Address PR comments - code cleanup
jenniferoum
parent
593beed1e1
commit
880bd0cf90
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@ -16,7 +16,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 13,
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"execution_count": 68,
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"metadata": {},
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"outputs": [
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{
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@ -33,16 +33,228 @@
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},
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{
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"cell_type": "code",
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"execution_count": 14,
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"execution_count": 69,
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"import pandas as pd\n",
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"import progressbar\n",
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"import pandas as pd\n",
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"import matplotlib.pyplot as plt\n",
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"import math\n",
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"\n",
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"from gtsam import findExampleDataFile\n",
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"import gtsam\n",
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"from gtsam import findExampleDataFile, Rot3\n",
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"\n",
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"from EqF import formatCSV, blockDiag, repBlock, sim\n"
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"from EqF import *\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 70,
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"metadata": {},
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"outputs": [],
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"source": [
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"def formatCSV(df): # pass the dataframe in to this function and get \"data_list\" as an output\n",
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" \"\"\"Read data from csv file formatted as follows:\n",
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"\n",
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" | -------------------------------------------------------------------------------------------- |\n",
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" | t: time |\n",
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" | -------------------------------------------------------------------------------------------- |\n",
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" | q_x, q_y, q_z, q_w: Quaternion representing the attitude |\n",
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" | -------------------------------------------------------------------------------------------- |\n",
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" | b_x, b_y, b_z: Gyro bias |\n",
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" | -------------------------------------------------------------------------------------------- |\n",
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" | cq_x_0, cq_yv, cq_z_0, cq_w_0: Quaternion representing the first calibration |\n",
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" | ... |\n",
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" | cq_x_n, cq_y_n, cq_z_n, cq_w_n: Quaternion representing the last calibration |\n",
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" | -------------------------------------------------------------------------------------------- |\n",
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" | w_x, w_y, w_z: Gyro measurements |\n",
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" | -------------------------------------------------------------------------------------------- |\n",
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" | std_w_x, std_w_x, std_w_z: Gyro measurements noise standard deviation |\n",
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" | -------------------------------------------------------------------------------------------- |\n",
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" | std_b_x, std_b_x, std_b_z: Gyro bias random walk standard deviation |\n",
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" | -------------------------------------------------------------------------------------------- |\n",
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" | y_x_0, y_y_0, y_z_0: Direction measurement in sensor frame associated to calibration state 0 |\n",
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" | ... |\n",
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" | y_x_n, y_y_n, y_z_n: Direction measurement in sensor frame associated to calibration state n |\n",
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" | y_x_n+1, y_y_n+1, y_z_n+1: Direction measurement in sensor frame from calibrated sensor |\n",
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" | ... |\n",
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" | y_x_m, y_y_m, y_z_m: Direction measurement in sensor frame from calibrated sensor |\n",
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" | -------------------------------------------------------------------------------------------- |\n",
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" | std_y_x_0, std_y_y_0, std_y_z_0: Standard deviation of direction measurement y_0 |\n",
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" | ... |\n",
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" | std_y_x_m, std_y_y_m, std_y_z_m: Standard deviation of direction measurement y_m |\n",
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" | -------------------------------------------------------------------------------------------- |\n",
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" | d_x_0, d_y_0, d_z_0: Known direction in global frame associated to direction measurement 0 |\n",
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" | ... |\n",
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" | d_x_m, d_y_m, d_z_m: Known direction in global frame associated to direction measurement m |\n",
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" | -------------------------------------------------------------------------------------------- |\n",
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"\n",
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" NaN cell means that value is not present at that time\n",
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"\n",
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" Max allowd n = 5\n",
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" Max allowd m = 10\n",
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"\n",
