiments in the tree canopy and high-building environments are conducted, and results show that the proposed PPP approach improves the horizontal positioning accuracy by over 31% and 14% and vertical positioning accuracy by over 23% and 10% when compared to the PPP approaches without predictions and with linear predictions, respectively.

Non-Cooperative LEO Satellite Orbit Determination Using Single Station for Space-Based Opportunistic Positioning

Space-based opportunistic positioning is a crucial component of resilient positioning, navigation, and timing (PNT) systems, and it requires the acquisition of orbit information for non-cooperative low Earth orbit (LEO) satellites. Traditional methods for orbit determination (OD) of non-cooperative LEO satellites have difficulty in achieving a balance between reliability, hardware costs, and availability duration. To address these challenges, this study proposes a framework for single-station orbit determination of non-cooperative LEO satellites. By utilizing signals of opportunity (SOPs) captured by a single ground station, the system performs initial orbit determination (IOD), precise orbit determination (POD), and orbit prediction (OP), enabling the long-term determination of satellite positions and velocities. Under the proposed framework, the reliability and real-time performance are dependent on the initial orbit determination and the orbit calculation based on the dynamical model. To achieve initial orbit determination, a three-step algorithm is designed. (1) An improved search method is employed to estimate a coarse orbit using single-pass Doppler measurements. (2) Data association is conducted to obtain multi-pass Doppler observations. (3) The least squares (LS) is implemented to determine the initial orbit using the associated multi-pass Doppler measurements and the coarse orbit. Additionally, to enhance computational efficiency, two fast orbit calculation algorithms are devised. These algorithms leverage the numerical stability of the Runge–Kutta integrator to reduce computations and exploit the strong correlation among nearby time intervals of orbits with small eccentricities to minimize redundant calculations, thereby achieving orbit calculation efficiently. Finally, through positioning experiments, the determined orbits are demonstrated to have accuracy comparable to that of two-line elements (TLE) updated by the North American Aerospace Defense Command (NORAD).

Expanding the frontiers of cool-dwarf asteroseismology with ESPRESSO

Fuelled by space photometry, asteroseismology is vastly benefitting the study of cool main-sequence stars, which exhibit convection-driven solar-like oscillations. Even so, the tiny oscillation amplitudes in K dwarfs continue to pose a challenge to space-based asteroseismology. A viable alternative is offered by the lower stellar noise over the oscillation timescales in Doppler observations. In this Letter we present the definite detection of solar-like oscillations in the bright K5 dwarf ϵ Indi based on time-intensive observations collected with the ESPRESSO spectrograph at the VLT, thus making it the coolest seismic dwarf ever observed. We measured the frequencies of a total of 19 modes of degree ℓ = 0–2 along with νmax = 5305 ± 176 μHz and Δν = 201.25 ± 0.16 μHz. The peak amplitude of radial modes is 2.6 ± 0.5 cm s−1, or a mere ∼14% of the solar value. Measured mode amplitudes are ∼2 times lower than predicted from a nominal L/M scaling relation and favour a scaling closer to (L/M)1.5 below ∼5500 K, carrying important implications for our understanding of the coupling efficiency between pulsations and near-surface convection in K dwarfs. This detection conclusively shows that precise asteroseismology of cool dwarfs is possible down to at least the mid-K regime using next-generation spectrographs on large-aperture telescopes, effectively opening up a new domain in observational asteroseismology.

Automated Scheduling of Doppler Exoplanet Observations at Keck Observatory

Precise Doppler studies of extrasolar planets require fine-grained control of observational cadence, i.e., the timing of and spacing between observations. We present a novel framework for scheduling a set of Doppler campaigns with different cadence requirements at the W. M. Keck Observatory. For a set of observing programs and allocated nights on an instrument, our software optimizes the timing and ordering of ∼1000 observations within a given observing semester. We achieve a near-optimal solution in real-time using a hierarchical Integer Linear Programming framework. Our scheduling formulation optimizes over the roughly 103000 possible orderings. A top level optimization finds the most regular sequence of allocated nights by which to observe each host star in the request catalog based on a frequency specified in the request. A second optimization scheme minimizes the slews and downtime of the instrument. We have assessed our algorithms performance with simulated data and with the real suite of Doppler observations of the California Planet Search in 2023.

Time Convolutional Network-Based Maneuvering Target Tracking with Azimuth-Doppler Measurement.

