Accurate estimation of relative atmospheric density error on the example of uncertain geomagnetic activity information

Errors in neutral atmospheric density are the dominant contributor to unrealistic orbital state-vector covariances in low Earth orbits (LEO). Density uncertainty is caused by model-uncertainty at spatial scales below and within the model resolution, as well as input-uncertainty of the environmental parameters supplied to the semi-empirical atmospheric model.The paper at hand provides multiple contributions. First, analytic equations are derived to estimate the relative density error due to an input parameter uncertainty in any of the environmental parameters supplied to the model. Second, it is shown on the example of uncertain geomagnetic activity information, how to compute the required inputs to facilitate the accurate estimation of the relative density error.A clamped cubic splining approach for the conversion from geomagnetic amplitude (ap) to the kp index is postulated to perform this uncertainty propagation, as other algorithms were found unsuitable for this task. Results of numerical simulations with three popular semi-empirical models are provided to validate the set of derived equations. It is found that geomagnetic input uncertainty is especially important to consider in case of low global geomagnetic activity. The findings seamlessly integrate with prior work by the authors to perform density-uncertainty considering orbit estimation.     

NRLMSISE-00大气模型与GRACE和CHAMP卫星大气密度数据的对比分析

利用GRACE(Gravity Recovery And Climate Experiment)和CHAMP(Challenging Mini-Satellite Payload)卫星2002-2008年的大气密度数据与NRLMSISE-00大气模型密度结果进行比较,分析了模型密度误差及其特点.结果显示,NRLMSISE-00大气模型计算的密度值普遍偏大,其相对误差随经纬度变化,在高纬度相对较小;相对误差随地方时变化,在02:00LT和15:00LT左右较大,10:00LT和20:00LT左右较小.通过模型密度相对误差与太阳F_10.7指数的对比分析发现,在太阳活动低年模型相对误差最大,而在太阳活动高年相对误差较小;将模型结果分别与GRACEA/B双星和CHAMP卫星的密度数据进行比较,发现对于轨道高度更高的GRACE卫星轨道,模型相对误差更大;在地磁平静期,相对误差与地磁ap指数(当前3h)相关性不强,但是在大磁暴发生时,误差急剧增大.     

Intra-annual variations of the thermospheric density at 400 km altitude from 1996 to 2006

We investigate the intra-annual variations of globally averaged thermospheric density at 400 km altitude from 1996 to 2006 by using Artificial Neural Network Method (ANNM). The results indicate that thermospheric density is governed by solar activity, and the absolute error of our model is 13.67%, less than NRLMSISE-00 model. Fourier representation can catch the intra-annual variations more accurately than NRLMSISE-00 model and JB2008 model especially during 2002. We find that the Autumn maximum is slightly greater than Spring maximum during solar minimum, while the reverse is correct during solar maximum. There is a strong linear relation between solar activity and the amplitude of annual/semiannual variations, and the correlation coefficients are 0.9534 and 0.9424, respectively. Moreover, the amplitude ratio of the annual to semiannual variation is about 1.3 averaged, and changes in different years, but it has little relation with solar activity. Besides that, the amplitude of annual variation is larger than semiannual variation during 1996 and 2006 except 1998 and 2000. The relative error of NRLMSISE-00 model is 14.95%, decreasing to 12.49% after revising, and the correlation coefficients between this empirical model and its improved results and the observation are 0.8185 and 0.9210, respectively. Finally, we suggest the revised version of MSIS series of model should use the Fourier representation to express the intra-annual variations.     

