diff --git a/applications/pctaddnoise/pctaddnoise.py b/applications/pctaddnoise/pctaddnoise.py
new file mode 100644
index 0000000..67ff37f
--- /dev/null
+++ b/applications/pctaddnoise/pctaddnoise.py
@@ -0,0 +1,144 @@
+#!/usr/bin/env python
+import argparse
+import json
+import sys
+import itk
+from itk import PCT as pct
+import numpy as np
+import numpy.lib.recfunctions as rfn
+import hepunits
+
+
+def build_parser():
+    parser = pct.PCTArgumentParser(description="Add noise to ROOT data")
+    parser.add_argument(
+        "-i",
+        "--input",
+        help="Root phase space file of particles",
+        required=True,
+    )
+    parser.add_argument("-t", "--tree", help="Root tree name", required=True)
+    parser.add_argument("-o", "--output", help="Output file name", required=True)
+
+    parser.add_argument("--seed", help="Random number generator seed", type=int)
+    parser.add_argument(
+        "--noise-energy",
+        help="Standard deviation of the Gaussian noise on the energy",
+        type=float,
+    )
+    parser.add_argument(
+        "--noise-time",
+        help="Standard deviation of the Gaussian noise on the time",
+        type=float,
+    )
+
+    parser.add_argument(
+        "--verbose", "-v", help="Verbose execution", default=False, action="store_true"
+    )
+
+    tracker_uncertainty_group = parser.add_argument_group("Tracker uncertainty")
+    tracker_uncertainty_group.add_argument(
+        "--material-budget", help="Material budget x/x0", type=float, default=5e-3
+    )
+    tracker_uncertainty_group.add_argument(
+        "--noise-position",
+        help="Standard deviation of the tracker uncertainty (mm)",
+        type=float,
+    )
+    tracker_uncertainty_group.add_argument(
+        "--tracker-distance", help="Distance between trackers (cm)", type=float
+    )
+
+    return parser
+
+
+def get_sigma_sc(energy, x_over_x0, sp, dt):
+    proton_mass_c2 = 938.272013 * hepunits.MeV
+    betap = (energy + 2 * proton_mass_c2) * energy / (energy + proton_mass_c2)
+
+    # Equation (25) and (26) from [Krah et al, PMB, 2018]:
+    T = np.zeros((2, 2))
+    T[0, 1] = 1
+    T[1, 0] = -1 / dt
+    T[1, 1] = 1 / dt
+
+    sigma = (
+        13.6
+        * hepunits.MeV
+        / betap
+        * np.sqrt(x_over_x0)
+        * (1 + 0.038 * np.log(x_over_x0))
+    )
+    sigma_sc = np.zeros((energy.size, 2, 2))
+    sigma_sc[:, 1, 1] = sigma**2
+    return np.tile(sp**2 * T @ T.T, (energy.size, 1, 1)) + sigma_sc
+
+
+def add_tracker_uncertainty(
+    data, rng, material_budget, noise_position, tracker_distance
+):
+    e = data["KineticEnergy"]
+    sigma = get_sigma_sc(
+        e, material_budget, noise_position * hepunits.mm, tracker_distance * hepunits.cm
+    )
+    w, q = np.linalg.eig(np.linalg.inv(sigma))
+    xr = rng.standard_normal((e.size, 2, 2))
+    W = np.zeros((e.size, 2, 2))
+    W[:, 0, 0] = 1.0 / np.sqrt(w[:, 0])
+    W[:, 1, 1] = 1.0 / np.sqrt(w[:, 1])
+    dy_uncert = np.matmul(np.matmul(q, W), xr)
+    data["Position_X"] += dy_uncert[:, 0, 0]
+    data["Position_Y"] += dy_uncert[:, 0, 1]
+    data["Direction_X"] += dy_uncert[:, 1, 0]
+    data["Direction_Y"] += dy_uncert[:, 1, 1]
+
+
+def add_gaussian_noise(data, branch, rng, noise):
+    if noise is not None:
+        try:
+            data[branch] += rng.normal(scale=noise, size=len(data["KineticEnergy"]))
+        except KeyError:
+            print(
+                f"Warning: cannot apply noise of {noise} on branch {branch} as the branch does not exist in the Root file! Skipping.",
+                file=sys.stderr,
+            )
+
+
+def process(args_info: argparse.Namespace):
+    import uproot
+
+    rng = np.random.default_rng(args_info.seed)
+
+    if args_info.verbose:
+        print("Reading input Root file")
+    tree = uproot.open(args_info.input)[args_info.tree]
+    data = tree.arrays(library="np")
+
+    if args_info.verbose:
+        print("Applying noise…")
+
+    add_tracker_uncertainty(
+        data,
+        rng,
+        args_info.material_budget,
+        args_info.noise_position,
+        args_info.tracker_distance,
+    )
+
+    add_gaussian_noise(data, "KineticEnergy", rng, args_info.noise_energy)
+    add_gaussian_noise(data, "LocalTime", rng, args_info.noise_time)
+
+    if args_info.verbose:
+        print("Writing output Root file…")
+    with uproot.recreate(args_info.output) as output_file:
+        output_file[args_info.tree] = data
+
+
+def main(argv=None):
+    parser = build_parser()
+    args_info = parser.parse_args(argv)
+    process(args_info)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/applications/pctpairprotons/pctpairprotons.py b/applications/pctpairprotons/pctpairprotons.py
index 147f401..4fa9a3a 100644
--- a/applications/pctpairprotons/pctpairprotons.py
+++ b/applications/pctpairprotons/pctpairprotons.py
@@ -88,7 +88,7 @@ def verbose(message):
         def verbose(message):
             pass
 
-    measurement_column = "PreGlobalTime" if args_info.store_time else "KineticEnergy"
+    measurement_column = "LocalTime" if args_info.store_time else "KineticEnergy"
 
     def load_tree_as_df(root_file, tree_name):
 
diff --git a/gate/protonct.py b/gate/protonct.py
index 8ddc185..ff043c9 100644
--- a/gate/protonct.py
+++ b/gate/protonct.py
@@ -148,7 +148,7 @@ def add_detector(sim, name, translation):
             "EventID",
             "TrackID",
             "KineticEnergy",
-            "PreGlobalTime",
+            "LocalTime",
             "Position",
             "Direction",
         ]