In the field of maneuvering target tracking, the combined observations of azimuth and Doppler may cause weak observation or non-observation in the application of traditional target-tracking algorithms. Additionally, traditional target tracking algorithms require pre-defined multiple mathematical models to accurately capture the complex motion states of targets, while model mismatch and unavoidable measurement noise lead to significant errors in target state prediction. To address those above challenges, in recent years, the target tracking algorithms based on neural networks, such as recurrent neural networks (RNNs), long short-term memory (LSTM) networks, and transformer architectures, have been widely used for their unique advantages to achieve accurate predictions. To better model the nonlinear relationship between the observation time series and the target state time series, as well as the contextual relationship among time series points, we present a deep learning algorithm called recursive downsample-convolve-interact neural network (RDCINN) based on convolutional neural network (CNN) that downsamples time series into subsequences and extracts multi-resolution features to enable the modeling of complex relationships between time series, which overcomes the shortcomings of traditional target tracking algorithms in using observation information inefficiently due to weak observation or non-observation. The experimental results show that our algorithm outperforms other existing algorithms in the scenario of strong maneuvering target tracking with the combined observations of azimuth and Doppler.

Improved Velocity Determination Method by the Integration of Multi-GNSS Satellites’ Doppler and Phase Observations

Improved Velocity Determination Method by the Integration of Multi-GNSS Satellites’ Doppler and Phase Observations

Velocity Estimation Using Time-Differenced Carrier Phase and Doppler Shift with Different Grades of Devices: From Smartphones to Professional Receivers

Velocity estimation has a key role in several applications; for instance, velocity estimation in navigation or in mobile mapping systems and GNSSs is currently a common way to achieve reliable and accurate velocity. Two approaches are mainly used to obtain velocity based on GNSS measurements, i.e., Doppler observations and carrier phases differenced in time (that is, TDCP). In a benign environment, Doppler-based velocity can be estimated accurately to within a few cm/s, while TDCP-based velocity can be estimated accurately to within a few mm/s. On the other hand, the TDCP technique is more prone to availability shortage and the presence of blunders. In this work, the two mentioned approaches are tested, using three devices of different grades: a high-grade geodetic receiver, a high-sensitivity receiver, and a GNSS chip mounted on a smartphone. The measurements of geodetic receivers are inherently cleaner, providing an accurate solution, while the remaining two receivers provide worse results. The case of smartphone GNSS chips can be particularly critical owing to the equipped antenna, which makes the measurements noisy and largely affected by blunders. The GNSSs are considered separately in order to assess the performance of the single systems. The analysis carried out in this research confirms the previous considerations about receiver grades and processing techniques. Additionally, the obtained results highlight the necessity of adopting a diagnostic approach to the measurements, such as RAIM-FDE, especially for low-grade receivers.

QUALITY ANALYSIS OF SMARTPHONE GNSS OBSERVATIONS AND IMPACT ON PRECISE POSITIONING

Abstract. The use of low-cost and ultra-low-cost receivers such as smartphones and wearables has been raising these days due to their affordability and widespread availability. Along with the release of Android Version 7 in 2016, the raw GNSS measurements became accessible through the location API, which includes the GNSSMeasurement class and GNSSClock class. However, the users are required to extract the typical GNSS observations, such as pseudorange, carrier-phase, and Doppler observations, from the raw data coming from these two classes. It should be mentioned some quality concerns may arise during the conversion process from the raw GNSS measurements to the typical GNSS measurements. These quality concerns would subsequently affect GNSS data processing such as cycle slip detection, code smoothing and ultimately positioning performance. In this paper, we first analyse the quality of GNSS observations logged from smartphones. Furthermore, we address potential issues that can arise during the generation of GNSS observations. We also introduce our developed in-house software, UofC CSV2RINEX, which is designed to convert CSV files into RINEX files.

4D RADAR/IMU/GNSS INTEGRATED POSITIONING AND MAPPING FOR LARGE-SCALE ENVIRONMENTS

Abstract. 4D millimeter-wave radar can work in harsh weather conditions such as fog and snow, and measure the position and radial Doppler velocity of objects in three-dimensional space. Some existing methods perform positioning by fusing 3D velocity or point cloud matching information estimated by 4D radar with IMU information. However, the sparsity of radar point clouds and the interference of large amount of noise lead to low accuracy of odometry, and most of the existing work cannot achieve the global consistent mapping with radar point clouds. In this paper, a 4D radar/IMU/GNSS localization and mapping method, G-iRIOM, is proposed. We tightly coupled IMU measurement, Doppler observation information and point cloud matching information from 4D radar by iterative extended Kalman filtering (iEKF) method, and introduced GNSS RTK and loop closure information as global observation to correct the positioning drift of the odometry. The experimental results show that the tightly coupled Doppler velocity information can effectively improve the control of the pose on the local point cloud position, thus enhancing the mapping accuracy. Meanwhile, the introduction of GNSS and loop closure information can significantly improve the positioning accuracy of 4D radar odometry as a kind of global observation, and achieve global consistent mapping of large-scale outdoor scenes based on 4D radar point clouds.