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" :param pname: path name\n",
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" \"\"\"\n",
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"\n",
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" # read .csv file into pandas dataframe\n",
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" df = df.reset_index()\n",
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"\n",
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" # Define data_list as list\n",
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" data_list = []\n",
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" last_timestamp = df.t[0]\n",
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"\n",
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" # Check for existence of bias ground-truth into loaded data\n",
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" bias_exist = False\n",
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" if {'b_x', 'b_y', 'b_z'}.issubset(df.columns):\n",
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" bias_exist = True\n",
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"\n",
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" # Check for existence of calibration ground-truth (yaw, pitch, roll angles) into loaded data\n",
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" cal_exist = False\n",
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" n_cal = 0\n",
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" for i in range(6):\n",
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" if {'cq_x_' + str(i), 'cq_y_' + str(i), 'cq_z_' + str(i), 'cq_w_' + str(i)}.issubset(df.columns):\n",
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" cal_exist = True\n",
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" n_cal = i+1\n",
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"\n",
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" # Check for existence of direction measurements\n",
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" n_meas = 0\n",
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" for i in range(11):\n",
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" if {'y_x_' + str(i), 'y_y_' + str(i), 'y_z_' + str(i)}.issubset(df.columns):\n",
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" n_meas = i + 1\n",
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"\n",
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" for index, row in df.iterrows():\n",
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"\n",
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" # Load timestamps and record dt\n",
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" t = float(row['t'])\n",
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" dt = t - last_timestamp\n",
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"\n",
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" # Skip data_list if dt is smaller than a micro second\n",
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" if dt < 1e-6:\n",
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" continue\n",
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"\n",
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" last_timestamp = t\n",
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"\n",
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" # Load groundtruth values\n",
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" quat = np.array([float(row['q_x']), float(row['q_y']), float(row['q_z']), float(row['q_w'])])\n",
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"\n",
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" R = Rot3(gtsam.Rot3.Quaternion(float(row['q_w']), float(row['q_x']), float(row['q_y']), float(row['q_z'])).matrix())\n",
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"\n",
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" # Load Gyro biases\n",
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" if bias_exist:\n",
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" b = np.array([float(row['b_x']), float(row['b_y']), float(row['b_z'])]).reshape(3,)\n",
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" else:\n",
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" b = np.zeros(3)\n",
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"\n",
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" # Load GNSS calibration\n",
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" S = []\n",
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" if cal_exist:\n",
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" for i in range(n_cal):\n",
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" cal = np.array([float(row['cq_x_' + str(i)]), float(row['cq_y_' + str(i)]), float(row['cq_z_' + str(i)]), float(row['cq_w_' + str(i)])])\n",
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" S.append(Rot3(gtsam.Rot3.Quaternion(float(row['cq_w_' + str(i)]), float(row['cq_x_' + str(i)]), float(row['cq_y_' + str(i)]), float(row['cq_z_' + str(i)])).matrix()))\n",
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"\n",
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"\n",
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" # Load Gyro inputs\n",
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" w = np.array([float(row['w_x']), float(row['w_y']), float(row['w_z'])]).reshape(3,)\n",
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" std_w = np.array([float(row['std_w_x']), float(row['std_w_y']), float(row['std_w_z'])]).reshape(3,)\n",
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" std_b = np.array([float(row['std_b_x']), float(row['std_b_y']), float(row['std_b_z'])]).reshape(3,)\n",
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" Sigma_wb = blockDiag(np.eye(3) * (std_w ** 2), np.eye(3) * (std_b ** 2))\n",
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"\n",
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" # Load measurements\n",
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" meas = []\n",
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" for i in range(n_meas):\n",
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" y = np.array([float(row['y_x_' + str(i)]), float(row['y_y_' + str(i)]), float(row['y_z_' + str(i)])]).reshape(3,)\n",
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" d = np.array([float(row['d_x_' + str(i)]), float(row['d_y_' + str(i)]), float(row['d_z_' + str(i)])]).reshape(3,)\n",
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" std_y = np.array([float(row['std_y_x_' + str(i)]), float(row['std_y_y_' + str(i)]), float(row['std_y_z_' + str(i)])]).reshape(3,)\n",
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" if i < n_cal:\n",
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" meas.append(Measurement(y, d, np.eye(3) * (std_y ** 2), i))\n",
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" else:\n",
