Forecasting, and averting, major asteroid impacts: from science fiction to reality (shortened version)
By T. Bewley, B. Hanson, and A. Rosengren
Fossil records confirm that major asteroid collisions with Earth happen routinely, and will certainly happen again. Can we forecast such collisions with enough time to actually do something about them? UC San Diego researchers say yes.
Introduction. In engineering and applied science, it is common to estimate the evolving “state” of a physical system leveraging an imperfect model of its dynamics (often, several equations of the form f=ma, coupled appropriately, with added unknown “state disturbances” that disrupt the system evolution). This estimated state is updated from time to time based on incomplete measurements corrupted with some unknown “measurement noise” using Bayes’ rule. If the system of interest is linear, the solution to this problem is given by the customary Kalman filter; if the system is nonlinear and the uncertainty of the state sufficiently small, the solution to this problem is given by the extended Kalman filter, which is similar. In both cases, such estimation methods propagate the “central” or “most likely” trajectory of the system of interest through “phase space”, together with, effectively, a set of concentric ellipsoids forming an “uncertainty cloud” (aka a Gaussian distribution) about this most likely trajectory, indicating what the true state of the system might actually be at any given time, based in part on estimates of the intensities of both the state disturbances and the measurement noise. In short, the smaller the uncertainty cloud, the more reliable is the state estimate.
Non-Gaussian estimation. Our work focuses on the estimation of dynamic systems (that is, physical systems that evolve in time) for which the approach described above breaks down, because the system of interest is nonlinear and the uncertainty of the state is, at least at times, not small.
Figure 1. Visualization of the Lorenz attractor, the prototypical “chaotic” system, in which small perturbations of the system’s initial state lead to perturbed trajectories that eventually diverge exponentially. The black curve shown represents a single trajectory of the (simple, 3-state) Lorenz system from t=0 to t=1 over the 3-dimensional (3D) phase space visualizing the evolution in time of the state of the Lorenz system. The 3D “cloud” around t=0 represents Gaussian uncertainty of the initial state (that is, the initial state should be somewhere within this ellipsoidal cloud). This uncertainty cloud evolves in time, as shown in light blue at successive time intervals up to t=1, by which time the uncertainty cloud is strongly non-Gaussian (that is, no longer shaped like an ellipsoid).
Consider, for example, the evolution of the Lorenz equation, a simple 3-state nonlinear ordinary differential equation (ODE). At any moment, the 3 states of this system, {x,y,z}, may be represented as a point in a 3-dimensional (3D) phase space, as shown in Figure 1. This point moves in time as the system evolves. Let’s say at time t=0 there is an ellipsoidal, nearly spherical, uncertainty cloud about some initial state estimate, as shown. The model of the system can be used to march both the “central” state estimate in time, as illustrated by the black line, in addition to the “uncertainty cloud”, as shown at 5 later times in Figure 1. Since the Lorenz system is nonlinear and the state uncertainties are not small in this problem, the uncertainty cloud quickly becomes highly non-Gaussian (not ellipsoidal) for times t>0.
For simplicity, most folks who perform a calculation of how an uncertainty cloud evolves in this sort of nonlinear problem simply distribute thousands of “candidate” initial conditions within the initial (ellipsoidal) uncertainty cloud, each with equal probability assigned, then march each of the corresponding “candidate trajectories” in time. At any given later time, the value of these state “candidates” at that time can then be used to approximate the “uncertainty cloud” characterizing what the state actually is at that time. This approach, called a Particle Filter (PF), is conceptually quite simple. However, it is plagued by a “degeneracy” phenomenon: after applying several measurement updates, the probability associated with most candidate trajectories tends to diminish towards zero, and the probability associated with a few candidate trajectories increases, with their sum remaining unity. Those candidate trajectories with vanishing probability associated must eventually be “pruned” (eliminated) from the simulation, and those with increasing probability must eventually be “split” somehow in order to maintain resolution; it is this splitting process that is, in general, unsatisfactory (that is, ad hoc).
An alternative approach to track the evolution of the non-Gaussian uncertainty cloud of the 3-state Lorenz system, representing the possible values of this state over the 3D phase space shown in Figure 1, is to evolve a partial differential equation (PDE) known as the Fokker-Plank equation (FPE). It is numerically tractable to march this 3D PDE using existing computational methods on current-generation laptop/desktop computers, by discretizing phase space into a bunch of small “cells” (cubes), and propagating the evolution of the probability associated with each cell in time, simply by computing and applying a “flux” of probability from one cell to its neighbors at each timestep. Figure 1 in fact visualizes the result of such a computation.
GBEES: Exploiting Sparsity. Now, instead of discretizing the entire 3D volume illustrated in Figure 1 (or, the d-dimensional volume, with d>3, in harder problems), the key observation motivating our work is that, at any instant, the probability associated with almost all of the cells covering the domain of interest is nearly zero. Thus, the central idea implemented in our legacy reference on this subject, [1], is to make a list of only those “active cells” with nonzero probability at any given time, and their neighbors, and to only calculate and apply the flux of probability between neighboring cells in this list. This general approach is called Grid-based Bayesian Estimation Exploiting Sparsity (GBEES).
Extending from 3D to 6D. Non-Gaussian estimation problems of practical interest generally have d>3 state variables, and a corresponding d-dimensional phase space. Note that the number of cells in a computational grid grows exponentially with each added state dimension; the (difficult) challenge of extending our original work in 3D to such higher-dimensional problem is often called the curse of dimensionality. The key challenges in extending GBEES to problems in d>3 dimensions are threefold:
how to efficiently manage the list of active cells and their neighbors,
how to quickly eliminate all cells that aren’t actually needed from this list, and
how to accelerate the execution of the resulting algorithm on modern massively-parallel (GPU-based) computational architectures.