Preliminary Estimations of Mars Atmospheric and Ionospheric Profiles from Tianwen-1 Radio Occultation One-Way, Two-Way, and Three-Way Observations

The radio occultation method, one of the methods used to provide planetary atmospheric profiles with high vertical resolution, was applied to China’s first Mars mission, Tianwen-1. We carried out observations based on the Chinese Deep Space Network, and one-way, two-way, and three-way modes were used for Doppler observations from the Tianwen-1 spacecraft. We successfully obtained effective observations from Tianwen-1 on 22 and 25 March 2022. An inversion system developed for Tianwen-1 radio occultation observations enabled the derivation of neutral atmospheric density, pressure, temperature, and electron density profiles of Mars. Utilizing one-way tracking data, Martian ionospheric electron density profiles were retrieved at latitudes between 68.7 and 70.7 degrees (N). However, the presence of strong random walk noise in one-way tracking data led to poor inversion results. Meanwhile, Martian ionospheric electron density and neutral atmosphere profiles were extracted from two-way and three-way tracking data at latitudes between 55.1 and 57.0 degrees (S) on 22 March and at latitudes between 62.8 and 63.4 degrees (S) on 25 March. Importantly, our inversion results from Tianwen-1 maintained consistency with results from the Mars Express and the Chapman theory (mainly in the M2 layer). Through two days’ observation experiments, we established and verified the occultation solution system and prepared for the follow-up occultation plans.

Doppler LiDAR Observation of Subsidence in Synoptic Scale and Performance of a Global Numerical Weather Prediction Model in Capturing the Subsidence

The vertical velocity data from a Doppler LiDAR situated at the centre of Hong Kong were examined to look for signature of subsidence within the atmospheric boundary layer against a synoptic background. Two case studies were performed, namely, stable atmospheric conditions in foggy weather and possible “subsidence heating” at the periphery of the outer circulation of an intense tropical cyclone. The LiDAR’s Doppler velocity data were found to provide insights into the vertical motion of the air on the synoptic scale. They appear to confirm subsidence in foggy weather but provide new information about the mechanism for the occurrence of extremely hot weather. The data were also compared with vertical velocity forecasts from a numerical weather prediction model to assess the quality of the forecast. The Doppler LiDAR’s vertical velocity data were found to be useful in the verification of omega forecasts from the global numerical weather prediction model. They were found to provide further insights into the subsidence of the troposphere, particularly the atmospheric boundary layer, in certain synoptic patterns.

Ultrasound and Doppler Diagnostic Capabilities of Lymph Nodes in Thyroid Cancer

nodular lesions, autoimmune thyroiditis and neoplastic processes are the leading diseases of the thyroid gland (TG), when it is characterized by the cervical lymph nodes (LN) enlargement. They can undergo macro- and microscopic changes due to inflammatory processes of bacterial or viral origin, benign and malignant lesions of the neck, head and mediastinum. Doppler ultrasonography (US) plays a significant role among the new methods of screening for altered LN and differential diagnosis of pathological processes. The aim of this work is to determine the prospects for the use of LN lesions’ ultrasound diagnostics in inflammatory and oncological processes of the TG. Ultrasound diagnostics was performed to determine Doppler signs (EDV, PSV, RI) and changes in neck LN in 175 patients with and without TG pathologies. According to the results of histopathology, the patients were divided into 4 groups: 46 healthy patients without any thyroid pathology, 44 patients with inflammatory thyroid diseases, 42 patients with thyroid cancer but without metastatic LN involvement, 43 patients with metastatic LN involvement – Thyroid cancer. B-mode ultrasound diagnostic data demonstrated positive complementation with echostructural signs and changes in vascularization. It manifested in a wide range of velocities and atypical angioarchitectonics. 13 (31%) patients had increased vascularization with PSV – 23-45 cm/s, EDV – 14- 8 cm/s, RI – 0.32-0.46. It shows the progression of proliferative processes without necrotic changes in the hilus and its periphery. In 18 (43%) patients dynamic Doppler observation indicated the appearance of accelerated blood flow and an atypical vascular concentration outside nodular capsules. It is an indicator of the cancer spread. Color Doppler mapping and energy Doppler coding of cervical metastases are important diagnostic techniques, that qualitatively and quantitatively complements and details B-mode ultrasound diagnosis.