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" meas.append(Measurement(y, d, np.eye(3) * (std_y ** 2), -1))\n",
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"\n",
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" # Append to data_list\n",
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" d = Data(State(R, b, S), n_cal, Input(w, Sigma_wb), meas, n_meas, t, dt)\n",
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" \n",
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" data_list.append(d)\n",
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"\n",
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" return data_list"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 71,
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"metadata": {},
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"outputs": [],
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"source": [
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"def sim(filter_args, data):\n",
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"\n",
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" # Define progressbar\n",
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" p = progressbar.ProgressBar()\n",
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"\n",
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" # EqF\n",
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" filter = EqF(*filter_args)\n",
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"\n",
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" # Allocate variables\n",
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" t = []\n",
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" est = []\n",
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"\n",
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" # Filter loop\n",
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" for d in p(data):\n",
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"\n",
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" t.append(d.t)\n",
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"\n",
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" # Run filter\n",
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" try:\n",
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" filter.propagation(d.u, d.dt)\n",
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" except:\n",
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" print('Filter.propagation Error\\n')\n",
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" for y in d.y:\n",
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" if not (np.isnan(np.linalg.norm(y.y.d.unitVector())) or np.isnan(np.linalg.norm(y.d.d.unitVector()))):\n",
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" try:\n",
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" filter.update(y)\n",
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" except:\n",
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" print('Filter.update Error\\n')\n",
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" est.append(filter.stateEstimate())\n",
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"\n",
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" # Plot Attitude1\n",
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" fig, (ax0, ax1, ax2) = plt.subplots(3, 1)\n",
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" ax = [ax0, ax1, ax2]\n",
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" for i in range(3):\n",
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" ax[i].plot(t, [d.xi.R.rpy()[i] * 180 / math.pi for d in data], color=\"C0\")\n",
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" ax[i].plot(t, [xi.R.rpy()[i] * 180 / math.pi for xi in est], color=\"C1\")\n",
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" ax[i].set_xlabel(\"t\")\n",
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" ax0.set_title(\"Attitude: Roll\")\n",
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" ax1.set_title(\"Attitude: Pitch\")\n",
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" ax2.set_title(\"Attitude: Yaw\")\n",
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" plt.show()\n",
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"\n",
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" # Plot bias\n",
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" fig, (ax0, ax1, ax2) = plt.subplots(3, 1)\n",
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" ax = [ax0, ax1, ax2]\n",
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" for i in range(3):\n",
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" ax[i].plot(t, [d.xi.b[i] for d in data], color=\"C0\")\n",
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" ax[i].plot(t, [xi.b[i] for xi in est], color=\"C1\")\n",
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" ax[i].set_xlabel(\"t\")\n",
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" ax0.set_title(\"Bias: x\")\n",
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" ax1.set_title(\"Bias: y\")\n",
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" ax2.set_title(\"Bias: z\")\n",
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" plt.show()\n",
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"\n",
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"\n",
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" # Plot calibration states\n",
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" for j in range(data[0].n_cal):\n",
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" fig, (ax0, ax1, ax2) = plt.subplots(3, 1)\n",
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" ax = [ax0, ax1, ax2]\n",
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" for i in range(3):\n",
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" ax[i].plot(t, [d.xi.S[j].rpy()[i] * 180 / math.pi for d in data], color=\"C0\")\n",
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" ax[i].plot(t, [xi.S[j].rpy()[i] * 180 / math.pi for xi in est], color=\"C1\")\n",
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" ax[i].set_xlabel(\"t\")\n",
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" ax0.set_title(\"Calibration: Roll\")\n",
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" ax1.set_title(\"Calibration: Pitch\")\n",
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" ax2.set_title(\"Calibration: Yaw\")\n",
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" plt.show()"
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]
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},
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{
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@ -62,7 +274,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 15,
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"execution_count": 72,
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"metadata": {},
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"outputs": [
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{
