diff --git a/src/modules/simulation/sensor_gps_sim/SensorGpsSim.cpp b/src/modules/simulation/sensor_gps_sim/SensorGpsSim.cpp
index c6b94dcbf4..5bed55df26 100644
--- a/src/modules/simulation/sensor_gps_sim/SensorGpsSim.cpp
+++ b/src/modules/simulation/sensor_gps_sim/SensorGpsSim.cpp
@@ -116,11 +116,30 @@ void SensorGpsSim::Run()
 		vehicle_global_position_s gpos{};
 		_vehicle_global_position_sub.copy(&gpos);
 
-		double latitude = gpos.lat + math::degrees((double)generate_wgn() * 0.2 / CONSTANTS_RADIUS_OF_EARTH);
-		double longitude = gpos.lon + math::degrees((double)generate_wgn() * 0.2 / CONSTANTS_RADIUS_OF_EARTH);
-		double altitude = (double)(gpos.alt + (generate_wgn() * 0.5f));
+		// Correlated Markov process position noise (matching GZBridge model)
+		_gps_pos_noise_n = _pos_markov_time * _gps_pos_noise_n +
+				   _pos_random_walk * generate_wgn() * _pos_noise_amplitude;
 
-		Vector3f gps_vel = Vector3f{lpos.vx, lpos.vy, lpos.vz} + noiseGauss3f(0.06f, 0.077f, 0.158f);
+		_gps_pos_noise_e = _pos_markov_time * _gps_pos_noise_e +
+				   _pos_random_walk * generate_wgn() * _pos_noise_amplitude;
+
+		_gps_pos_noise_d = _pos_markov_time * _gps_pos_noise_d +
+				   _pos_random_walk * generate_wgn() * _pos_noise_amplitude * 1.5f;
+
+		const double latitude = gpos.lat + math::degrees((double)_gps_pos_noise_n / CONSTANTS_RADIUS_OF_EARTH);
+		const double longitude = gpos.lon + math::degrees((double)_gps_pos_noise_e / CONSTANTS_RADIUS_OF_EARTH);
+		const double altitude = (double)(gpos.alt + _gps_pos_noise_d);
+
+		_gps_vel_noise_n = _vel_markov_time * _gps_vel_noise_n +
+				   _vel_noise_density * generate_wgn() * _vel_noise_amplitude;
+
+		_gps_vel_noise_e = _vel_markov_time * _gps_vel_noise_e +
+				   _vel_noise_density * generate_wgn() * _vel_noise_amplitude;
+
+		_gps_vel_noise_d = _vel_markov_time * _gps_vel_noise_d +
+				   _vel_noise_density * generate_wgn() * _vel_noise_amplitude * 1.2f;
+
+		const Vector3f gps_vel = Vector3f{lpos.vx + _gps_vel_noise_n, lpos.vy + _gps_vel_noise_e, lpos.vz + _gps_vel_noise_d};
 
 		// device id
 		device::Device::DeviceId device_id;
diff --git a/src/modules/simulation/sensor_gps_sim/SensorGpsSim.hpp b/src/modules/simulation/sensor_gps_sim/SensorGpsSim.hpp
index 9c74fc6528..a02360917a 100644
--- a/src/modules/simulation/sensor_gps_sim/SensorGpsSim.hpp
+++ b/src/modules/simulation/sensor_gps_sim/SensorGpsSim.hpp
@@ -84,6 +84,22 @@ private:
 
 	perf_counter_t _loop_perf{perf_alloc(PC_ELAPSED, MODULE_NAME": cycle")};
 
+	// GPS Markov process noise state
+	float _gps_pos_noise_n{0.0f};
+	float _gps_pos_noise_e{0.0f};
+	float _gps_pos_noise_d{0.0f};
+	float _gps_vel_noise_n{0.0f};
+	float _gps_vel_noise_e{0.0f};
+	float _gps_vel_noise_d{0.0f};
+
+	// Gauss-Markov noise parameters, rate-corrected from GZBridge (30 Hz) to SIH (8 Hz)
+	static constexpr float _pos_noise_amplitude{0.8f};
+	static constexpr float _pos_random_walk{0.02f};
+	static constexpr float _pos_markov_time{0.76f};
+	static constexpr float _vel_noise_amplitude{0.05f};
+	static constexpr float _vel_noise_density{0.4f};
+	static constexpr float _vel_markov_time{0.54f};
+
 	DEFINE_PARAMETERS(
 		(ParamInt<px4::params::SIM_GPS_USED>) _sim_gps_used
 	)