Download NASA dataset and trace flight by Kalman Filter by ThreeMonth03 · Pull Request #684 · solvcon/modmesh

ThreeMonth03 · 2026-03-01T11:36:47Z

Introduction

In this pull request, I download NASA fligth dataset. It includes observation data of flight, which is measured by Inertial Measurement Unit(IMU), Commercial LiDAR and ground truth.

Furthermore, I predict the position, velocity and direction of Center of Navigation(CON) with IMU data only, and the following output is the performance of baseline.

(base) threemonth03@threemonthwin:~/Downloads/modmesh$ PYTHONPATH=/home/threemonth03/Downloads/modmesh/modmesh /home/threemonth03/devenv/flavors/prime/usr/bin/python3 -m track.track_flight --no-earth-rotation
Kalman Filter Prediction Result:
final_con_pos_in_ecef = [-1330901.12447895 -5268174.02295982  3297021.64236977]
final_gt_con_pos_in_ecef = [-1387989.68147338 -5267172.39836541  3309312.46171108]
final_pos_error_ecef = [ 57088.55699443  -1001.62459441 -12290.81934131]
final_error_m = 58405.22948859141
final_quat_con_ecef = [-0.157174   -0.47091926  0.86318824  0.09185558]
final_gt_quat_con_ecef = [ 0.17784711  0.46345816 -0.86384828 -0.08569185]
final_attitude_error_deg = 2.6168453892731907

Last but not least, I also adjust the state with centrifugal force model and Coriolis force model, which can make our estimation better.

(base) threemonth03@threemonthwin:~/Downloads/modmesh$ make track
PYTHONPATH=/home/threemonth03/Downloads/modmesh/modmesh /home/threemonth03/devenv/flavors/prime/usr/bin/python3 -m track.track_flight
Kalman Filter Prediction Result:
final_con_pos_in_ecef = [-1336224.91707701 -5279162.81365069  3298133.01314272]
final_gt_con_pos_in_ecef = [-1387989.68147338 -5267172.39836541  3309312.46171108]
final_pos_error_ecef = [ 51764.76439637 -11990.41528528 -11179.44856836]
final_error_m = 54298.62762554346
final_quat_con_ecef = [-0.157174   -0.47091926  0.86318824  0.09185558]
final_gt_quat_con_ecef = [ 0.17784711  0.46345816 -0.86384828 -0.08569185]
final_attitude_error_deg = 2.6168453892731907

Implementation Method

First, I ask GPT-5.3-Codex to survey how to transform the attitude and how to interpolate the data, which is implemented in ThreeMonth03/nasa_data. After finding a decent baseline, I refactor code and rename variable bymyself. Last, I fill the Sphinx-style comment by GPT-5.3-Codex.

ThreeMonth03

@yungyuc Please review this pull request when you are available.

ThreeMonth03 · 2026-03-01T11:48:34Z

Makefile

+.PHONY: track
+NASA_DATASET_DIR := download/Flight1_Catered_Dataset-20201013
+NASA_DLC_CSV := $(NASA_DATASET_DIR)/Data/dlc.csv
+NASA_TRUTH_CSV := $(NASA_DATASET_DIR)/Data/truth.csv
+
+$(NASA_DLC_CSV) $(NASA_TRUTH_CSV) &:
+	@mkdir -p download
+	PYTHONPATH=$(MODMESH_ROOT)/modmesh $(WHICH_PYTHON) -m track.dataset
+
+track: $(NASA_DLC_CSV) $(NASA_TRUTH_CSV)
+	PYTHONPATH=$(MODMESH_ROOT)/modmesh $(WHICH_PYTHON) -m track.track_flight


We can reproduce the best experiment result by the command make track.