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@ -12,48 +12,21 @@ Authors: Jennifer Oum & Darshan Rajasekaran
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import numpy as np
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import gtsam
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from gtsam import Rot3, Unit3
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import math
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from dataclasses import dataclass
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import progressbar
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import pandas as pd
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import matplotlib.pyplot as plt
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from typing import List
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coordinate = "EXPONENTIAL"
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def Rot3LeftJacobian(arr: np.ndarray) -> np.ndarray:
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"""Return the SO(3) Left Jacobian
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:param arr: A numpy array with size 3
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:return: The left Jacobian of SO(3)
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"""
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if not (isinstance(arr, np.ndarray) and arr.size == 3):
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raise ValueError("A numpy array with size 3 has to be provided")
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angle = np.linalg.norm(arr)
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# Near |phi|==0, use first order Taylor expansion
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if np.isclose(angle, 0.):
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return np.eye(3) + 0.5 * Rot3.Hat(arr)
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axis = arr / angle
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s = np.sin(angle)
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c = np.cos(angle)
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return (s / angle) * np.eye(3) + \
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(1 - (s / angle)) * np.outer(axis, axis) + \
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((1 - c) / angle) * Rot3.Hat(axis)
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def checkNorm(x: np.ndarray, tol: float = 1e-3):
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"""Check norm of a vector being 1 or nan
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"""Check norm of a vector being 1 or nan
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:param x: A numpy array
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:param tol: tollerance, default 1e-3
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:return: Boolean true if norm is 1 or nan
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"""
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return abs(np.linalg.norm(x) - 1) < tol or np.isnan(np.linalg.norm(x))
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:param x: A numpy array
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:param tol: tollerance, default 1e-3
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:return: Boolean true if norm is 1 or nan
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"""
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return abs(np.linalg.norm(x) - 1) < tol or np.isnan(np.linalg.norm(x))
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class State:
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"""Define the state of the Biased Attitude System
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@ -76,9 +49,14 @@ class State:
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b: np.ndarray
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# Sensor calibrations S
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S: List[Rot3]
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S: List[Rot3]
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def __init__(self, R : Rot3 = Rot3.Identity(), b : np.ndarray = np.zeros(3), S: List[Rot3] = None):
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def __init__(
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self,
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R: Rot3 = Rot3.Identity(),
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b: np.ndarray = np.zeros(3),
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S: List[Rot3] = None,
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):
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"""Initialize State
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:param R: A SO3 element representing the attitude of the system as a rotation matrix
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@ -89,11 +67,16 @@ class State:
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if not isinstance(R, gtsam.Rot3):
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raise TypeError("the attitude rotation matrix R has to be of type SO3 but type is", type(R))
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raise TypeError(
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"the attitude rotation matrix R has to be of type SO3 but type is",
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type(R),
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)
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self.R = R
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if not (isinstance(b, np.ndarray) and b.size == 3):
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raise TypeError("The gyroscope bias has to be probvided as numpy array with size 3")
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raise TypeError(
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"The gyroscope bias has to be probvided as numpy array with size 3"
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)
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self.b = b
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if S is None:
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@ -103,7 +86,9 @@ class State:
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raise TypeError("Calibration states has to be provided as a list")
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for calibration in S:
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if not isinstance(calibration, Rot3):
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raise TypeError("Elements of the list of calibration states have to be of type SO3")
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raise TypeError(
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"Elements of the list of calibration states have to be of type SO3"
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)
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self.S = S
