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We present the current status and first results from a Monte Carlo-type simulation toolbox for Solar System small body dynamics. We also present fundamental methods for evaluating the results of this type of simulations using convergence criteria. The calculations consider a body in the Solar System with a mass loss mechanism that generates smaller particles. In our application the body, or parent body, is a comet and the mass loss mechanism is a sublimation process. In order to study mass propagation from parent bodies to Earth, we use the toolbox to sample the uncertainty distributions of relevant comet parameters and to find the resulting Earth influx distributions. The initial distributions considered represent orbital elements, sublimation distance, cometary and meteoroid densities, comet and meteoroid sizes and cometary surface activity. Simulations include perturbations from all major planets, radiation pressure and the Poynting-Robertson effect. In this paper we present the results of an initial software validation performed by producing synthetic versions of the 1933, 1946, 2011 and 2012 October Draconids meteor outbursts and comparing them with observational data and previous models. The synthetic meteor showers were generated by ejecting and propagating material from the recognized parent body of the October Draconids; the comet 21P/Giacobini-Zinner. Material was ejected during 17 perihelion passages between 1866 and 1972. Each perihelion passage was sampled with 50 clones of the parent body, all producing meteoroid streams. The clones were drawn from a multidimensional Gaussian distribution on the orbital elements, with distribution variances proportional to observational uncertainties. In the simulations, each clone ejected 8000 particles. Each particle was assigned an individual weight proportional to the mass loss it represented. This generated a total of 6.7 million test particles, out of which 43 thousand entered the Earth's Hill sphere during 1900–2020 and were considered encounters. The simulation reproduces the predictions and observations of the 1933, 1946, 2011 and 2012 October Draconids, including the unexpected but measured deviation of the meteoroid mass index from a power law in 2012 as compared to 2011. We show that when convergence is sufficient in the simulation, the fraction between two encountered mass distributions is independent of the assumed input mass distribution. Finally, we predict an outburst for the 2018 October Draconids with a peak on October 8–9 that could be up to twice as large as the 2011 and 2012 outbursts.

The extraterrestrial material, called meteoroids, that constantly enters the Earth's atmosphere gives us a unique opportunity to examine the motion and population of small bodies in the Solar system. This exploration requires simulating the motion of these particles. Currently, only the timing of meteoroids encountering the Earth is well predicted by such simulations, while other parameters are uncertain. This can be remedied by proper stochastic representation and estimation using a sufficient number of samples. We propose methods to both represent simulations in a stochastic manner and to improve sampling using Importance Sampling. We also demonstrate these methods practically with a test model. Using the test model resulted in an error reduction by a factor of 3 without increase in computation time. Thus, we validated that these techniques can be implemented on and are compatible with Solar system small body dynamics models. Based on these results we predict that when properly implemented on a larger and more complex model, Importance Sampling can improve sampling numbers by several orders of magnitude without increasing computation time, depending on the simulation in question. The methods presented here bring advantages such as; greatly reduced estimation errors, fitting models without re-running simulations, model comparisons without sample variations, circumventing unknown properties using invariant measures, representing large particle numbers without additional errors. This methodology has wide application possibility and will enable larger, more reliable and reusable simulations of dynamical astronomy.

