feat(docs): baro throttle compensation

Tools/baro_compensation/README.md

@@ -110,6 +110,11 @@ vs offline correction applied.
 **Online vs Offline Scatter** — Error vs thrust scatter for raw, online-
 corrected, and offline-corrected data.
 
+**CF Bandwidth Sensitivity** (range sensor required) — Sweeps `SENS_BAR_CF_BW`
+to show how the CF crossover frequency affects K identification and
+compensation quality. See [CF Bandwidth Tuning](#cf-bandwidth-tuning) for
+how to interpret this page.
+
 ## Manual Calibration Procedure
 
 If not using the online estimator, you can calibrate manually:
@@ -145,9 +150,43 @@ If not using the online estimator, you can calibrate manually:
 - **Online/offline K disagreement > 2 m**: The estimator may not have had
   enough excitation. Fly longer or with more altitude variation.
 
+## CF Bandwidth Tuning
+
+The default `SENS_BAR_CF_BW` (0.1 Hz) works well for most vehicles. Only
+adjust it if the online estimator consistently fails to converge or produces
+a K that disagrees with range-sensor ground truth.
+
+When a range sensor is present, the tool generates a **CF Bandwidth
+Sensitivity** page with two panels:
+
+**Left — K vs Bandwidth**: Shows how the identified K changes with CF
+crossover frequency. The green dashed line is the range-sensor ground truth K.
+
+- If the curve is **flat near ground truth** around the default (gray line):
+  the default bandwidth is fine, K identification is robust.
+- If the curve **crosses ground truth far from the default**: the default
+  bandwidth is producing a biased K. Consider setting `SENS_BAR_CF_BW` to
+  the "Best K match" bandwidth (blue dashed line).
+
+**Right — Compensated Error Std vs Bandwidth**: Shows the residual baro
+error standard deviation after applying the K identified at each bandwidth.
+Lower is better.
+
+- The green line is the theoretical minimum (range-sensor optimal PCOEF).
+- The orange line is the current PCOEF performance.
+- If the default bandwidth is already near the minimum: leave it alone.
+- If a different bandwidth gives significantly lower error std: consider
+  changing `SENS_BAR_CF_BW` to that value.
+
+In practice, the default is conservative and works across vehicle types.
+Raising the bandwidth makes K identification faster and more accurate when
+the IMU is good, but noisier when it's not. Lower bandwidth is more robust
+to IMU vibration but slower to converge.
+
 ## Parameters Reference
 
 | Parameter | Description | Range | Default |
 |-----------|-------------|-------|---------|
 | `SENS_BARO_PCOEF` | Baro altitude correction per unit vertical thrust [m] | -30 to 30 | 0.0 |
 | `SENS_BAR_AUTOCAL` | Bitmask: bit 0 = GNSS offset, bit 1 = online thrust cal | 0 to 3 | 1 |
+| `SENS_BAR_CF_BW` | CF crossover frequency for the online estimator [Hz] | 0.01 to 1.0 | 0.1 |

docs/en/SUMMARY.md

@@ -228,6 +228,7 @@
       - [Airspeed Validation](advanced_config/airspeed_validation.md)
       - [TFSlot Airspeed Sensor](sensor/airspeed_tfslot.md)
     - [Barometers](sensor/barometer.md)
+      - [Thrust Compensation](advanced_config/barometer_thrust_compensation.md)
     - [Distance Sensors \(Rangefinders\)](sensor/rangefinders.md)
       - [Ainstein US-D1 Standard Radar Altimeter](sensor/ulanding_radar.md)
       - [ARK DIST SR (CAN/UART)](dronecan/ark_dist.md)

