# 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.