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Zaynulla/OrbiCraft_Magnetometer_calibration.ipynb

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Программа для калибровки магнитометров и визуализации результата. Изначально написана для конструктора спутников OrbiCraft, но может использоваться и для других устройств с магнитометрами, например, квадрокоптеров и т.д.
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OrbiCraft_Magnetometer_calibration.ipynb
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Введение\n",
"Это интерактивная методичка по калибровке магнитометра.\n",
"Методичка не просто расскажет как откалибровать магнитометр, но и откалибрует его вместо Вас.\n",
"Заодно покажет 3d графики, которые можно вращать и промежуточные этапы вычислений."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<script>\n",
"code_show=true; \n",
"function code_toggle() {\n",
" if (code_show){\n",
" $('div.input').hide();\n",
" } else {\n",
" $('div.input').show();\n",
" }\n",
" code_show = !code_show\n",
"} \n",
"$( document ).ready(code_toggle);\n",
"</script>\n",
"Исходный код для этого Jupyter notebook для Python по умолчанию скрыт для простоты чтения.\n",
"Для отображения/скрытия исходного кода нажмите <a href=\"javascript:code_toggle()\">здесь</a>."
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from IPython.display import HTML\n",
"HTML('''<script>\n",
"code_show=true; \n",
"function code_toggle() {\n",
" if (code_show){\n",
" $('div.input').hide();\n",
" } else {\n",
" $('div.input').show();\n",
" }\n",
" code_show = !code_show\n",
"} \n",
"$( document ).ready(code_toggle);\n",
"</script>\n",
"Исходный код для этого Jupyter notebook для Python по умолчанию скрыт для простоты чтения.\n",
"Для отображения/скрытия исходного кода нажмите <a href=\"javascript:code_toggle()\">здесь</a>.''')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Автор методички [Зайнулла Жумаев](https://www.facebook.com/zaynulla.zhumaev).\n",
"\n",
"Компания [СПУТНИКС](http://sputnix.ru/ru/)"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from __future__ import print_function\n",
"\n",
"from IPython.display import display, clear_output\n",
"\n",
"from ipywidgets import interact, interactive, fixed, interact_manual\n",
"import ipywidgets as widgets\n",
"\n",
"# for data import from files\n",
"import pandas as pd\n",
"\n",
"# for open filedialog\n",
"from tkinter import filedialog\n",
"from tkinter import *\n",
"\n",
"# for plotly graphics (alternative to matplotlib method)\n",
"import plotly\n",
"from plotly.graph_objs import Scatter, Layout, Data, Surface\n",
"import plotly.plotly as py\n",
"import plotly.graph_objs as go\n",
"\n",
"\n",
"import numpy as np\n",
"from numpy import *\n",
"from numpy import linspace, pi\n",
"\n",
"from scipy.optimize import minimize\n",
"\n",
"# regular expressions\n",
"import re"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# Функция импортирования файла\n",
"root = Tk()\n",
"# Hide the main window\n",
"root.withdraw()\n",
"root.call('wm', 'attributes', '.', '-topmost', True)\n",
" \n",
"clear_output()\n",
"infile = filedialog.askopenfilename(multiple=False,filetypes = ((\"text files\",\"*.txt\"),(\"all files\",\"*.*\")))\n",
"%gui tk"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Считаем данные из файла\n",
"- Считаем все строки из файла\n",
"- Выведем несколько строк, например 10, чтобы убедиться что данные импортировались\n",
"- Мы выбрали вывод начиная с 30 строки, т.к. в начале файла с данными содержится несущественная информация."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"11: x=263 y=55 z=-611 \n",
"onmessage\n",
"12: x=85 y=-244 z=-409 \n",
"onmessage\n",
"13: x=29 y=-254 z=-395 \n",