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@staticmethod
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@ -114,9 +99,9 @@ class State:
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:return: The identity element of the State
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"""
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return State(Rot3.Identity(),
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np.zeros(3),
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[Rot3.Identity() for _ in range(n)])
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return State(Rot3.Identity(), np.zeros(3), [Rot3.Identity() for _ in range(n)])
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class Input:
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"""Define the input space of the Biased Attitude System
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----------
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@ -139,9 +124,15 @@ class Input:
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"""
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if not (isinstance(w, np.ndarray) and w.size == 3):
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raise TypeError("Angular velocity has to be provided as a numpy array with size 3")
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if not (isinstance(Sigma, np.ndarray) and Sigma.shape[0] == Sigma.shape[1] == 6):
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raise TypeError("Input measurement noise covariance has to be provided as a numpy array with shape (6. 6)")
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raise TypeError(
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"Angular velocity has to be provided as a numpy array with size 3"
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)
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if not (
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isinstance(Sigma, np.ndarray) and Sigma.shape[0] == Sigma.shape[1] == 6
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):
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raise TypeError(
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"Input measurement noise covariance has to be provided as a numpy array with shape (6. 6)"
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)
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if not np.all(np.linalg.eigvals(Sigma) >= 0):
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raise TypeError("Covariance matrix has to be semi-positive definite")
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@ -149,7 +140,7 @@ class Input:
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self.Sigma = Sigma
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@staticmethod
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def random() -> 'Input':
|
||||
def random() -> "Input":
|
||||
"""Return a random angular velocity
|
||||
|
||||
:return: A random angular velocity as a Input element
|
||||
|
|
@ -165,6 +156,7 @@ class Input:
|
|||
|
||||
return Rot3.Hat(self.w)
|
||||
|
||||
|
||||
class G:
|
||||
"""Symmetry group (SO(3) |x so(3)) x SO(3) x ... x SO(3)
|
||||
----------
|
||||
|
|
@ -181,7 +173,12 @@ class G:
|
|||
a: np.ndarray
|
||||
B: List[Rot3]
|
||||
|
||||
def __init__(self, A: Rot3 = Rot3.Identity(), a: np.ndarray = np.zeros((3, 3)), B: List[Rot3] = None):
|
||||
def __init__(
|
||||
self,
|
||||
A: Rot3 = Rot3.Identity(),
|
||||
a: np.ndarray = np.zeros((3, 3)),
|
||||
B: List[Rot3] = None,
|
||||
):
|
||||
"""Initialize the symmetry group G
|
||||
|
||||
:param A: SO3 element
|
||||
|
|
@ -203,21 +200,23 @@ class G:
|
|||
raise TypeError("Elements of B have to be of type SO3")
|
||||
self.B = B
|
||||
|
||||
def __mul__(self, other: 'G') -> 'G':
|
||||
def __mul__(self, other: "G") -> "G":
|
||||
"""Define the group operation
|
||||
|
||||
:param other: G
|
||||
:return: A element of the group G given by the "multiplication" of self and other
|
||||
"""
|
||||
|
||||
assert (isinstance(other, G))
|
||||
assert (len(self.B) == len(other.B))
|
||||
return G(self.A * other.A,
|
||||
self.a + Rot3.Hat(self.A.matrix() @ Rot3.Vee(other.a)),
|
||||
[self.B[i]*other.B[i] for i in range(len(self.B))])
|
||||
assert isinstance(other, G)
|
||||
assert len(self.B) == len(other.B)
|
||||
return G(
|
||||
self.A * other.A,
|
||||
self.a + Rot3.Hat(self.A.matrix() @ Rot3.Vee(other.a)),
|
||||
[self.B[i] * other.B[i] for i in range(len(self.B))],
|
||||
)
|
||||
|
||||
@staticmethod
|
||||
def identity(n : int):
|
||||
def identity(n: int):
|
||||
"""Return the identity of the symmetry group with n elements of SO3 related to sensor calibration states
|
||||
|
||||
:param n: number of elements in list B associated with calibration states
|
||||
|
|
@ -226,7 +225,28 @@ class G:
|
|||
|
||||
return G(Rot3.Identity(), np.zeros((3, 3)), [Rot3.Identity() for _ in range(n)])
|
||||
|
||||
def exp(x: np.ndarray) -> 'G':
|
||||
@staticmethod
|
||||
def Rot3LeftJacobian(arr: np.ndarray) -> np.ndarray:
|
||||
"""Return the SO(3) Left Jacobian
|
||||
:param arr: A numpy array with size 3
|
||||
:return: The left Jacobian of SO(3)
|
||||
"""
|
||||
if not (isinstance(arr, np.ndarray) and arr.size == 3):
|
||||
raise ValueError("A numpy array with size 3 has to be provided")
|
||||
angle = np.linalg.norm(arr)
|
||||
# Near |phi|==0, use first order Taylor expansion
|
||||
if np.isclose(angle, 0.0):
|
||||
return np.eye(3) + 0.5 * Rot3.Hat(arr)
|
||||
axis = arr / angle
|
||||
s = np.sin(angle)
|
||||
c = np.cos(angle)
|
||||
return (
|
||||
(s / angle) * np.eye(3)
|
||||
+ (1 - (s / angle)) * np.outer(axis, axis)
|
||||
+ ((1 - c) / angle) * Rot3.Hat(axis)
|
||||
)
|
||||
|
||||
def exp(x: np.ndarray) -> "G":
|
||||
"""Return a group element X given by X = exp(x) where x is a numpy array
|
||||
|
||||
:param x: A numpy array
|
||||
|
|
@ -234,24 +254,33 @@ class G:
|
|||
"""
|
||||
|
||||
if not (isinstance(x, np.ndarray) and x.size >= 6):
|
||||
raise ValueError("Wrong shape, a numpy array with size 3n has to be provided")
|
||||
raise ValueError(
|
||||
"Wrong shape, a numpy array with size 3n has to be provided"
|
||||
)
|
||||
if (x.size % 3) != 0:
|
||||
raise ValueError("Wrong size, a numpy array with size multiple of 3 has to be provided")
|
||||
raise ValueError(
|
||||
"Wrong size, a numpy array with size multiple of 3 has to be provided"
|
||||
)
|
||||
|
||||
n = int((x.size - 6) / 3)
|
||||
A = Rot3.Expmap(x[0:3])
|
||||
a = Rot3.Hat(Rot3LeftJacobian(x[0:3]) @ x[3:6])
|
||||
B = [Rot3.Expmap(x[(6 + 3 * i):(9 + 3 * i)]) for i in range(n)]
|
||||
a = Rot3.Hat(G.Rot3LeftJacobian(x[0:3]) @ x[3:6])
|
||||
B = [Rot3.Expmap(x[(6 + 3 * i) : (9 + 3 * i)]) for i in range(n)]
|
||||
|
||||
return G(A, a, B)
|
||||
|
||||
def inv(self) -> 'G':
|
||||
def inv(self) -> "G":
|
||||
"""Return the inverse element of the symmetry group
|
||||
|
||||
:return: A element of the group G given by the inverse of self
|
||||
"""
|
||||
|
||||