Our recent technical work, discussed in four major technical papers published over the last two years [2,3,4,5], has solved all three of these key challenges, as outlined more extensively here. Additionally, we have proposed and benchmarked effective new hybrid estimation strategies that switch from Kalman-based approaches to non-Gaussian estimation approaches, like GBEES, as necessary [6].
Application to spacecraft. The practical problems of interest now focusing our recent work relate to the evolution of the (3D) position and (3D) velocity of bodies moving around in our solar system under Newton’s law of universal gravitation; this problem thus has a 6D phase space (position & velocity), as indicated in Figures 2 and 3.
Figure 2. Simulation of an inclined orbit around Enceladus in a rotating (“synodic”) frame, where the rotation of the frame matches the speed at which Saturn and Enceladus rotate about their barycenter, approximating both orbits as circular.
Figure 3. At time t=0, the orbiter in Figure 2 is at apoapsis, the point in the orbit farthest from Enceladus; we here initialize, with Gaussian uncertainty, (grey) a Particle Filter (PF) simulation and (red) a variant of a Kalman Filter (above left). The dynamic model of the orbiter includes the gravity of Saturn and Enceladus. Both the PF and the Kalman filter variant are propagated using this force model for 5.95 hours until periapsis, the point closest to Enceladus. As seen (above right), the state uncertainty is now highly non-Gaussian, and the Kalman filter variant does not accurately represent it. In such settings, when new measurements are accounted for, the new GBEES estimation method works particularly well.
Application to predicting asteroid impacts. A related problem of particular interest to life on Earth is the motion of large asteroids (known in this context as near-Earth objects) through space, which if they collide with the Earth can lead to massive destruction and, possibly, another mass extinction event. This class of problems focuses specifically on highly “unlikely” events, way out in the “tail” of the associated (highly non-Gaussian) probability distributions. The odds that any given large asteroid will hit Earth, based on what we know many years in advance of such a collision, is generally quite small. However, there are lots of such asteroids, and the potential consequences of a single such collision with Earth is quite large indeed, as seen in fossil records. With a sufficiently early and accurate prediction of the probability of such events, it is possible to better prepare, and potentially to redirect the trajectory of an asteroid of concern with a relatively small ΔV (that is, a small “nudge”), thus averting potential disaster, as demonstrated in the Dart Asteroid Redirection Test. Accurate prediction of unlikely events out in the (non-Gaussian) tails of probability distributions, years in advance of any possible such collision, is essential for this to be done properly; the present work addresses this need.
One near-Earth object of particular interest, dubbed 2024 YR4, currently has (according to our calculations) a 4% chance of colliding with Earth’s moon on Dec 22, 2032. YR4 currently has a negligible probability of hitting Earth on that pass (an older estimate, made in Feb 2025, put this chance at as high as 3.1%). Given the proximity of the moon to the Earth, the reader can well appreciate the importance of getting such predictions right; if YR4 were to hit Earth in some future pass near Earth, the explosion would be equivalent, roughly, to that of 500 Hiroshima bombs.
YR4 will also (safely) pass, relatively close (within 5 million miles) to Earth on Dec 17, 2028; if as a species humans deemed YR4’s trajectory as an imminent threat to life on Earth (at this time, it is NOT), and if we were to attempt a redirection (“nudge”) of YR4’s orbit around the sun, that would be the ideal time to do it (that is, 4 years in advance of any potential collision). Our study of YR4’s potential collision with our moon on Dec 22, 2032, and what it would take to redirect it to avoid such a collision, better prepares us to refine our prediction (and, our asteroid redirection) infrastructure for the (many) future highly unlikely (yet, each potentially devastating) events of this type.
Postscript. If you made it this far in this (somewhat technical) article, kudos; if you seek even more technical details, see here. Science like this is difficult to get right (much more difficult than suggested in various related sensational movies, like Armageddon, Deep Impact, Don’t Look Up, Greenland). Rather, it takes attention to detail and years of focused development. When you do get it right, its real-world impact can be substantial, from successfully navigating the moons of the outer planets of our solar system in order to better understand physics and, possibly, the origins of life itself, to predicting and possibly averting major life-threatening asteroid collisions here on Earth. Science may, in the end, be the very thing that saves humanity from another major asteroid collision, or perhaps even from itself. Keep looking up.
[1] Bewley & Sharma (2012) Efficient grid-based Bayesian estimation of nonlinear low-dimensional systems with sparse non-Gaussian PDFs. Automatica 48, 1286.
[2] Hanson, Rosengren, & Bewley (2024) State Estimation of Chaotic Trajectories: A Higher-Dimensional, Grid-Based, Bayesian Approach to Uncertainty Propagation, AIAA 24-426.
[3] Hanson, Rosengren, Bewley, & Ely (2025) Non-Gaussian recursive Bayesian filtering for outer planetary orbilander navigation, AIAA 25-194.
[4] Hanson, Ely, Bewley, & Rosengren (2025) Bayesian Benchmarking of GBEES Applied to Outer Planet Orbiter Estimation, Journal of Guidance, Control, and Dynamics, DOI:10.2514/1.G009146.
[5] Hanson, Rubio, García-Gutiérrez, & Bewley (2025) GBEES-GPU: An efficient parallel GPU algorithm for high-dimensional nonlinear uncertainty propagation, Computer Physics Communications Computer Physics Communications 317, 109819.
[6] Hanson, Carton, Bewley, Ely, Rosengren (preprint) Hybrid, Ephemeris-Quality, Measurement-Free Estimation of the Potential 2024 YR4 Lunar Impact. Preprint.