The core challenge here is not about choosing between a Kalman filter or double exponential smoothing, it is about acknowledging that linear extrapolation on noisy data is fundamentally unreliable for predicting reversals. The current approach achieves direction accuracy that is statistically equivalent to a coin flip, which means the model is effectively guessing when crowd flow changes direction. That is not a tool you can trust for safety-critical decisions like estimating time-to-critical-threshold.
What this user needs is a method that respects the physics of crowd movement: velocity is persistent, acceleration is bounded, and direction changes are not random. A constant-velocity Kalman filter is the natural starting point because it explicitly models the state as position and velocity, then updates both as new frames arrive. The noise term in the measurement model can be set to match the observed ±10% variance, and the process noise can be tuned to allow gradual velocity changes without overreacting to every spike. This is not about theoretical elegance, it is about giving the filter a structural advantage over simple EMA smoothing, which has no memory of momentum.
The practical tradeoff is computational cost. A Kalman filter on per-zone head counts is cheap: a few matrix operations per frame, easily within CPU budget. The real constraint is that there is no training data, so the filter must self-tune online. That is doable by initializing the noise covariance with a reasonable guess and letting the filter's innovation sequence adjust it. For time-to-critical-threshold estimation, the filter's velocity estimate provides a clean slope, and the uncertainty from the covariance matrix lets you compute a confidence interval around the predicted crossing time. That is a concrete improvement over the current Gaussian-weighted linear fit, which has no mechanism to report uncertainty at all.
The user should also consider double exponential smoothing as a fallback: it handles trend and level separately, and it requires no matrix math. But it struggles with the same reversal problem because it is still a weighted average of past values, not a physical model. The Kalman filter is the right tool for this job, not because it is sophisticated, but because it matches the structure of the problem. The next step is to implement it, run it side by side with the current method, and compare MAE and direction accuracy on the same clips. If the filter cannot beat a coin flip on direction, then the data itself may be too noisy to predict reversals at all, and that is a finding worth acting on, not a failure to tune.