ThreeMonth03 · 2026-03-01T11:52:07Z

modmesh/track/npkalmanfilter.py

+class KalmanFilter:
+    """
+    Minimal linear Kalman filter implementation using NumPy.
+    """
+
+    def __init__(self, dim_x, dim_z):
+        """
+        Initialize filter dimensions and default matrices.
+
+        :param dim_x: State dimension.
+        :type dim_x: int
+        :param dim_z: Measurement dimension.
+        :type dim_z: int
+        :raises ValueError: If any dimension is non-positive.
+        """
+        if dim_x <= 0 or dim_z <= 0:
+            raise ValueError("dim_x and dim_z must be positive")
+
+        self.dim_x = dim_x
+        self.dim_z = dim_z
+
+        self.x = np.zeros(dim_x, dtype=np.float64)
+        self.F = np.eye(dim_x, dtype=np.float64)
+        self.P = np.eye(dim_x, dtype=np.float64)
+        self.Q = np.eye(dim_x, dtype=np.float64)
+        self.H = np.zeros((dim_z, dim_x), dtype=np.float64)
+        self.R = np.eye(dim_z, dtype=np.float64)
+
+    def predict(self, u=None, B=None):
+        """
+        Perform linear prediction step.
+
+        Implements:
+        ``x = F x + B u`` and ``P = F P F^T + Q``.
+
+        :param u: Optional control input.
+        :type u: numpy.ndarray or None
+        :param B: Optional control-input matrix.
+        :type B: numpy.ndarray or None
+        :return: Predicted state and covariance.
+        :rtype: tuple[numpy.ndarray, numpy.ndarray]
+        :raises ValueError: If ``u`` is provided but ``B`` is ``None``.
+        """
+        self.x = self.F @ self.x
+        if u is not None:
+            if B is None:
+                raise ValueError("B is required when u is provided")
+            self.x = self.x + B @ u
+        self.P = self.F @ self.P @ self.F.T + self.Q
+        return self.x, self.P
+
+    def update(self, z, H=None, R=None):
+        """
+        Perform linear measurement update step.
+
+        :param z: Measurement vector. If ``None``, update is skipped.
+        :type z: numpy.ndarray or None
+        :param H: Optional measurement matrix overriding ``self.H``.
+        :type H: numpy.ndarray or None
+        :param R: Optional measurement covariance overriding ``self.R``.
+        :type R: numpy.ndarray or None
+        :return: Updated state and covariance.
+        :rtype: tuple[numpy.ndarray, numpy.ndarray]
+        """
+        if z is None:
+            return self.x, self.P
+
+        z = np.asarray(z, dtype=np.float64).reshape(-1)
+        h = self.H if H is None else np.asarray(H, dtype=np.float64)
+        r = self.R if R is None else np.asarray(R, dtype=np.float64)
+
+        y = z - h @ self.x
+        s = h @ self.P @ h.T + r
+        k = self.P @ h.T @ np.linalg.inv(s)
+
+        self.x = self.x + k @ y
+
+        identity = np.eye(self.dim_x, dtype=np.float64)
+        i_kh = identity - k @ h
+        self.P = i_kh @ self.P @ i_kh.T + k @ r @ k.T
+
+        return self.x, self.P
+


I make a numpy based Kalman Filter to predict data now. I will use the modmesh.KalmanFilter in the later pull request.

ThreeMonth03 · 2026-03-01T11:56:18Z

modmesh/track/earth.py

+    @staticmethod
+    def gravity_ecef(pos_ecef):
+        """
+        Compute central gravity acceleration in ECEF frame.
+
+        :param pos_ecef: Position in ECEF coordinates, shape ``(3,)``.
+        :type pos_ecef: numpy.ndarray
+        :return: Gravity acceleration in m/s^2, shape ``(3,)``.
+        :rtype: numpy.ndarray
+        """
+        r = np.linalg.norm(pos_ecef)
+        return -Earth.MU_EARTH / (r ** 3) * pos_ecef


The adjustment of gravity is necessary. If we don't consider gravity, the error is huge.

PYTHONPATH=/home/threemonth03/Downloads/modmesh/modmesh /home/threemonth03/devenv/flavors/prime/usr/bin/python3 -m track.track_flight Kalman Filter Prediction Result: final_con_pos_in_ecef = [-2112100.18722017 -7828473.02794707 4914963.02325346] final_gt_con_pos_in_ecef = [-1387989.68147338 -5267172.39836541 3309312.46171108] final_pos_error_ecef = [ -724110.50574679 -2561300.62958166 1605650.56154238] final_error_m = 3108490.094146941 final_quat_con_ecef = [-0.157174 -0.47091926 0.86318824 0.09185558] final_gt_quat_con_ecef = [ 0.17784711 0.46345816 -0.86384828 -0.08569185] final_attitude_error_deg = 2.6168453892731907

yungyuc · 2026-03-01T14:09:41Z

Good job. The code will need a very different organization than modmesh.track, which should be reserved for features more general. The code specific to the NASA problem should be outside the namespace modmesh.

We will need more discussions before moving forward the code review. I am converting the PR to draft before the conclusion is drawn. But feel free to change code any time.

j8xixo12 · 2026-03-01T16:26:48Z

modmesh/track/track_flight.py

+    dv_ecef = dcm_ecef_imu @ imu_dvel_in_imu
+    accel_ecef = dv_ecef / dt
+    accel_ecef = accel_ecef + Earth.gravity_ecef(con_pos_in_ecef)
+    if use_earth_rotation:


@ThreeMonth03 Could you please try to compensate the centrifugal and tangential acceleration induced by IMU lever arm effect ?

You can find the equation in my note, i think this could reduce the final position error.

Download Nasa dataset and trace flight by Kalman Filter

8fa2d38

ThreeMonth03 commented Mar 1, 2026

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yungyuc assigned ThreeMonth03 Mar 1, 2026

yungyuc added the array Multi-dimensional array implementation label Mar 1, 2026

yungyuc marked this pull request as draft March 1, 2026 14:10

j8xixo12 reviewed Mar 1, 2026

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ThreeMonth03 mentioned this pull request Mar 3, 2026

Estimate the position and attitude of NASA flight using Kalman Filter #685

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Download NASA dataset and trace flight by Kalman Filter#684

Download NASA dataset and trace flight by Kalman Filter#684
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ThreeMonth03 commented Mar 1, 2026

Introduction

Implementation Method

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