Orbital error propagation considering atmospheric density uncertainty

Due to the influence of various errors, the orbital uncertainty propagation of artificial celestial objects while orbit prediction is required, especially in some applications such as conjunction analysis. In the orbital error propagation of artificial celestial objects in low Earth orbits (LEOs), atmospheric density uncertainty is one of the important factors that require special attention. In this paper, on the basis of considering the uncertainties of position and velocity, the atmospheric density uncertainty is also taken into account to further investigate the orbital error propagation of artificial celestial objects in LEOs. Artificial intelligence algorithms are introduced, the MC Dropout neural network and the heteroscedastic loss function are used to realize the correction of the empirical atmospheric density model, as well as to provide the quantification of model uncertainty and input uncertainty for the corrected atmospheric densities. It is shown that the neural network we built achieves good results in atmospheric density correction, and the uncertainty quantization obtained from the neural network is also reasonable. Moreover, using the Gaussian mixture model - unscented transform (GMM-UT) method, the atmospheric density uncertainty is taken into account in the orbital uncertainty propagation, by adding a sampled random term to the corrected atmospheric density when calculating atmospheric density. The feasibility of the GMM-UT method considering atmospheric density uncertainty is proved by the further comparison of abundant sampling points and GMM-UT results (with and without considering atmospheric density uncertainty).     

A Partially Orthogonal EnKF approach to atmospheric density estimation using orbital debris

A key requirement for accurate trajectory prediction and space situational awareness is knowledge of how non-conservative forces affect space object motion. These forces vary temporally and spatially, and are driven by the underlying behavior of space weather particularly in Low Earth Orbit (LEO). Existing trajectory prediction algorithms adjust space weather models based on calibration satellite observations. However, lack of sufficient data and mismodeling of non-conservative forces cause inaccuracies in space object motion prediction, especially for uncontrolled debris objects. The uncontrolled nature of debris objects makes them particularly sensitive to the variations in space weather. Our research takes advantage of this behavior by utilizing observations of debris objects to infer the space environment parameters influencing their motion.The hypothesis of this research is that it is possible to utilize debris objects as passive, indirect sensors of the space environment. We focus on estimating atmospheric density and its spatial variability to allow for more precise prediction of LEO object motion. The estimated density is parameterized as a grid of values, distributed by latitude and local sidereal time over a spherical shell encompassing Earth at a fixed altitude of 400 km. The position and velocity of each debris object are also estimated. A Partially Orthogonal Ensemble Kalman Filter (POEnKF) is used for assimilation of space object measurements to estimate density.For performance comparison, the scenario characteristics (number of objects, measurement cadence, etc.) are based on a sensor tasking campaign executed for the High Accuracy Satellite Drag Model project. The POEnKF analysis details spatial comparisons between the true and estimated density fields, and quantifies the improved accuracy in debris object motion predictions due to more accurate drag force models from density estimates. It is shown that there is an advantage to utilizing multiple debris objects instead of just one object. Although the work presented here explores the POEnKF performance when using information from only 16 debris objects, the research vision is to utilize information from all routinely observed debris objects. Overall, the filter demonstrates the ability to estimate density to within a threshold of accuracy dependent on measurement/sensor error. In the case of a geomagnetic storm, the filter is able to track the storm and provide more accurate density estimates than would be achieved using a simple exponential atmospheric density model or MSIS Atmospheric Model (when calm conditions are assumed).     

Non-Gaussian clutter characterization applied to OTHR using a mixture of two Rayleigh probability density functions

A practical technique for characterizing non-Gaussian radar clutter is specified and demonstrated using Over The Horizon Radar (OTHR) data, as an example. The technique employs maximum likelihood to fit the probability density of the clutter amplitude returns to a mixture of two Rayleigh probability densities instead of the single Rayleigh density typically used for Gaussian clutter. This model for non-Gaussian clutter is fully specified for any set of clutter amplitudes by a log likelihood, two Rayleigh parameters, and a mixing coefficient. A 3D plot of these values yields an easily-visualized clutter characterization, as is illustrated using OTHR data. This technique is a demonstration of clutter characterization using OTHR data, but the method can be applied to characterize other types of clutter data.     

