feat(train): elevation from the barometer, its pressure kept raw (ADR 0030, D49)

11c: where a recording has GPS and the phone a barometer, the service
averages its readings over 5 s into the file's `b` lines and the
workout's new `pressure` series (tenths of a pascal). The page, Health
Connect's totals and the exported files take the fixes' altitudes from
it: the standard atmosphere's height at the pressure, levelled by the
median of GPS's altitudes less those; climbs count above 1 m. Workouts
recorded before keep GPS's altitudes; an older app skips the series.

Not tried on a phone yet.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Signed-off-by: Tizian 「ティツィアーン」 <raisondetredev@pm.me>

apps/train/halkyon_train_flutter/test/feature/workout/workout_analysis_test.dart

@@ -1,3 +1,5 @@
+import 'dart:math';
+
 import 'package:flutter_test/flutter_test.dart';
 import 'package:halkyon_train_flutter/src/feature/plan/model/plan.dart';
 import 'package:halkyon_train_flutter/src/feature/recording/data/recorded_workout.dart';
@@ -131,6 +133,67 @@ void main() {
     expect(analysis.elevationGainMetres, 12);
   });
 
+  group("the barometer's elevation (D49)", () {
+    /// The pressure, in tenths of a pascal, [metres] above the standard sea
+    /// level.
+    int pressureAt(num metres) =>
+        (1013250 * pow(1 - metres / 44330, 5.255)).round();
+
+    test("it gives the climb, its level the GPS altitudes' median", () {
+      // GPS wobbles by 6 m around 100 m; the air says a steady 20 m climb.
+      final noisy = [100, 106, 94, 106, 94, 106, 94, 106, 94, 106, 100];
+      final recording = Recording(
+        activity: Activity.running,
+        startedAt: start,
+        fixes: [
+          for (final (i, m) in noisy.indexed)
+            north(i * 10, i * 30, altitudeCm: m * 100),
+        ],
+        pressures: [
+          for (var i = 0; i <= 10; i++)
+            Pressure(time: at(i * 10), decipascals: pressureAt(500 + 2 * i)),
+        ],
+        endedAt: at(100),
+      );
+
+      final analysis = analysed(recording);
+      // Each 2 m counts: the barometer's noise is a fraction of a metre.
+      expect(analysis.elevationGainMetres, 20);
+      // 500 m by the standard air, moved by the median of GPS's altitudes
+      // less the barometer's (410 m).
+      expect(analysis.elevation.first.value, closeTo(90, 0.1));
+      expect(analysis.elevation.last.value, closeTo(110, 0.1));
+
+      final gps = analysed(
+        Recording(
+          activity: Activity.running,
+          startedAt: start,
+          fixes: recording.fixes,
+          endedAt: at(100),
+        ),
+      );
+      expect(gps.elevationGainMetres, greaterThan(20));
+    });
+
+    test('without GPS altitudes, it stands by the standard air', () {
+      final analysis = analysed(
+        Recording(
+          activity: Activity.running,
+          startedAt: start,
+          fixes: [for (var i = 0; i <= 4; i++) north(i * 10, i * 30)],
+          pressures: [
+            Pressure(time: at(0), decipascals: pressureAt(300)),
+            Pressure(time: at(40), decipascals: pressureAt(320)),
+          ],
+          endedAt: at(40),
+        ),
+      );
+      expect(analysis.elevationGainMetres, 20);
+      // Between two readings, the pressure is taken as it went.
+      expect(analysis.elevation[2].value, closeTo(310, 0.5));
+    });
+  });
+
   test('without altitudes it has no elevation gained, nor its chart', () {
     final analysis = analysed(run([north(0, 0), north(60, 200)]));