return G(self.A.inverse(), -Rot3.Hat(self.A.inverse().matrix() @ Rot3.Vee(self.a)), [B.inverse() for B in self.B])
|
||||
return G(
|
||||
self.A.inverse(),
|
||||
-Rot3.Hat(self.A.inverse().matrix() @ Rot3.Vee(self.a)),
|
||||
[B.inverse() for B in self.B],
|
||||
)
|
||||
|
||||
|
||||
class Direction:
|
||||
"""Define a direction as a S2 element"""
|
||||
|
|
@ -269,7 +298,8 @@ class Direction:
|
|||
raise TypeError("Direction has to be provided as a 3 vector")
|
||||
self.d = Unit3(d)
|
||||
|
||||
def blockDiag(A : np.ndarray, B : np.ndarray) -> np.ndarray:
|
||||
|
||||
def blockDiag(A: np.ndarray, B: np.ndarray) -> np.ndarray:
|
||||
"""Create a lock diagonal matrix from blocks A and B
|
||||
|
||||
:param A: numpy array
|
||||
|
|
@ -282,9 +312,15 @@ def blockDiag(A : np.ndarray, B : np.ndarray) -> np.ndarray:
|
|||
elif B is None:
|
||||
return A
|
||||
else:
|
||||
return np.block([[A, np.zeros((A.shape[0], B.shape[1]))],[np.zeros((B.shape[0], A.shape[1])), B]])
|
||||
return np.block(
|
||||
[
|
||||
[A, np.zeros((A.shape[0], B.shape[1]))],
|
||||
[np.zeros((B.shape[0], A.shape[1])), B],
|
||||
]
|
||||
)
|
||||
|
||||
def repBlock(A : np.ndarray, n: int) -> np.ndarray:
|
||||
|
||||
def repBlock(A: np.ndarray, n: int) -> np.ndarray:
|
||||
"""Create a block diagonal matrix repeating the A block n times
|
||||
|
||||
:param A: numpy array representing the block A
|
||||
|
|
@ -298,30 +334,6 @@ def repBlock(A : np.ndarray, n: int) -> np.ndarray:
|
|||
return res
|
||||
|
||||
|
||||
def Rot3LeftJacobian(arr: np.ndarray) -> np.ndarray:
|
||||
"""Return the SO(3) Left Jacobian
|
||||
|
||||
:param arr: A numpy array with size 3
|
||||
:return: The left Jacobian of SO(3)
|
||||
"""
|
||||
|
||||
if not (isinstance(arr, np.ndarray) and arr.size == 3):
|
||||
raise ValueError("A numpy array with size 3 has to be provided")
|
||||
|
||||
angle = np.linalg.norm(arr)
|
||||
|
||||
# Near |phi|==0, use first order Taylor expansion
|
||||
if np.isclose(angle, 0.):
|
||||
return np.eye(3) + 0.5 * Rot3.Hat(arr)
|
||||
|
||||
axis = arr / angle
|
||||
s = np.sin(angle)
|
||||
c = np.cos(angle)
|
||||
|
||||
return (s / angle) * np.eye(3) + \
|
||||
(1 - (s / angle)) * np.outer(axis, axis) + \
|
||||
((1 - c) / angle) * Rot3.Hat(axis)
|
||||
|
||||
def numericalDifferential(f, x) -> np.ndarray:
|
||||
"""Compute the numerical derivative via central difference"""
|
||||
|
||||
|
|
@ -335,9 +347,10 @@ def numericalDifferential(f, x) -> np.ndarray:
|
|||
for j in range(m):
|
||||
ej = np.zeros(m)
|
||||
ej[j] = 1.0
|
||||
Df[:, j:j+1] = (f(x + h * ej) - f(x - h * ej)).reshape(m, 1) / (2*h)
|
||||
Df[:, j : j + 1] = (f(x + h * ej) - f(x - h * ej)).reshape(m, 1) / (2 * h)
|
||||
return Df
|
||||
|
||||
|
||||
def lift(xi: State, u: Input) -> np.ndarray:
|
||||
"""The Lift of the system (Theorem 3.8, Equation 7)
|
||||
|
||||
|
|
@ -348,21 +361,23 @@ def lift(xi: State, u: Input) -> np.ndarray:
|
|||
|
||||
n = len(xi.S)
|
||||
L = np.zeros(6 + 3 * n)
|
||||
L[0:3] = (u.w - xi.b)
|
||||
L[0:3] = u.w - xi.b
|
||||
L[3:6] = -u.W() @ xi.b
|
||||
for i in range(n):
|
||||
L[(6 + 3 * i):(9 + 3 * i)] = xi.S[i].inverse().matrix() @ L[0:3]
|
||||
L[(6 + 3 * i) : (9 + 3 * i)] = xi.S[i].inverse().matrix() @ L[0:3]
|
||||
|
||||
return L
|
||||
|
||||
def checkNorm(x: np.ndarray, tol: float = 1e-3):
|
||||
"""Check norm of a vector being 1 or nan
|
||||
|
||||
:param x: A numpy array
|
||||
:param tol: tollerance, default 1e-3
|
||||
:return: Boolean true if norm is 1 or nan
|
||||
"""
|
||||
return abs(np.linalg.norm(x) - 1) < tol or np.isnan(np.linalg.norm(x))
|
||||
def checkNorm(x: np.ndarray, tol: float = 1e-3):
|
||||
"""Check norm of a vector being 1 or nan
|
||||
|
||||
:param x: A numpy array
|
||||
:param tol: tollerance, default 1e-3
|
||||
:return: Boolean true if norm is 1 or nan
|
||||
"""
|
||||
return abs(np.linalg.norm(x) - 1) < tol or np.isnan(np.linalg.norm(x))
|
||||
|
||||
|
||||
def stateAction(X: G, xi: State) -> State:
|
||||
"""Action of the symmetry group on the state space, return phi(X, xi) (Equation 4)
|
||||
|
|
@ -373,11 +388,15 @@ def stateAction(X: G, xi: State) -> State:
|
|||
"""
|
||||
|
||||
if len(xi.S) != len(X.B):
|
||||
raise ValueError("the number of calibration states and B elements of the symmetry group has to match")
|
||||
raise ValueError(
|
||||
"the number of calibration states and B elements of the symmetry group has to match"
|
||||
)
|
||||
|
||||
return State(xi.R * X.A,
|
||||
X.A.inverse().matrix() @ (xi.b - Rot3.Vee(X.a)),
|
||||
[(X.A.inverse() * xi.S[i] * X.B[i]) for i in range(len(X.B))])
|
||||
return State(
|
||||
xi.R * X.A,
|
||||
X.A.inverse().matrix() @ (xi.b - Rot3.Vee(X.a)),
|
||||
[(X.A.inverse() * xi.S[i] * X.B[i]) for i in range(len(X.B))],
|
||||
)
|
||||
|
||||
|
||||
def velocityAction(X: G, u: Input) -> Input:
|
||||
|
|
@ -388,7 +407,7 @@ def velocityAction(X: G, u: Input) -> Input:
|
|||
:return: A new element of the Input given by the action of psi of G in the Input space
|
||||
"""
|
||||
|
||||
return Input(X.A.inverse().matrix() @ (u.w - Rot3.Vee(X.a)), u.Sigma)
|
||||
return Input(X.A.inverse().matrix() @ (u.w - Rot3.Vee(X.a)), u.Sigma)
|
||||
|
||||
|
||||
def outputAction(X: G, y: Direction, idx: int = -1) -> np.ndarray:
|
||||
|
|
@ -415,7 +434,15 @@ def local_coords(e: State) -> np.ndarray:
|
|||
|
||||
if coordinate == "EXPONENTIAL":
|
||||
tmp = [Rot3.Logmap(S) for S in e.S]
|
||||
eps = np.concatenate((Rot3.Logmap(e.R), e.b, np.asarray(tmp).reshape(3 * len(tmp),)))
|
||||
eps = np.concatenate(
|
||||
(
|
||||
Rot3.Logmap(e.R),
|
||||
e.b,
|
||||
np.asarray(tmp).reshape(
|
||||
3 * len(tmp),
|
||||
),
|
||||
)
|
||||
)
|
||||
elif coordinate == "NORMAL":
|
||||
raise ValueError("Normal coordinate representation is not implemented yet")
|
||||
# X = G(e.R, -SO3.Rot3.Hat(e.R @ e.b), e.S)
|
||||
|
|
@ -433,9 +460,9 @@ def local_coords_inv(eps: np.ndarray) -> "State":
|
|||
:return: Local coordinates inverse assuming __xi_0 = identity
|
||||
"""
|
||||
|
||||
X = G.exp(eps) #G
|
||||
X = G.exp(eps) # G
|
||||
if coordinate == "EXPONENTIAL":
|
||||
e = State(X.A, eps[3:6, :], X.B) #State
|
||||
e = State(X.A, eps[3:6, :], X.B) # State
|
||||
elif coordinate == "NORMAL":
|
||||
raise ValueError("Normal coordinate representation is not implemented yet")
|
||||
# stateAction(X, State(SO3.identity(), np.zeros(3), [SO3.identity() for _ in range(len(X.B))]))
|
||||
|
|
@ -455,6 +482,7 @@ def stateActionDiff(xi: State) -> np.ndarray:
|
|||
differential = numericalDifferential(coordsAction, np.zeros(6 + 3 * len(xi.S)))
|
||||
return differential
|
||||
|
||||
|
||||
class Measurement:
|
||||
"""Define a measurement
|
||||
----------
|
||||
|
|
@ -491,8 +519,12 @@ class Measurement:
|
|||
raise TypeError("Measurement has to be provided as a (3, 1) vector")
|
||||
if not (isinstance(d, np.ndarray) and d.size == 3 and checkNorm(d)):
|
||||
raise TypeError("Direction has to be provided as a (3, 1) vector")
|
||||
if not (isinstance(Sigma, np.ndarray) and Sigma.shape[0] == Sigma.shape[1] == 3):
