L35 Pre-flight

L35 Pre-flight#

Block 4: Aircraft Survivability and Mission Planning — Lesson 35: Fusion Under Threat Work this before L35. Pre-flights are never collected — in class, anyone may be cold-called to present any question at the board, and that recitation is the participation grade.

Assumed pre-class reading#

  • L14’s least-squares fusion (many receivers, one instant) and the seam: a collinear geometry leaves range unobservable.

  • L33’s bearing Jacobian row \(H = [-\Delta E\;\;\Delta N]/R^2\), which points across the line of sight.

  • The Jupyter Book Reading page for L35 — the scalar fusion rule \(1/\sigma^2 = 1/\sigma_1^2 + 1/\sigma_2^2\) and the gain \(K\), the Kalman filter’s predict/update, the EKF’s linearized bearing, the bearings-only observability conditions, and why maneuvering to observe costs exposure.

Quiz questions (5 items, ~5 minutes)#

Q1. (Multiple choice) Your EKF’s prior puts a pop-up emitter at a range of 40 km with \(\sigma_1 = 8\) km. A wingman’s cross-fix, independent of your prior, says 34 km with \(\sigma_2 = 8\) km. The fused range and its \(1\sigma\) are:

  • [ ] (a) 37 km, with \(\sigma = 8.0\) km

  • [ ] (b) 37 km, with \(\sigma = 5.7\) km

  • [ ] (c) 34 km, with \(\sigma = 5.7\) km

  • [ ] (d) 37 km, with \(\sigma = 4.0\) km

Q2. (Multiple choice) An EKF holds a round prior on a stationary pop-up emitter 60 km away: \(\sigma = 5\) km in every direction. One RWR bearing with \(\sigma_\theta = 1^\circ\) arrives. Right after that update, the \(1\sigma\) error ellipse is about:

  • [ ] (a) 1 km across the line of sight, still 5 km along it

  • [ ] (b) 1 km along the line of sight, and still 5 km across it

  • [ ] (c) 1 km in every direction, centered on the new estimate

  • [ ] (d) 5 km in every direction: one bearing updates nothing

Q3. (Mark all that apply) An aircraft has one RWR and no wingman, and runs an EKF on its own bearings. Mark every statement below that is true.

  • [ ] (a) Emitter stationary and off to one side of a straight own-ship leg: its range becomes observable as the bearing swings.

  • [ ] (b) Emitter stationary and dead ahead on the own-ship’s straight track: its range stays unobservable until the own-ship turns.

  • [ ] (c) Emitter moving at constant velocity, own-ship straight and steady: bearings good to \(0.1^\circ\) make its range observable.

  • [ ] (d) Emitter moving at constant velocity, own-ship straight and steady: tripling the RWR’s update rate makes its range observable.

  • [ ] (e) Emitter moving at constant velocity: a dogleg by the own-ship makes its range observable.

Q4. (Multiple choice) An own-ship flies a straight leg at constant speed while its EKF tracks a ship-borne radar that is also moving at constant velocity. However accurate and frequent the bearings, the filter never pins down the range. Why?

  • [ ] (a) The bearing Jacobian row becomes singular once the emitter moves, so the filter cannot form a gain.

  • [ ] (b) A scaled copy of the true track at another range gives identical bearings and also moves at constant velocity.

  • [ ] (c) The predict step erases range information between bearings unless process noise \(Q\) is added.

  • [ ] (d) The emitter’s bearing changes faster than the update rate, so each innovation wraps and cancels.

Q5. (Short answer) A pop-up SAM’s bearing has held nearly steady for a minute, and your EKF’s ellipse on it is a long sliver along the line of sight. (i) Why won’t another minute on the same leg fix it? (ii) Name one way to get its range with a maneuver and one without, and what each costs.

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