docs/en/advanced_config/barometer_thrust_compensation.md

@@ -0,0 +1,116 @@
+# Barometer Thrust Compensation
+
+Propellers change the static pressure at the barometer sensor proportional to motor output.
+This creates a thrust-dependent altitude error that can reach several metres on small vehicles with the barometer close to the propellers.
+The direction and magnitude depend on sensor placement relative to the propellers.
+
+PX4 can compensate for this error by applying a correction proportional to the vertical thrust setpoint:
+
+```
+corrected_baro_alt = raw_baro_alt + SENS_BARO_PCOEF * |thrust_z|
+```
+
+where `thrust_z` is the Z body-axis component of `vehicle_thrust_setpoint` (negative for upward thrust in FRD frame).
+
+The compensation parameter [SENS_BARO_PCOEF](../advanced_config/parameter_reference.md#SENS_BARO_PCOEF) can be identified automatically during flight or manually from a flight log.
+
+::: info
+This feature compensates for _propwash-induced_ pressure error, which depends on motor output.
+For _airspeed-induced_ static pressure error (due to vehicle forward motion), see [Static Pressure Buildup](../advanced_config/static_pressure_buildup.md).
+:::
+
+## Online Calibration (Recommended)
+
+The online estimator identifies `SENS_BARO_PCOEF` automatically during flight and saves the result on disarm.
+
+### How It Works
+
+A complementary filter (CF) fuses barometer altitude with double-integrated accelerometer data at a very low crossover frequency (default 0.1 Hz).
+The CF trusts the accelerometer for fast altitude changes and the barometer for slow drift, so the CF residual (baro minus accel prediction) isolates thrust-correlated pressure error while rejecting real altitude changes.
+
+A Recursive Least Squares (RLS) estimator then fits the linear model `residual = K * thrust + bias` to identify the gain K.
+Once the estimate converges (stable K, low variance, sufficient thrust excitation), K is locked and saved to `SENS_BARO_PCOEF` on disarm.
+
+The estimator refines the parameter over subsequent flights — each flight corrects for whatever residual error remains after the previous calibration.
+
+### Setup
+
+1. Set [SENS_BAR_AUTOCAL](../advanced_config/parameter_reference.md#SENS_BAR_AUTOCAL) to **3** (enables both GNSS altitude calibration and thrust compensation).
+2. Fly normally for at least 60 seconds with some altitude variation.
+3. On disarm, the estimated `SENS_BARO_PCOEF` is saved automatically if the estimator converged.
+4. Check convergence after flight:
+   - In the console: `baro_thrust_estimator status`
+   - In a log: look at the `baro_thrust_estimate` topic — `converged` should be true.
+
+The estimator uses several convergence gates before saving:
+
+| Gate | Threshold | Purpose |
+|------|-----------|---------|
+| Minimum flight time | 30 s | Allow RLS to settle |
+| K variance (P[0][0]) | < 3.0 | Parameter estimate is precise |
+| Prediction error | Low absolute or relative | Model fits the data |
+| Thrust excitation | std > 0.05 | Enough signal to identify K |
+| K stability | Stable for 10 s | Estimate is not drifting |
+| Hold time | 10 s | Convergence is sustained |
+
+::: tip
+Altitude changes during hover provide the thrust excitation the estimator needs.
+Constant-thrust hover with no altitude variation will not converge.
+:::
+
+### Parameters
+
+| Parameter | Default | Description |
+|-----------|---------|-------------|
+| [SENS_BARO_PCOEF](../advanced_config/parameter_reference.md#SENS_BARO_PCOEF) | 0.0 | Baro altitude correction per unit vertical thrust \[m\]. Identified by the estimator or set manually. |