Ionospheric electron density over Resolute Bay according to E-CHAIM model and RISR radar measurements

In this study, predictions of the E-CHAIM ionospheric model are compared with measurements by the incoherent scatter radars RISR at Resolute Bay, Canada, in the northern polar cap. Reasonable coverage was available for all seasons except winter for which no conclusions were drawn. It is shown that ratios of the model-to measured electron densities are close to unity in the central part of the F layer, around its peak. This is particularly evident for summer daytime. Distributions of the ratios are wider for other seasons indicating larger number of cases when the model underestimates or overestimates. E-CHAIM underestimates the electron density at ionospheric topside and bottomside by ～ 10–20 %. At the bottomside, the underestimations are strongest in summer and equinoctial nighttime. At the topside, the underestimations are strongest in autumn nighttime. Model overestimations are noticeable in the middle part of the F layer during dawn hours in autumn. Overall, the model tends to not predict highest-observed peak electron densities and the largest-observed heights of the peak.     

Evaluation of the IRI-2007 model options for the topside electron density

The International Reference Ionosphere (IRI) 2007 provides two new options for the topside electron density profile: (a) a correction of the IRI-2001 model, and (b) the NeQuick topside formula. We use the large volume of Alouette 1, 2 and ISIS 1, 2 topside sounder data to evaluate these two new options with special emphasis on the uppermost topside where IRI-2001 showed the largest discrepancies. We will also study the accurate representation of profiles in the equatorial anomaly region where the profile function has to accommodate two latitudinal maxima (crests) at lower altitudes but only a single maximum (at the equator) higher up. In addition to IRI-2001 and the two new IRI-2007 options we also include the Intercosmos-based topside model of Triskova, Truhlik, and Smilauer [Triskova, L., Truhlik, V., Smilauer, J. An empirical topside electron density model for calculation of absolute ion densities in IRI. Adv. Space Res. 37 (5), 928–934, 2006] (TTS model) in our analysis. We find that overall IRI-2007-NeQ gives the best results but IRI-2007-corrected provides a more realistic representation of the altitudinal–latitudinal structure in the equatorial anomaly region. The applicability of the TTS model is limited by the fact that it is not normalized to the F2 peak density and height.     

An empirical model of electron density in low latitude at 600 km obtained by Hinotori satellite

An empirical model of electron density (Ne) was constructed by using the data obtained with an impedance probe on board Japanese Hinotori satellite. The satellite was in circular orbit of the height of 600 km with the inclination of 31 degrees from February 1981 to June 1982. The constructed model gives Ne at any local time with the time resolution of 90 min and between −25 and 25 degrees in magnetic latitude with its resolution of 5 degrees in the range of F_10.7 from 150 to 250 under the condition of K_p < 4. Spline interpolations are applied to the functions of day of year, geomagnetic latitude and solar local time, and linear interpolation is applied to the function of F_10.7. Longitude dependence of Ne is not taken into account. Our density model can reproduce solar local time variation of electron density at 600 km altitude better than current International Reference Ionosphere (IRI2001) model which overestimates Ne in night time and underestimates Ne in day time. Our density model together with electron temperature model which has been constructed before will enable more understanding of upper ionospheric phenomenon in the equatorial region.     

Accuracy of IRI profiles of ionospheric density and temperatures derived from comparisons to Kharkov incoherent scatter radar measurements

The incoherent scatter radar (ISR) facility in Kharkov, Ukraine (49.6°N, 36.3°E) measures vertical profiles of electron density, electron and ion temperature, and ion composition of the ionospheric plasma up to 1100 km altitude. Acquired measurements constitute an accurate ionospheric reference dataset for validation of the variety of models and alternative measurement techniques. We describe preliminary results of comparing the Kharkov ISR profiles to the international reference ionosphere (IRI), an empirical model recognized for its reliable representation of the monthly-median climatology of the density and temperature profiles during quiet-time conditions, with certain extensions to the storm times. We limited our comparison to only quiet geomagnetic conditions during the autumnal equinoxes of 2007 and 2008. Overall, we observe good qualitative agreement between model and data both in time and with altitude. Magnitude-wise, the measured and modeled electron density and plasma temperatures profiles appear different. We discovered that representation accuracy improves significantly when IRI is driven by observed-averaged values of the solar activity index rather than their predictions. This result motivated us to study IRI performance throughout protracted solar minimum of the 24th cycle. The paper summarizes our observations and recommendations for optimal use of the IRI.