|
||||
raise TypeError("Direction measurement noise covariance has to be provided as a numpy array with shape (3. 3)")
|
||||
if not (
|
||||
isinstance(Sigma, np.ndarray) and Sigma.shape[0] == Sigma.shape[1] == 3
|
||||
):
|
||||
raise TypeError(
|
||||
"Direction measurement noise covariance has to be provided as a numpy array with shape (3. 3)"
|
||||
)
|
||||
if not np.all(np.linalg.eigvals(Sigma) >= 0):
|
||||
raise TypeError("Covariance matrix has to be semi-positive definite")
|
||||
if not (isinstance(i, int) or i == -1 or i > 0):
|
||||
|
|
@ -503,6 +535,7 @@ class Measurement:
|
|||
self.Sigma = Sigma
|
||||
self.cal_idx = i
|
||||
|
||||
|
||||
@dataclass
|
||||
class Data:
|
||||
"""Define ground-truth, input and output data"""
|
||||
|
|
@ -522,8 +555,8 @@ class Data:
|
|||
t: float
|
||||
dt: float
|
||||
|
||||
class EqF:
|
||||
|
||||
class EqF:
|
||||
def __init__(self, Sigma: np.ndarray, n: int, m: int):
|
||||
"""Initialize EqF
|
||||
|
||||
|
|
@ -536,8 +569,13 @@ class EqF:
|
|||
self.__n_cal = n
|
||||
self.__n_sensor = m
|
||||
|
||||
if not (isinstance(Sigma, np.ndarray) and (Sigma.shape[0] == Sigma.shape[1] == self.__dof)):
|
||||
raise TypeError(f"Initial covariance has to be provided as a numpy array with shape ({self.__dof}, {self.__dof})")
|
||||
if not (
|
||||
isinstance(Sigma, np.ndarray)
|
||||
and (Sigma.shape[0] == Sigma.shape[1] == self.__dof)
|
||||
):
|
||||
raise TypeError(
|
||||
f"Initial covariance has to be provided as a numpy array with shape ({self.__dof}, {self.__dof})"
|
||||
)
|
||||
if not np.all(np.linalg.eigvals(Sigma) >= 0):
|
||||
raise TypeError("Covariance matrix has to be semi-positive definite")
|
||||
if not (isinstance(n, int) and n >= 0):
|
||||
|
|
@ -548,8 +586,8 @@ class EqF:
|
|||
self.__X_hat = G.identity(n)
|
||||
self.__Sigma = Sigma
|
||||
self.__xi_0 = State.identity(n)
|
||||
self.__Dphi0 = stateActionDiff(self.__xi_0) # Within equation 23
|
||||
self.__InnovationLift = np.linalg.pinv(self.__Dphi0) # Within equation 23
|
||||
self.__Dphi0 = stateActionDiff(self.__xi_0) # Within equation 23
|
||||
self.__InnovationLift = np.linalg.pinv(self.__Dphi0) # Within equation 23
|
||||
|
||||
def stateEstimate(self) -> State:
|
||||
"""Return estimated state
|
||||
|
|
@ -566,20 +604,24 @@ class EqF:
|
|||
"""
|
||||
|
||||
if not isinstance(u, Input):
|
||||
raise TypeError("angular velocity measurement has to be provided as a Input element")
|
||||
raise TypeError(
|
||||
"angular velocity measurement has to be provided as a Input element"
|
||||
)
|
||||
|
||||
L = lift(self.stateEstimate(), u) # Equation 7
|
||||
L = lift(self.stateEstimate(), u) # Equation 7
|
||||
|
||||
Phi_DT = self.__stateTransitionMatrix(u, dt) # Equation 17
|
||||
Phi_DT = self.__stateTransitionMatrix(u, dt) # Equation 17
|
||||
# Equivalent
|
||||
# A0t = self.__stateMatrixA(u) # Equation 14a
|
||||
# Phi_DT = expm(A0t * dt)
|
||||
|
||||
Bt = self.__inputMatrixBt() # Equation 27
|
||||
M_DT = (Bt @ blockDiag(u.Sigma, repBlock(1e-9 * np.eye(3), self.__n_cal)) @ Bt.T) * dt
|
||||
Bt = self.__inputMatrixBt() # Equation 27
|
||||
M_DT = (
|
||||
Bt @ blockDiag(u.Sigma, repBlock(1e-9 * np.eye(3), self.__n_cal)) @ Bt.T
|
||||
) * dt
|
||||
|
||||
self.__X_hat = self.__X_hat * G.exp(L * dt) # Equation 18
|
||||
self.__Sigma = Phi_DT @ self.__Sigma @ Phi_DT.T + M_DT # Equation 19
|
||||
self.__X_hat = self.__X_hat * G.exp(L * dt) # Equation 18
|
||||
self.__Sigma = Phi_DT @ self.__Sigma @ Phi_DT.T + M_DT # Equation 19
|
||||
|
||||
def update(self, y: Measurement):
|
||||
"""Update the filter state
|
||||
|
|
@ -588,16 +630,18 @@ class EqF:
|
|||
"""
|
||||
|
||||
# Cross-check calibration
|
||||
assert (y.cal_idx <= self.__n_cal)
|
||||
assert y.cal_idx <= self.__n_cal
|
||||
|
||||
Ct = self.__measurementMatrixC(y.d, y.cal_idx) # Equation 14b
|
||||
delta = Rot3.Hat(y.d.d.unitVector()) @ outputAction(self.__X_hat.inv(), y.y, y.cal_idx)
|
||||
Ct = self.__measurementMatrixC(y.d, y.cal_idx) # Equation 14b
|
||||
delta = Rot3.Hat(y.d.d.unitVector()) @ outputAction(
|
||||
self.__X_hat.inv(), y.y, y.cal_idx
|
||||
)
|
||||
Dt = self.__outputMatrixDt(y.cal_idx)
|
||||
S = Ct @ self.__Sigma @ Ct.T + Dt @ y.Sigma @ Dt.T # Equation 21
|
||||
K = self.__Sigma @ Ct.T @ np.linalg.inv(S) # Equation 22
|
||||
Delta = self.__InnovationLift @ K @ delta # Equation 23
|
||||
self.__X_hat = G.exp(Delta) * self.__X_hat # Equation 24
|
||||
self.__Sigma = (np.eye(self.__dof) - K @ Ct) @ self.__Sigma # Equation 25
|
||||
S = Ct @ self.__Sigma @ Ct.T + Dt @ y.Sigma @ Dt.T # Equation 21
|
||||
K = self.__Sigma @ Ct.T @ np.linalg.inv(S) # Equation 22
|
||||
Delta = self.__InnovationLift @ K @ delta # Equation 23
|
||||
self.__X_hat = G.exp(Delta) * self.__X_hat # Equation 24
|
||||
self.__Sigma = (np.eye(self.__dof) - K @ Ct) @ self.__Sigma # Equation 25
|
||||
|
||||
def __stateMatrixA(self, u: Input) -> np.ndarray:
|
||||
"""Return the state matrix A0t (Equation 14a)
|
||||
|
|
@ -675,9 +719,11 @@ class EqF:
|
|||
|
||||
# If the measurement is related to a sensor that has a calibration state
|
||||
if idx >= 0:
|
||||
Cc[(3 * idx):(3 + 3 * idx), :] = Rot3.Hat(d.d.unitVector())
|
||||
Cc[(3 * idx) : (3 + 3 * idx), :] = Rot3.Hat(d.d.unitVector())
|
||||
|
||||
return Rot3.Hat(d.d.unitVector()) @ np.hstack((Rot3.Hat(d.d.unitVector()), np.zeros((3, 3)), Cc))
|
||||
return Rot3.Hat(d.d.unitVector()) @ np.hstack(
|
||||
(Rot3.Hat(d.d.unitVector()), np.zeros((3, 3)), Cc)
|
||||
)
|
||||
|
||||
def __outputMatrixDt(self, idx: int) -> np.ndarray:
|
||||
"""Return the measurement output matrix Dt
|
||||
|
|
@ -691,197 +737,3 @@ class EqF:
|
|||
return self.__X_hat.B[idx].matrix()
|
||||
else:
|
||||
return self.__X_hat.A.matrix()
|
||||
|
||||
def formatCSV(df): # pass the dataframe in to this function and get "data_list" as an output
|
||||
"""Read data from csv file formatted as follows:
|
||||
|
||||
| -------------------------------------------------------------------------------------------- |
|
||||
| t: time |
|
||||
| -------------------------------------------------------------------------------------------- |
|
||||
| q_x, q_y, q_z, q_w: Quaternion representing the attitude |
|
||||
| -------------------------------------------------------------------------------------------- |
|
||||
| b_x, b_y, b_z: Gyro bias |
|
||||
| -------------------------------------------------------------------------------------------- |
|
||||
| cq_x_0, cq_yv, cq_z_0, cq_w_0: Quaternion representing the first calibration |
|
||||
| ... |
|
||||
| cq_x_n, cq_y_n, cq_z_n, cq_w_n: Quaternion representing the last calibration |
|
||||
| -------------------------------------------------------------------------------------------- |
|
||||
| w_x, w_y, w_z: Gyro measurements |
|
||||
| -------------------------------------------------------------------------------------------- |
|
||||
| std_w_x, std_w_x, std_w_z: Gyro measurements noise standard deviation |
|
||||