Meteors and hard targets produce coherent radar echoes. If measured with an interferometric radar system, these echoes can be used to determine the position of the target through finding the direction of arrival (DOA) of the incoming echo onto the radar. Depending on the spatial configuration of radar-receiving antennas and their individual gain patterns, there may be an ambiguity problem when determining the DOA of an echo. Radars that are theoretically ambiguity-free are known to still have ambiguities that depend on the total radar signal-to-noise ratio (SNR). In this study, we investigate robust methods which are easy to implement to determine the effect of ambiguities on any hard target DOA determination by interferometric radar systems. We apply these methods specifically to simulate four different radar systems measuring meteor head and trail echoes, using the multiple signal classification (MUSIC) DOA determination algorithm. The four radar systems are the Middle And Upper Atmosphere (MU) radar in Japan, a generic Jones 2.5 lambda specular meteor trail radar configuration, the Middle Atmosphere Alomar Radar System (MAARSY) radar in Norway and the Program of the Antarctic Syowa Mesosphere Stratosphere Troposphere Incoherent Scatter (PANSY) radar in the Antarctic. We also examined a slightly perturbed Jones 2.5 lambda configuration used as a meteor trail echo receiver for the PANSY radar. All the results are derived from simulations, and their purpose is to grant understanding of the behaviour of DOA determination. General results are as follows: there may be a region of SNRs where ambiguities are relevant; Monte Carlo simulation determines this region and if it exists; the MUSIC function peak value is directly correlated with the ambiguous region; a Bayesian method is presented that may be able to analyse echoes from this region; the DOA of echoes with SNRs larger than this region are perfectly determined; the DOA of echoes with SNRs smaller than this region completely fail to be determined; the location of this region is shifted based on the total SNR versus the channel SNR in the direction of the target; and asymmetric subgroups can cause ambiguities, even for ambiguity-free radars. For a DOA located at the zenith, the end of the ambiguous region is located at 17 dB SNR for the MU radar and 3 dB SNR for the PANSY radar. The Jones radars are usually used to measure specular trail echoes far from zenith. The ambiguous region for a DOA at 75.5 degrees elevation and 0 degrees azimuth ends at 12 dB SNR. Using the Bayesian method, it may be possible to analyse echoes down to 4 dB SNR for the Jones configuration when given enough data points from the same target. The PANSY meteor trail echo receiver did not deviate significantly from the generic Jones configuration. The MAARSY radar could not resolve arbitrary DOAs su degrees ciently well enough to determine a stable region. However, if the DOA search is restricted to 70 degrees elevation or above by assumption, stable DOA determination occurs above 15 dB SNR.

Meteor phenomena cause ionized plasmas that can be roughly divided into two distinctly different regimes: a dense and transient plasma region co-moving with the ablating meteoroid and a trail of diffusing plasma left in the atmosphere and moving with the neutral wind. Interferometric radar systems are used to observe the meteor trails and determine their positions and drift velocities. Depending on the spatial configuration of the receiving antennas and their individual gain patterns, the voltage response can be the same for several different plane wave directions of arrival (DOAs), thereby making it impossible to determine the correct direction. A low signal-to-noise ratio (SNR) can create the same effect probabilistically even if the system contains no theoretical ambiguities. Such is the case for the standard meteor trail echo data products of the Sodankyl Geophysical Observatory SKiYMET all-sky interferometric meteor radar. Meteor trails drift slowly enough in the atmosphere and allow for temporal integration, while meteor head echo targets move too fast. Temporal integration is a common method to increase the SNR of radar signals. For meteor head echoes, we instead propose to use direct Monte Carlo (DMC) simulations to validate DOA measurements. We have implemented two separate temporal integration methods and applied them to 2222 events measured by the Sodankyl meteor radar to simultaneously test the usefulness of such DMC simulations on cases where temporal integration is possible, validate the temporal integration methods, and resolve the ambiguous SKiYMET data products. The two methods are the temporal integration of the signal spatial correlations and matchedfilter integration of the individual radar channel signals. The results are compared to Bayesian inference using the DMC simulations and the standard SkiYMET data products. In the examined data set, 13% of the events were indicated as ambiguous. Out of these, 13% contained anomalous signals. In 95% of all ambiguous cases with a nominal signal, the three methods found one and the same output DOA, which was also listed as one of the ambiguous possibilities in the SkiYMET analysis. In all unambiguous cases, the results from all methods concurred.

