# L33 Pre-flight **Block 4: Aircraft Survivability and Mission Planning — Lesson 33: Information Geometry Under Threat** *Work this before L33. 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 crossing geometry (the cut angle, the seam, the PDOP tile and DOP map in the Geolocation Explorer) and Project 2's information matrix $\mathbf{J}$. - The Jupyter Book Reading page for L33 — one bearing as one row of information, the Fisher information $\mathbf{J}$ and the Cramér–Rao bound, reading the ellipse from eigenvalues, PDOP named ($\text{DRMS} = \text{PDOP}\cdot\bar R\cdot\sigma_\theta$ and $\sqrt{2}/\sin\beta$), seams, and range filling the gap. --- ## Quiz questions (5 items, ~5 minutes) **Q1.** (Multiple choice) Two of their passive ES sites sit 40 km apart on an east–west line. You fly 30 km due north of the midpoint between them, so their two bearings to you cross at about $67^\circ$. Along which direction does the **long** axis of the CRLB ellipse on your position lie? - [ ] (a) North–south, along the bisector of the two sites' lines of sight - [ ] (b) East–west, parallel to the baseline joining the two sites - [ ] (c) Neither — a symmetric pair always gives a circular ellipse - [ ] (d) Northeast–southwest, along the west site's line of sight --- **Q2.** (Multiple choice) The same two sites. Where on the map is their information matrix $\mathbf{J}$ **singular** ($\lambda_{\min} = 0$) — the seam, where they cannot fix you in one direction at all? - [ ] (a) On the perpendicular bisector of the baseline, where your two ranges are equal - [ ] (b) Only on the extensions beyond each site; between them the cut is a wide $180^\circ$ - [ ] (c) On the whole line through the two sites: beyond both ends and between them - [ ] (d) On the circle through both sites, where their two bearings cross at $90^\circ$ --- **Q3.** (Multiple choice) At your position, their network's $\mathbf{J}$ has eigenvalues $\lambda_1 = 0.04$ km⁻² (eigenvector pointing north) and $\lambda_2 = 0.64$ km⁻² (eigenvector pointing east). Which describes the $1\sigma$ CRLB ellipse? - [ ] (a) $a = 5.0$ km east–west, $b = 1.25$ km north–south; DRMS 5.15 km - [ ] (b) $a = 0.80$ km east–west, $b = 0.20$ km north–south; DRMS 0.82 km - [ ] (c) $a = 5$ km north–south, $b = 1.25$ km east–west; DRMS 6.25 km - [ ] (d) $a = 5.0$ km north–south, $b = 1.25$ km east–west; DRMS 5.15 km --- **Q4.** (Multiple choice) Two of their ES sites each see your stand-off jammer at the same range $\bar R = 50$ km, their bearings crossing at $\beta = 45^\circ$, each bearing good to $\sigma_\theta = 0.8^\circ$ ($1\sigma$). What are their PDOP and their DRMS on the jammer? - [ ] (a) PDOP 1.41, DRMS 0.99 km - [ ] (b) PDOP 2.00, DRMS 1.40 km - [ ] (c) PDOP 3.70, DRMS 2.58 km - [ ] (d) PDOP 2.00, DRMS 80.0 km --- **Q5.** (Short answer) Your stand-off jammer noise-jams two of their search radars, so each radar sees only a strobe on your azimuth (L17). In two or three sentences: what does that do to their $\mathbf{J}$ on the jammer, compared with those radars tracking an aircraft normally — and where would you orbit the jammer to make their fix on it worst?