| -------------------------------------------------------------------------------------------- |
|
||||
| std_b_x, std_b_x, std_b_z: Gyro bias random walk standard deviation |
|
||||
| -------------------------------------------------------------------------------------------- |
|
||||
| y_x_0, y_y_0, y_z_0: Direction measurement in sensor frame associated to calibration state 0 |
|
||||
| ... |
|
||||
| y_x_n, y_y_n, y_z_n: Direction measurement in sensor frame associated to calibration state n |
|
||||
| y_x_n+1, y_y_n+1, y_z_n+1: Direction measurement in sensor frame from calibrated sensor |
|
||||
| ... |
|
||||
| y_x_m, y_y_m, y_z_m: Direction measurement in sensor frame from calibrated sensor |
|
||||
| -------------------------------------------------------------------------------------------- |
|
||||
| std_y_x_0, std_y_y_0, std_y_z_0: Standard deviation of direction measurement y_0 |
|
||||
| ... |
|
||||
| std_y_x_m, std_y_y_m, std_y_z_m: Standard deviation of direction measurement y_m |
|
||||
| -------------------------------------------------------------------------------------------- |
|
||||
| d_x_0, d_y_0, d_z_0: Known direction in global frame associated to direction measurement 0 |
|
||||
| ... |
|
||||
| d_x_m, d_y_m, d_z_m: Known direction in global frame associated to direction measurement m |
|
||||
| -------------------------------------------------------------------------------------------- |
|
||||
|
||||
NaN cell means that value is not present at that time
|
||||
|
||||
Max allowd n = 5
|
||||
Max allowd m = 10
|
||||
|
||||
:param pname: path name
|
||||
"""
|
||||
|
||||
# read .csv file into pandas dataframe
|
||||
df = df.reset_index()
|
||||
|
||||
# Define data_list as list
|
||||
data_list = []
|
||||
last_timestamp = df.t[0]
|
||||
|
||||
# Check for existence of bias ground-truth into loaded data
|
||||
bias_exist = False
|
||||
if {'b_x', 'b_y', 'b_z'}.issubset(df.columns):
|
||||
bias_exist = True
|
||||
|
||||
# Check for existence of calibration ground-truth (yaw, pitch, roll angles) into loaded data
|
||||
cal_exist = False
|
||||
n_cal = 0
|
||||
for i in range(6):
|
||||
if {'cq_x_' + str(i), 'cq_y_' + str(i), 'cq_z_' + str(i), 'cq_w_' + str(i)}.issubset(df.columns):
|
||||
cal_exist = True
|
||||
n_cal = i+1
|
||||
|
||||
# Check for existence of direction measurements
|
||||
n_meas = 0
|
||||
for i in range(11):
|
||||
if {'y_x_' + str(i), 'y_y_' + str(i), 'y_z_' + str(i)}.issubset(df.columns):
|
||||
n_meas = i + 1
|
||||
|
||||
for index, row in df.iterrows():
|
||||
|
||||
# Load timestamps and record dt
|
||||
t = float(row['t'])
|
||||
dt = t - last_timestamp
|
||||
|
||||
# Skip data_list if dt is smaller than a micro second
|
||||
if dt < 1e-6:
|
||||
continue
|
||||
|
||||
last_timestamp = t
|
||||
|
||||
# Load groundtruth values
|
||||
quat = np.array([float(row['q_x']), float(row['q_y']), float(row['q_z']), float(row['q_w'])])
|
||||
|
||||
R = Rot3(gtsam.Rot3.Quaternion(float(row['q_w']), float(row['q_x']), float(row['q_y']), float(row['q_z'])).matrix())
|
||||
|
||||
# Load Gyro biases
|
||||
if bias_exist:
|
||||
b = np.array([float(row['b_x']), float(row['b_y']), float(row['b_z'])]).reshape(3,)
|
||||
else:
|
||||
b = np.zeros(3)
|
||||
|
||||
# Load GNSS calibration
|
||||
S = []
|
||||
if cal_exist:
|
||||
for i in range(n_cal):
|
||||
cal = np.array([float(row['cq_x_' + str(i)]), float(row['cq_y_' + str(i)]), float(row['cq_z_' + str(i)]), float(row['cq_w_' + str(i)])])
|
||||
S.append(Rot3(gtsam.Rot3.Quaternion(float(row['cq_w_' + str(i)]), float(row['cq_x_' + str(i)]), float(row['cq_y_' + str(i)]), float(row['cq_z_' + str(i)])).matrix()))
|
||||
|
||||
|
||||
# Load Gyro inputs
|
||||
w = np.array([float(row['w_x']), float(row['w_y']), float(row['w_z'])]).reshape(3,)
|
||||
std_w = np.array([float(row['std_w_x']), float(row['std_w_y']), float(row['std_w_z'])]).reshape(3,)
|
||||
std_b = np.array([float(row['std_b_x']), float(row['std_b_y']), float(row['std_b_z'])]).reshape(3,)
|
||||
Sigma_wb = blockDiag(np.eye(3) * (std_w ** 2), np.eye(3) * (std_b ** 2))
|
||||
|
||||
# Load measurements
|
||||
meas = []
|
||||
for i in range(n_meas):
|
||||
y = np.array([float(row['y_x_' + str(i)]), float(row['y_y_' + str(i)]), float(row['y_z_' + str(i)])]).reshape(3,)
|
||||
d = np.array([float(row['d_x_' + str(i)]), float(row['d_y_' + str(i)]), float(row['d_z_' + str(i)])]).reshape(3,)
|
||||
std_y = np.array([float(row['std_y_x_' + str(i)]), float(row['std_y_y_' + str(i)]), float(row['std_y_z_' + str(i)])]).reshape(3,)
|
||||
if i < n_cal:
|
||||
meas.append(Measurement(y, d, np.eye(3) * (std_y ** 2), i))
|
||||
else:
|
||||
meas.append(Measurement(y, d, np.eye(3) * (std_y ** 2), -1))
|
||||
|
||||
# Append to data_list
|
||||
d = Data(State(R, b, S), n_cal, Input(w, Sigma_wb), meas, n_meas, t, dt)
|
||||
|
||||
data_list.append(d)
|
||||
|
||||
return data_list
|
||||
|
||||
|
||||
def sim(filter_args, data):
|
||||
|
||||
# Define progressbar
|
||||
p = progressbar.ProgressBar()
|
||||
|
||||
# EqF
|
||||
filter = EqF(*filter_args)
|
||||
|
||||
# Allocate variables
|
||||
t = []
|
||||
est = []
|
||||
|
||||
# Filter loop
|
||||
for d in p(data):
|
||||
|
||||
t.append(d.t)
|
||||
|
||||
# Run filter
|
||||
try:
|
||||
filter.propagation(d.u, d.dt)
|
||||
except:
|
||||
print('Filter.propagation Error\n')
|
||||
for y in d.y:
|
||||
if not (np.isnan(np.linalg.norm(y.y.d.unitVector())) or np.isnan(np.linalg.norm(y.d.d.unitVector()))):
|
||||
try:
|
||||
filter.update(y)
|
||||
except:
|
||||
print('Filter.update Error\n')
|
||||
est.append(filter.stateEstimate())
|
||||
|
||||
# Plot Attitude1
|
||||
fig, (ax0, ax1, ax2) = plt.subplots(3, 1)
|
||||
ax = [ax0, ax1, ax2]
|
||||
for i in range(3):
|
||||
ax[i].plot(t, [d.xi.R.rpy()[i] * 180 / math.pi for d in data], color="C0")
|
||||
ax[i].plot(t, [xi.R.rpy()[i] * 180 / math.pi for xi in est], color="C1")
|
||||
ax[i].set_xlabel("t")
|
||||
ax0.set_title("Attitude: Roll")
|
||||
ax1.set_title("Attitude: Pitch")
|
||||
ax2.set_title("Attitude: Yaw")
|
||||
plt.show()
|
||||
|
||||
# Plot bias
|
||||
fig, (ax0, ax1, ax2) = plt.subplots(3, 1)
|
||||
ax = [ax0, ax1, ax2]
|
||||
for i in range(3):
|
||||
ax[i].plot(t, [d.xi.b[i] for d in data], color="C0")
|
||||
ax[i].plot(t, [xi.b[i] for xi in est], color="C1")
|
||||
ax[i].set_xlabel("t")
|
||||
ax0.set_title("Bias: x")
|
||||
ax1.set_title("Bias: y")
|
||||
ax2.set_title("Bias: z")
|
||||
plt.show()
|
||||
|
||||
|
||||
# Plot calibration states
|
||||
for j in range(data[0].n_cal):
|
||||
fig, (ax0, ax1, ax2) = plt.subplots(3, 1)
|
||||
ax = [ax0, ax1, ax2]
|
||||
for i in range(3):
|
||||
ax[i].plot(t, [d.xi.S[j].rpy()[i] * 180 / math.pi for d in data], color="C0")
|
||||
ax[i].plot(t, [xi.S[j].rpy()[i] * 180 / math.pi for xi in est], color="C1")
|
||||
ax[i].set_xlabel("t")
|
||||
ax0.set_title("Calibration: Roll")
|
||||
ax1.set_title("Calibration: Pitch")
|
||||
ax2.set_title("Calibration: Yaw")
|
||||
plt.show()
|
||||
|
|
|
|||
Loading…
Reference in New Issue