We present an automated radar data analysis algorithm developed to calculate probability distributions of meteor- and meteoroid parameters for head echoes detected with the Middle and Upper atmosphere (MU) radar in Shigaraki, Japan. The algorithm utilizes direct Monte Carlo simulations of uncertainties, with Bayesian Markov-chain Monte Carlo estimation of meteor model parameters and N-body propagation of distributions to perform orbit determination. The implementation has been validated using raw data simulations and a comparison with previous analysis methods. The concepts are applicable on a wide range of possible head echo measurements with other radar systems. The generated probability distributions provide quantitative reliability, which enables improved statistical studies and investigating the origins of detected meteoroids. The methodology section is highly detailed in order for the methods to be reproducible and provide a solid reference foundation for future studies. One such study is presented in a companion paper called ‘High-altitude meteors detected by the interferometric MU radar’.

We have re-analysed part of the middle and upper atmosphere (MU) radar meteor head echo data set collected during 2009–2010 and confirmed the existence of a rare high-altitude radar meteor population reaching up to ∼150 km altitude. The number of detections decreases significantly as a function of initial altitude. Out of the total amount of 106 000 events, 74 had an initial altitude >130 km while four of those had an initial altitude >145 km. High-altitude radar meteor observations have been reported before, e.g. using the EISCAT VHF radar and the Jicamarca Radio Observatory. The main novelty of this study is that the observations were performed using methods that render the final data set unambiguous in direction of arrival together with rigorously tested analysis routines that were validated by noisy raw data simulations. Due to our experimental set-up the maximum detectable range was limited to 148 km. Hence, we cannot confirm or deny the existence of radar meteors above that altitude.

Radar observations can be used to obtain accurate orbital elements for near-Earth objects (NEOs) as a result of the very accurate range and range rate measureables. These observations allow the prediction of NEO orbits further into the future and also provide more information about the properties of the NEO population. This study evaluates the observability of NEOs with the EISCAT 3D 233 MHz 5 MW high-power, large-aperture radar, which is currently under construction. Three different populations are considered, namely NEOs passing by the Earth with a size distribution extrapolated from fireball statistics, catalogued NEOs detected with ground-based optical telescopes and temporarily captured NEOs, i.e. mini-moons. Two types of observation schemes are evaluated, namely the serendipitous discovery of unknown NEOs passing the radar beam and the post-discovery tracking of NEOs using a priori orbital elements. The results indicate that 60-1200 objects per year, with diameters D > 0.01 m, can be discovered. Assuming the current NEO discovery rate, approximately 20 objects per year can be tracked post-discovery near the closest approach to Earth. Only a marginally smaller number of tracking opportunities are also possible for the existing EISCAT ultra-high frequency (UHF) system. The mini-moon study, which used a theoretical population model, orbital propagation, and a model for radar scanning, indicates that approximately seven objects per year can be discovered using 8 %-16% of the total radar time. If all mini-moons had known orbits, approximately 80-160 objects per year could be tracked using a priori orbital elements. The results of this study indicate that it is feasible to perform routine NEO post-discovery tracking observations using both the existing EISCAT UHF radar and the upcoming EISCAT 3D radar. Most detectable objects are within 1 lunar distance (LD) of the radar. Such observations would complement the capabilities of the more powerful planetary radars that typically observe objects further away from Earth. It is also plausible that EISCAT 3D could be used as a novel type of an instrument for NEO discovery, assuming that a sufficiently large amount of radar time can be used. This could be achieved, for example by time-sharing with ionospheric and space-debris-observing modes.

We describe the use of radar beam-park experiments to characterize the space debris resulting from a recent fragmentation event, the deliberate demolition of the defunct Kosmos-1408 satellite. We identify the Kosmos-1408 fragments and present distribution of measurement parameters as well as proxy orbit parameters. We present and apply a novel technique to estimate the size of objects by matching the signal to noise ratio of the detection to the radiation pattern of the radar. With this method we estimate the size distribution of the debris cloud. We also demonstrate how a pair of beam-park observations can be used to perform a crude, yet seemingly reliable, initial orbit determination. Finally, we present followup observations ∼5 months after the fragmentation that show a still compact cloud of debris.