+| [SENS_BAR_AUTOCAL](../advanced_config/parameter_reference.md#SENS_BAR_AUTOCAL) | 1 | Bitmask: bit 0 = GNSS altitude offset, bit 1 = online thrust compensation. Set to 3 for both. |
+| [SENS_BAR_CF_BW](../advanced_config/parameter_reference.md#SENS_BAR_CF_BW) | 0.1 | CF crossover frequency \[Hz\]. Lower = more conservative, higher = faster identification but noisier. |
+
+### Soft Guards
+
+The estimator pauses RLS updates (while keeping the CF running) when:
+
+- Vertical speed exceeds 2 m/s
+- Horizontal speed exceeds 5 m/s
+
+This prevents high-speed flight dynamics from corrupting the estimate.
+Once converged, the RLS is frozen entirely to prevent ground-effect contamination during landing.
+
+## Manual Calibration
+
+If you prefer not to use the online estimator, you can identify `SENS_BARO_PCOEF` from a flight log using a range sensor as ground truth.
+
+1. Set `SENS_BARO_PCOEF` to 0 (disable existing compensation).
+2. Fly a hover at 2-5 m AGL for at least 60 seconds with gentle altitude changes. A downward-facing range sensor must be installed.
+3. Run the analysis script on the log:
+   ```sh
+   python3 Tools/baro_compensation/baro_thrust_calibration.py <path/to/log.ulg>
+   ```
+4. Apply the recommended `SENS_BARO_PCOEF` value.
+5. Fly again and re-run the script to verify the compensation.
+
+The script automatically selects an analysis mode based on available data:
+
+| Mode | Data Required | Output |
+|------|--------------|--------|
+| Estimator review | Online estimator logged | K convergence, residual analysis |
+| Full validation | Estimator + range sensor | Cross-validation of online vs offline K |
+| Standalone calibration | Range sensor only | Recommended PCOEF from least-squares fit |
+
+## Interpreting Results
+
+| Metric | Good | Marginal | Poor |
+|--------|------|----------|------|
+| Thrust correlation \|r\| | > 0.6 | 0.3 - 0.6 | < 0.3 |
+| Model R^2 | > 0.3 | 0.1 - 0.3 | < 0.1 |
+| Compensated \|r\| | < 0.2 | 0.2 - 0.4 | > 0.4 |
+
+- **Low R^2**: Thrust is not the dominant baro error source. Check for thermal drift, ground effect, or sensor placement issues.
+- **Online/offline K disagreement > 2 m**: The estimator may need more excitation. Fly longer or with more altitude variation.
+
+## See Also
+
+- [Static Pressure Buildup](../advanced_config/static_pressure_buildup.md) — airspeed-induced barometer error
+- [Compass Power Compensation](../advanced_config/compass_power_compensation.md) — analogous compensation for magnetometer
+- [Sensor Thermal Compensation](../advanced_config/sensor_thermal_calibration.md) — temperature-induced sensor error
+- [Using PX4's Navigation Filter (EKF2)](../advanced_config/tuning_the_ecl_ekf.md) — EKF2 height fusion configuration

docs/en/advanced_config/index.md

@@ -22,6 +22,7 @@ This topic lists configuration topics that are not particularly vehicle specific
 - [Compass Power Compensation](../advanced_config/compass_power_compensation.md)
 - [Advanced Controller Orientation](../advanced_config/advanced_flight_controller_orientation_leveling.md)
 - [Static Pressure Buildup](../advanced_config/static_pressure_buildup.md)
+- [Barometer Thrust Compensation](../advanced_config/barometer_thrust_compensation.md)
 
 ## Serial port/Ethernet configuration
 

src/modules/baro_thrust_estimator/baro_thrust_cf_rls.cpp

@@ -186,8 +186,8 @@ void BaroThrustCfRls::RlsEstimator::update(float residual, float thrust, float d
 	const float e = residual - (theta[0] * phi[0] + theta[1] * phi[1]);
 
 	const float Pphi[2] = {
-		P[0][0] * phi[0] + P[0][1] * phi[1],
-		P[1][0] * phi[0] + P[1][1] * phi[1]
+		P[0][0] *phi[0] + P[0][1] *phi[1],
+		P[1][0] *phi[0] + P[1][1] *phi[1]
 	};
 
 	const float phiPphi = phi[0] * Pphi[0] + phi[1] * Pphi[1];