In practice, an aircraft’s filed flight plan does not represent its true flown trajectory. Environmental disturbances and vehicle abnormalities all serve to deviate an aircraft from its nominal path, so strategic planners need a robust mechanism to estimate vehicle deviations. Underestimate that, and you get clear flight plans that end up too close to weather cells or restricted airspace. Overestimate it, and every flight plan looks so risky that the airspace can’t handle any real traffic.
Most existing methods for getting that estimate force a choice between two bad options: run a Monte Carlo simulation and get an honest answer at a computational cost that doesn’t scale, or use a simplified model and get an answer fast but so conservative it defeats the purpose of planning.
The framework in our technical paper, “Kalman Filtering Based Flight Management System Modeling for AAM Aircraft,” avoids that choice entirely. We repurpose a linear Kalman Filter, not as a way to estimate an aircraft’s position, but as a model of how a Flight Management System (FMS) corrects a flight back toward its planned trajectory. The result is an uncertainty model that runs in a fraction of a second, doesn’t require repeatedly simulating the same flight to produce an answer, and still lines up with real flight data.
The Problem with How Uncertainty Modeling Is Usually Done
Strategic planners for Advanced Air Mobility (AAM) need to check submitted flight plans against potential hazards before clearing them. Doing that well means predicting not just where an aircraft should be at a given time, but how much it might reasonably deviate from that plan.
Monte Carlo simulation provides the most direct way to get that answer. Simulate a flight hundreds or thousands of times, and the spread of outcomes tells you how much uncertainty to expect. It’s also the most computationally expensive method, counter to strategic planning services’ goals to evaluate large numbers of flight plans, which makes an approach that takes seconds per flight a real bottleneck when considering thousands of flights.
The alternatives are simplified models like the Light Propagation Algorithm (LPA), which assumes an aircraft’s uncertainty grows at a constant rate until a point on a flight segment, at which point the FMS is assumed to snap into full corrective control and decrease uncertainty. This is a computationally fast method, but a constant growth rate doesn’t adapt to environmental conditions like wind, and thus produces an unrealistic uncertainty profile. The discrete point where the uncertainty estimate flips from “no correction” to “full correction” also doesn’t reflect how modern FMS systems correct deviations gradually throughout a flight segment.
A New Way to Model FMS Behavior
Our approach starts from a simple reframing: a Kalman Filter is normally used to estimate an unknown state from noisy sensor readings, but its two-step structure, predict and then correct, happens to map almost exactly onto how an FMS behaves. The prediction step models an aircraft drifting off its flight plan due to unmodeled disturbances like wind. The update step models the FMS pulling the aircraft back toward its intended trajectory.
The key piece we add is what governs how much the filter trusts that correction at any given moment. Instead of snapping at a fixed point like the LPA method, we use a smooth transition between two states: no FMS correction and full FMS correction. As an aircraft progresses along a segment toward its next waypoint, the model shifts gradually from one state to the other, and the aircraft’s uncertainty grows and then contracts in step with that shift. The result is a continuous, realistic uncertainty profile instead of the sharp discontinuity that discrete threshold models produce.
Grounding the Model in Real Flight Data
AAM and UAM aircraft are not flying commercial routes yet, so there is no dataset of eVTOL flight plans versus actual eVTOL flight tracks to calibrate against. Instead, we used commercial IFR flights, specifically Boeing 737 and Airbus A3xx-series aircraft, as stand-ins. These aircraft run automated FMS systems that track filed flight plans closely, which is the same core behavior we expect from AAM vehicles with similar or more advanced avionics.
We pulled 100 FAA-filed flight plans and matched them against their real ADS-B tracks, keeping only the flights where the aircraft stayed near its filed route, which left a calibration set of 12 flights. We then tested the calibrated model against a separate, later set of 36 flights that the model had never seen. The actual arrival times landed within the model’s predicted range more often than a standard theoretical model would expect, erring slightly on the side of caution without being overly conservative.
The Results
We compared our method (KF-FMS) against Monte Carlo simulation and the older LPA-based approaches on the same flight route:
- Speed without sacrificing realism: KF-FMS reached a final position uncertainty of 90 meters in 0.15 seconds. Monte Carlo without FMS modeling took 9.2 seconds and still landed on a wildly unrealistic 212,788-meter uncertainty bound, since it never accounts for the aircraft correcting back toward its plan. Monte Carlo with FMS corrections produced a tighter bound (35.7 meters) but took 21.69 seconds, 145 times slower than KF-FMS.
- The old approach overstated the risk: switching from the old two-thirds activation threshold to continuous correction cut the final uncertainty estimate by 30 to 50%, without changing anything else about the model. The LPA method introduced a discontinuity and was a conservative estimate of the uncertainty.
- It passes the test on flights it never saw: of the 36 verification flights, 28 landed within the model’s predicted range. The flights that fell outside it had unusually large arrival deviations, 400 to 833 seconds off schedule on relatively short flights, consistent with rerouting or air traffic control delays that no flight-plan-based model could have anticipated.
This approach only earns its place if its key settings can be recalibrated independently for a different aircraft type or operational environment once real AAM flight data becomes available. That matters because the commercial aircraft used for calibration here fly for hours at altitudes well above where AAM aircraft will operate, so the current calibration is a starting point, not a permanent answer.
The core idea here, treating FMS correction as a gradual process inside a Kalman Filter instead of a discrete on-off switch, held up in a majority of the tests we ran it against. For strategic planning services that need to check flight plans against real-world hazards without overstating risk or taking too long to do it, that’s a meaningful win. Read the paper to learn more.