ekf2 wind: use noise spectral density for process noise tuning

The noise spectral density, NSD, (square root of power spectral density) is a
continuous-time parameter that makes the tuning independent from the EKF
prediction rate.
NSD corresponds to the rate at which the state uncertainty increases
when no measurements are fused into the filter.
Given that the current prediction rate of EKF2 is 100Hz, the
same tuning is obtained by dividing the std_dev legacy parameter by 10:
nsd = sqrt(std_dev^2 / 100Hz)

src/modules/ekf2/EKF/common.h

@@ -263,8 +263,8 @@ struct parameters {
 	float accel_bias_p_noise{1.0e-2f};      ///< process noise for IMU accelerometer bias prediction (m/sec**3)
 	float mage_p_noise{1.0e-3f};            ///< process noise for earth magnetic field prediction (Gauss/sec)
 	float magb_p_noise{1.0e-4f};            ///< process noise for body magnetic field prediction (Gauss/sec)
-	float wind_vel_p_noise{1.0e-1f};        ///< process noise for wind velocity prediction (m/sec**2)
-	const float wind_vel_p_noise_scaler{0.5f};      ///< scaling of wind process noise with vertical velocity
+	float wind_vel_nsd{1.0e-2f};        ///< process noise spectral density for wind velocity prediction (m/sec**2/sqrt(Hz))
+	const float wind_vel_nsd_scaler{0.5f};      ///< scaling of wind process noise with vertical velocity
 
 	float terrain_p_noise{5.0f};            ///< process noise for terrain offset (m/sec)
 	float terrain_gradient{0.5f};           ///< gradient of terrain used to estimate process noise due to changing position (m/m)

src/modules/ekf2/EKF/covariance.cpp

@@ -187,7 +187,7 @@ void Ekf::predictCovariance()
 		mag_B_sig = 0.0f;
 	}
 
-	float wind_vel_sig;
+	float wind_vel_nsd_scaled;
 
 	// Calculate low pass filtered height rate
 	float alpha_height_rate_lpf = 0.1f * dt; // 10 seconds time constant
@@ -195,10 +195,10 @@ void Ekf::predictCovariance()
 
 	// Don't continue to grow wind velocity state variances if they are becoming too large or we are not using wind velocity states as this can make the covariance matrix badly conditioned
 	if (_control_status.flags.wind && (P(22,22) + P(23,23)) < sq(_params.initial_wind_uncertainty)) {
-		wind_vel_sig = dt * math::constrain(_params.wind_vel_p_noise, 0.0f, 1.0f) * (1.0f + _params.wind_vel_p_noise_scaler * fabsf(_height_rate_lpf));
+		wind_vel_nsd_scaled = math::constrain(_params.wind_vel_nsd, 0.0f, 1.0f) * (1.0f + _params.wind_vel_nsd_scaler * fabsf(_height_rate_lpf));
 
 	} else {
-		wind_vel_sig = 0.0f;
+		wind_vel_nsd_scaled = 0.0f;
 	}
 
 	// compute noise variance for stationary processes
@@ -216,7 +216,7 @@ void Ekf::predictCovariance()
 	// body frame magnetic field states
 	process_noise.slice<3, 1>(19, 0) = sq(mag_B_sig);
 	// wind velocity states
-	process_noise.slice<2, 1>(22, 0) = sq(wind_vel_sig);
+	process_noise.slice<2, 1>(22, 0) = sq(wind_vel_nsd_scaled) * dt;
 
 	// assign IMU noise variances
 	// inputs to the system are 3 delta angles and 3 delta velocities

src/modules/ekf2/EKF2.cpp

@@ -72,7 +72,7 @@ EKF2::EKF2(bool multi_mode, const px4::wq_config_t &config, bool replay_mode):
 	_param_ekf2_acc_b_noise(_params->accel_bias_p_noise),
 	_param_ekf2_mag_e_noise(_params->mage_p_noise),
 	_param_ekf2_mag_b_noise(_params->magb_p_noise),
-	_param_ekf2_wind_noise(_params->wind_vel_p_noise),
+	_param_ekf2_wind_nsd(_params->wind_vel_nsd),
 	_param_ekf2_terr_noise(_params->terrain_p_noise),
 	_param_ekf2_terr_grad(_params->terrain_gradient),
 	_param_ekf2_gps_v_noise(_params->gps_vel_noise),

src/modules/ekf2/EKF2.hpp

@@ -377,8 +377,8 @@ private:
 		_param_ekf2_mag_e_noise,	///< process noise for earth magnetic field prediction (Gauss/sec)
 		(ParamExtFloat<px4::params::EKF2_MAG_B_NOISE>)
 		_param_ekf2_mag_b_noise,	///< process noise for body magnetic field prediction (Gauss/sec)
-		(ParamExtFloat<px4::params::EKF2_WIND_NOISE>)
-		_param_ekf2_wind_noise,	///< process noise for wind velocity prediction (m/sec**2)
+		(ParamExtFloat<px4::params::EKF2_WIND_NSD>)
+		_param_ekf2_wind_nsd,	///< process noise spectral density for wind velocity prediction (m/sec**2/sqrt(Hz))
 		(ParamExtFloat<px4::params::EKF2_TERR_NOISE>) _param_ekf2_terr_noise,	///< process noise for terrain offset (m/sec)
 		(ParamExtFloat<px4::params::EKF2_TERR_GRAD>)
 		_param_ekf2_terr_grad,	///< gradient of terrain used to estimate process noise due to changing position (m/m)

src/modules/ekf2/ekf2_params.c

@@ -320,15 +320,17 @@ PARAM_DEFINE_FLOAT(EKF2_MAG_B_NOISE, 1.0e-4f);
 PARAM_DEFINE_FLOAT(EKF2_MAG_E_NOISE, 1.0e-3f);
 
 /**
- * Process noise for wind velocity prediction.
+ * Process noise spectral density for wind velocity prediction.
+ *
+ * When unaided, the wind estimate uncertainty (1-sigma, in m/s) increases by this amount every second.
  *
  * @group EKF2
  * @min 0.0
  * @max 1.0
- * @unit m/s^2
+ * @unit m/s^2/sqrt(Hz)
  * @decimal 3
  */
-PARAM_DEFINE_FLOAT(EKF2_WIND_NOISE, 1.0e-1f);
+PARAM_DEFINE_FLOAT(EKF2_WIND_NSD, 1.0e-2f);
 
 /**
  * Measurement noise for gps horizontal velocity.