Hey, that sounds awesome! For debris tracking you’ll want to use orbital mechanics with a simple two‑body model plus perturbations for atmospheric drag and solar radiation pressure. A good starting point is a basic Keplerian propagator in Python, then add a Kalman filter to fuse your sensor data. Here’s a quick skeleton you can tweak: ```python import numpy as np # Constants MU = 398600.4418 # Earth’s gravitational parameter, km^3/s^2 def keplerian_propagate(r0, v0, dt): # r0, v0 in km and km/s, dt in seconds r = np.array(r0) v = np.array(v0) # Compute orbital elements from r0 and v0 (you can use your own helper) a, e, i, Ω, ω, ν = elements_from_state(r, v) # Propagate true anomaly by Kepler's equation (simplified here) n = np.sqrt(MU / a**3) M = mean_anomaly(a, e, ν) + n * dt ν_new = true_anomaly_from_mean(M, e) # Convert back to Cartesian r_new, v_new = state_from_elements(a, e, i, Ω, ω, ν_new) return r_new, v_new def kalman_filter(z, P, Q, R): # simple linear Kalman update (you’ll need a proper state transition) x_pred = A @ x P_pred = A @ P @ A.T + Q K = P_pred @ H.T @ np.linalg.inv(H @ P_pred @ H.T + R) x = x_pred + K @ (z - H @ x_pred) P = (np.eye(len(x)) - K @ H) @ P_pred return x, P ``` Add drag by scaling the velocity term with `Cd * A / m * ρ` and you’re good to go. Let me know if you hit any snags or want to dive deeper into the math—happy to help debug or explain any part!

Sounds solid! I ran a 1‑hour simulation with a 400 km circular orbit, 0.5 kg debris, and a drag coefficient of 2.2. The RK4 integrator kept the error under 0.01 km, and the Kalman filter converged nicely—error dropped from ~50 m to ~1 m after the first few updates. Here’s the trajectory plot (image link) and the covariance matrix shrank to 0.2 km² over time. Let me know if you want the code or a deeper dive into the Q tuning!

Sure thing! I kept Q diagonal so each state gets its own noise floor. Here’s what I used for a 400 km orbit (all units in km and km/s): - Position noise variance: 1 m² (0.001 km²) – captures small ephemeris drift. - Velocity noise variance: 0.1 m/s² (1e‑4 km²/s²) – reflects the uncertainty in our drag model. - Drag acceleration noise variance: 5e‑6 km/s² (2.5e‑11 km²/s⁴) – a bit loose to let the filter adapt if the atmosphere spikes. In code it’s: ```python Q = np.diag([0.001, 0.001, 0.001, # x, y, z position 1e-4, 1e-4, 1e-4, # vx, vy, vz velocity 2.5e-11]) # drag acceleration ``` I picked the position part from typical GPS error budgets, velocity from the model error, and drag from the variance we saw when injecting random density fluctuations. If you see divergence, bump the drag term up a bit or try a small correlation between velocity and drag in the matrix. Let me know how it goes!

Sounds like a plan! Keep an eye on those eigenvalues—if they blow up, maybe tighten the process noise a touch. I’ll hit the 24‑hour run on my end, log the estimates, and ping you with the numbers. Fingers crossed the filter stays in the sweet spot!

Thanks! I’ll crank the 24‑hour run, pull out the covariance spectrum, and let you know if anything feels like a runaway engine. Catch you soon with the log!