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)