Create accelerations.py

accelerations.py

@@ -0,0 +1,151 @@
+import math
+
+import numpy as np
+
+
+def smooth_derivative(t_in, v_in):
+ #
+ # Function to compute a smooth estimation of a derivative.
+ # [REF: http://holoborodko.com/pavel/numerical-methods/numerical-derivative/smooth-low-noise-differentiators/]
+ #
+
+ # Configuration
+ #
+ # Derivative method: two options: 'smooth' or 'centered'. Smooth is more conservative
+ # but helps to supress the very noisy signals. 'centered' is more agressive but more noisy
+ method = "smooth"
+
+ t = t_in.copy()
+ v = v_in.copy()
+
+ # (0) Prepare inputs
+
+ # (0.1) Time needs to be transformed to seconds
+ try:
+ for i in range(0, t.size):
+ t.iloc[i] = t.iloc[i].total_seconds()
+ except:
+ pass
+
+ t = np.array(t)
+ v = np.array(v)
+
+ # (0.1) Assert they have the same size
+ assert t.size == v.size
+
+ # (0.2) Initialize output
+ dvdt = np.zeros(t.size)
+
+ # (1) Manually compute points out of the stencil
+
+ # (1.1) First point
+ dvdt[0] = (v[1] - v[0]) / (t[1] - t[0])
+
+ # (1.2) Second point
+ dvdt[1] = (v[2] - v[0]) / (t[2] - t[0])
+
+ # (1.3) Third point
+ dvdt[2] = (v[3] - v[1]) / (t[3] - t[1])
+
+ # (1.4) Last points
+ n = t.size
+ dvdt[n - 1] = (v[n - 1] - v[n - 2]) / (t[n - 1] - t[n - 2])
+ dvdt[n - 2] = (v[n - 1] - v[n - 3]) / (t[n - 1] - t[n - 3])
+ dvdt[n - 3] = (v[n - 2] - v[n - 4]) / (t[n - 2] - t[n - 4])
+
+ # (2) Compute the rest of the points
+ if method == "smooth":
+ c = [5.0 / 32.0, 4.0 / 32.0, 1.0 / 32.0]
+ for i in range(3, t.size - 3):
+ for j in range(1, 4):
+ if (t[i + j] - t[i - j]) == 0:
+ dvdt[i] += 0
+ else:
+ dvdt[i] += (
+ 2 * j * c[j - 1] * (v[i + j] - v[i - j]) / (t[i + j] - t[i - j])
+ )
+ elif method == "centered":
+ for i in range(3, t.size - 2):
+ for j in range(1, 4):
+ if (t[i + j] - t[i - j]) == 0:
+ dvdt[i] += 0
+ else:
+
+ dvdt[i] = (v[i + 1] - v[i - 1]) / (t[i + 1] - t[i - 1])
+
+ return dvdt
+
+
+def truncated_remainder(dividend, divisor):
+ divided_number = dividend / divisor
+ divided_number = (
+ -int(-divided_number) if divided_number < 0 else int(divided_number)
+ )
+
+ remainder = dividend - divisor * divided_number
+
+ return remainder
+
+
+def transform_to_pipi(input_angle):
+ pi = math.pi
+ revolutions = int((input_angle + np.sign(input_angle) * pi) / (2 * pi))
+
+ p1 = truncated_remainder(input_angle + np.sign(input_angle) * pi, 2 * pi)
+ p2 = (
+ np.sign(
+ np.sign(input_angle)
+ + 2
+ * (
+ np.sign(
+ math.fabs(
+ (truncated_remainder(input_angle + pi, 2 * pi)) / (2 * pi)
+ )
+ )
+ - 1
+ )
+ )
+ ) * pi
+
+ output_angle = p1 - p2
+
+ return output_angle, revolutions
+
+
+def remove_acceleration_outliers(acc):
+ acc_threshold_g = 7.5
+ if math.fabs(acc[0]) > acc_threshold_g:
+ acc[0] = 0.0
+
+ for i in range(1, acc.size - 1):
+ if math.fabs(acc[i]) > acc_threshold_g:
+ acc[i] = acc[i - 1]
+
+ if math.fabs(acc[-1]) > acc_threshold_g:
+ acc[-1] = acc[-2]
+
+ return acc
+
+
+def compute_accelerations(telemetry):
+ v = np.array(telemetry["Speed"]) / 3.6
+ lon_acc = smooth_derivative(telemetry["Time"], v) / 9.81
+
+ dx = smooth_derivative(telemetry["Distance"], telemetry["X"])
+ dy = smooth_derivative(telemetry["Distance"], telemetry["Y"])
+
+ theta = np.zeros(dx.size)
+ theta[0] = math.atan2(dy[0], dx[0])
+ for i in range(0, dx.size):
+ theta[i] = (
+ theta[i - 1] + transform_to_pipi(math.atan2(dy[i], dx[i]) - theta[i - 1])[0]
+ )
+
+ kappa = smooth_derivative(telemetry["Distance"], theta)
+ lat_acc = v * v * kappa / 9.81
+
+ # Remove outliers
+ lon_acc = remove_acceleration_outliers(lon_acc)
+ lat_acc = remove_acceleration_outliers(lat_acc)
+
+ return np.round(lon_acc, 2), np.round(lat_acc, 2)