GPS Noise Computation

[rafaeljer]

I have some doubts regarding how GPS noise is being computed.

PX4-SITL_gazebo-classic/src/gazebo_gps_plugin.cpp

Lines 262 to 272 in f754540

	if (gps_noise_) {
	noise_gps_pos_.X() = gps_xy_noise_density_ * sqrt(dt) * randn_(rand_);
	noise_gps_pos_.Y() = gps_xy_noise_density_ * sqrt(dt) * randn_(rand_);
	noise_gps_pos_.Z() = gps_z_noise_density_ * sqrt(dt) * randn_(rand_);
	noise_gps_vel_.X() = gps_vxy_noise_density_ * sqrt(dt) * randn_(rand_);
	noise_gps_vel_.Y() = gps_vxy_noise_density_ * sqrt(dt) * randn_(rand_);
	noise_gps_vel_.Z() = gps_vz_noise_density_ * sqrt(dt) * randn_(rand_);
	random_walk_gps_.X() = gps_xy_random_walk_ * sqrt(dt) * randn_(rand_);
	random_walk_gps_.Y() = gps_xy_random_walk_ * sqrt(dt) * randn_(rand_);
	random_walk_gps_.Z() = gps_z_random_walk_ * sqrt(dt) * randn_(rand_);
	}

Noise density for XY has, as unit, (m) / sqrt(hz) and the noise has as unit (m).

PX4-SITL_gazebo-classic/include/gazebo_gps_plugin.h

Line 57 in f754540

static constexpr double kDefaultGpsXYNoiseDensity = 2.0e-4; // (m) / sqrt(hz)

So, by the current formula, noise_gps_pos_.X() = (m) / sqrt(hz) * (1/sqrt(Hz)) = (m) / (Hz).

So, it would make me sense that the formula divides noise density by sqrt(df) [sqrt(s)], so that the result is in (m) instead of multiplying:
noise_gps_pos_.X() = ((m) / sqrt(hz)) / (1/sqrt(Hz)) = (m)

The formula I referred is also used in other places of the code, like here

PX4-SITL_gazebo-classic/src/gazebo_imu_plugin.cpp

Line 198 in f754540

double sigma_g_d = 1 / sqrt(dt) * imu_parameters_.gyroscope_noise_density;

If you could clarify, I would appreciate.

[Jaeyoung-Lim]

@rafaeljer I think you may be right. If you want to make a PR to make it more correct, it would be greatly appreciated