Cycle Slip Detection By Combining TECR And Reconstructed Doppler Integral Method

Poor observation environment and other factors lead to the whole cycle slips of carrier phase observation value, which affects the positioning accuracy. There are detection loopholes in the traditional cycle slips detection methods, especially the small value cycle slips, equivalent cycle slips and special value cycle slips are difficult to detect. A method combining Total Electron Contents Rate (TECR) and Doppler Value Reconstruction is proposed to solve the deficiency of cycle slip detection. Based on Doppler observations and Doppler detection method, the Doppler observations are reconstructed. This method improves the accuracy of Doppler observations. The proposed method has been verified that the reconstructed Doppler observations can improve the detection accuracy of small cycle slips, and can accurately detect any large value, small value of 1 cycle, Both frequency equivalent cycle slips and special value cycle slips can be accurately detected.

EXPRES. IV. Two Additional Planets Orbiting ρ Coronae Borealis Reveal Uncommon System Architecture

Thousands of exoplanet detections have been made over the last 25 years using Doppler observations, transit photometry, direct imaging, and astrometry. Each of these methods is sensitive to different ranges of orbital separations and planetary radii (or masses). This makes it difficult to fully characterize exoplanet architectures and to place our solar system in context with the wealth of discoveries that have been made. Here, we use the EXtreme PREcision Spectrograph to reveal planets in previously undetectable regions of the mass–period parameter space for the star ρ Coronae Borealis. We add two new planets to the previously known system with one hot Jupiter in a 39 day orbit and a warm super-Neptune in a 102 day orbit. The new detections include a temperate Neptune planet ( M ⊕) in a 281.4 day orbit and a hot super-Earth ( M ⊕) in a 12.95 day orbit. This result shows that details of planetary system architectures have been hiding just below our previous detection limits; this signals an exciting era for the next generation of extreme precision spectrographs.

Characterisation and position-aiding performance analysis of Doppler observation from android smartphones

AbstractIt has been acknowledged that the Doppler is beneficial to the GNSS positioning of smartphones. However, analysis of Doppler precision on smartphones is insufficient. In this paper, we focus on the characteristic analysis of the raw Doppler measurement from Android smartphones. A comprehensive investigation of the Doppler was conducted. The results illustrate that the availability of Doppler is stable and higher than that of carrier measurements, which means that the Doppler-smoothed code (DSC) method is more effective. However, there is a constant bias between the Doppler and the code rate in Xiaomi MI8, which indicates that extra processing of the DSC method is necessary for this phone. Additionally, it is demonstrated that the relationship between the Doppler and C/N0 can be expressed as an exponential function, and the fitting parameters are provided. The numerical experiment in car-borne and hand-held scenes was conducted for evaluating the performance of the Doppler-aided positioning algorithm. For positioning, the improvement reaches 37 ⋅ 69%/37 ⋅ 14%/26 ⋅ 61% in the east, north and up components, respectively, after applying the Doppler aiding. For velocity estimation, the improvement reaches 29 ⋅ 62%/39 ⋅ 63%/29 ⋅ 37% in the three components, respectively.

Analysis of 5G Smart Communication Base Station Doppler-Smoothed Pseudorange Single-Point Geodesic Positioning Accuracy

With the continuous development of mobile communication and satellite navigation technologies, the positioning requirements of 5G smart communication base stations are becoming higher and higher. With the opening of GNSS raw observation data, research on the positioning of a 5G smart communication base station has become a research hotspot in the surveying and mapping disciplines. In this paper, based on the GNSS observation data of the 5G smart communication base station, the quality of the original GNSS observation data of the 5G smart communication base station is studied and analyzed. A method based on Doppler smoothing pseudorange solves the problem that the original pseudorange observation values of the 5G smart communication base station are noisy and prone to multipath errors due to the limitations of the base station chips and processes, which makes the traditional data processing methods unable to meet the demand for higher accuracy positioning. This method uses Doppler observations to smooth the pseudorange and determines the Doppler smoothing strategy and closure values to improve the data quality. The experimental data show that Doppler smoothing pseudorange can improve data quality and positioning accuracy by 67.9% in the E direction, 64.8% in the N direction, and 65.5% in the U direction. The future world will develop in the direction of intelligence, and the wireless network 5G technology used to support the construction of this intelligent system will become the core driver for the development of a leading intelligent society. 5G network signals have higher reliability and lower latency and can meet the specific needs of smart manufacturing, autonomous driving, and other industrial applications. This new base station product can meet the construction needs of future 5G base stations, adapt to the future intensive, miniaturized, intelligent station construction mode, and realize safe and fast station construction, providing the necessary hardware support for 5G network coverage.