diff --git a/src/modules/simulation/gz_bridge/GZBridge.cpp b/src/modules/simulation/gz_bridge/GZBridge.cpp
index 3ef65e186f..8a93b8b378 100644
--- a/src/modules/simulation/gz_bridge/GZBridge.cpp
+++ b/src/modules/simulation/gz_bridge/GZBridge.cpp
@@ -410,6 +410,43 @@ void GZBridge::airPressureCallback(const gz::msgs::FluidPressure &msg)
 {
 	const uint64_t timestamp = hrt_absolute_time();
 
+	// To simulate atmospheric pressure drift, we use a time-discretised
+	// Ornstein-Uhlenbeck process (= integral of gaussian white noise with a
+	// linear stabilising feedback term). This has the advantage that we
+	// retain the statistical properties (stationary distribution, mixing
+	// time) regardless of dt.
+
+	// Ref: Gillespie, Daniel T.. (1996). Exact numerical simulation of the
+	// Ornstein-Uhlenbeck process and its integral. Physical Review E,
+	// 54(2), 2084–2091. doi:10.1103/PhysRevE.54.2084
+
+	const float dt = (float)(timestamp - _last_baro_pressure_drift_update) / 1_s;
+	const bool init = dt > 10;
+
+	// Parameterisation used in Gillespie 1996, but instead of c we use
+	// sigma_stationary - equivalent with c = 2 * sigma_stationary^2 / tau
+
+	// Relaxation time [sec]
+	const float tau = 3600.f * 24;
+
+	// Standard deviation of stationary distribution [Pa]
+	// 1000 Pa corresponds to about 80m of altitude error
+	const float sigma_stationary = 200;
+
+	const float mu = exp(-dt / tau);   // (3.3)
+	const float sigma_update = sigma_stationary * sqrtf(1 - mu * mu); // (3.4a)
+
+	if (init) {
+		// Sample from the stationary distribution to match long time behaviour
+		_baro_pressure_drift = sigma_stationary * generate_wgn();
+
+	} else {
+		// Update equation (3.5a)
+		_baro_pressure_drift = mu * _baro_pressure_drift + sigma_update * generate_wgn();
+	}
+
+	_last_baro_pressure_drift_update = timestamp;
+
 	device::Device::DeviceId id{};
 	id.devid_s.bus_type = device::Device::DeviceBusType::DeviceBusType_SIMULATION;
 	id.devid_s.devtype = DRV_BARO_DEVTYPE_BAROSIM;
@@ -420,7 +457,7 @@ void GZBridge::airPressureCallback(const gz::msgs::FluidPressure &msg)
 	report.timestamp = timestamp;
 	report.timestamp_sample = timestamp;
 	report.device_id = id.devid;
-	report.pressure = msg.pressure();
+	report.pressure = (float) msg.pressure() + _baro_pressure_drift;
 	report.temperature = this->_temperature;
 	_sensor_baro_pub.publish(report);
 }
diff --git a/src/modules/simulation/gz_bridge/GZBridge.hpp b/src/modules/simulation/gz_bridge/GZBridge.hpp
index 9f90f4dfea..8a58ae3566 100644
--- a/src/modules/simulation/gz_bridge/GZBridge.hpp
+++ b/src/modules/simulation/gz_bridge/GZBridge.hpp
@@ -193,6 +193,9 @@ private:
 	const float _vel_noise_density = 0.2f;      // Velocity noise process density
 	const float _vel_markov_time = 0.85f;       // Velocity Markov process coefficient
 
+	float _baro_pressure_drift{};
+	hrt_abstime _last_baro_pressure_drift_update;
+
 	DEFINE_PARAMETERS(
 		(ParamInt<px4::params::SIM_GPS_USED>) _sim_gps_used,
 		(ParamInt<px4::params::SIM_GZ_EN_LIDAR>) _sim_gz_en_lidar,