"onmessage\n",
"14: x=-105 y=-170 z=-443 \n",
"onmessage\n",
"15: x=-329 y=-246 z=-190 \n",
"onmessage\n"
]
}
],
"source": [
"all_lines = []\n",
"with open(infile,\"r\") as f:\n",
" all_lines = f.readlines() # readlines() возвращает список строк файла\n",
"for i in range(30,40): # вывод начинаем с 30 строки, т.к. в начале файла может находиться несущественная информация\n",
" print(all_lines[i],end=\"\") # вывод без добавления переходов на новую строку"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Выберем из списка только те строки, в которых содержаться данные\n",
"Т.е. строки, в которых 3 раза встречается символ '=', между которыми не менее одного другого символа.\n",
"\n",
"Выбирать такие строки будем с помощью [регулярных выражений](https://ru.wikipedia.org/wiki/%D0%A0%D0%B5%D0%B3%D1%83%D0%BB%D1%8F%D1%80%D0%BD%D1%8B%D0%B5_%D0%B2%D1%8B%D1%80%D0%B0%D0%B6%D0%B5%D0%BD%D0%B8%D1%8F \"Читать статью на Википедии\") и библиотеки [re](https://docs.python.org/3.1/library/re.html \"regex in python 3.1\") для Python\n",
"Проверить как работают регулярные выражения можно и в Notepad++ как показано в анимации ниже.\n",
"\n",
"<img src=\"https://media.giphy.com/media/Rd9DJAEl4SNtBgjHEB/giphy.gif\">"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"6: x=102 y=779 z=-50 \n",
"7: x=453 y=645 z=-268 \n",
"8: x=572 y=570 z=14 \n",
"9: x=503 y=623 z=56 \n",
"10: x=450 y=525 z=-445 \n"
]
}
],
"source": [
"def is_data_line(str_input):\n",
" p=re.compile('^.+=.+=.+=.+$')\n",
" out = p.match(str_input)!=None\n",
" return out\n",
"\n",
"data_lines = [line for line in all_lines if is_data_line(line)]\n",
"for i in range(0,5):\n",
" print(data_lines[i],end=\"\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Разобьем строки на столбцы данных\n",
"В качестве разделителей опять будем использовать [регулярные выражения](https://ru.wikipedia.org/wiki/%D0%A0%D0%B5%D0%B3%D1%83%D0%BB%D1%8F%D1%80%D0%BD%D1%8B%D0%B5_%D0%B2%D1%8B%D1%80%D0%B0%D0%B6%D0%B5%D0%BD%D0%B8%D1%8F \"Читать статью на Википедии\") вида:\n",
"- '[0-9]+: x='\n",
"- 'y='\n",
"- 'z='\n",
"\n",
"Работу регулярного выражения снова можно проверить в Notepad++\n",
"<img src=\"https://media.giphy.com/media/8L195WaACphKQFo0gT/giphy.gif\">"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"['', '102', '779', '-50 ', '']\n",
"['', '453', '645', '-268 ', '']\n",
"['', '572', '570', '14 ', '']\n",
"['', '503', '623', '56 ', '']\n",
"['', '450', '525', '-445 ', '']\n"
]
}
],
"source": [
"splited_data = [re.split('[0-9]+: x=| y=| z=|\\n',line) for line in data_lines]\n",
"for i in range(0,5):\n",
" print(splited_data[i])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Выберем столбцы с данными\n",
"Первый и последний столбцы - пустые, выберем все остальные, т.е. столбцы 1, 2, 3 или 1:4. Первый столбец имеет индекс 0!"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"['102' '779' '-50 ']\n",
"['453' '645' '-268 ']\n",
"['572' '570' '14 ']\n",
"['503' '623' '56 ']\n",
"['450' '525' '-445 ']\n"
]
}
],
"source": [
"str_data = np.array(splited_data)[:,1:4]\n",
"for i in range(0,5):\n",
" print(str_data[i])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Преобразуем данные из типа строка в численный тип"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"данные преобразованы в тип float:\n",
"[ 102. 779. -50.]\n",
"[ 453. 645. -268.]\n",
"[ 572. 570. 14.]\n",
"[ 503. 623. 56.]\n",
"[ 450. 525. -445.]\n"
]
}
],
"source": [
"points_raw = np.array([list(map(float, value)) for value in str_data])\n",
"print('\\nданные преобразованы в тип float:')\n",
"for i in range(0,5):\n",
" print(points_raw[i])"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# Функции для отображения различных типов графических объектов\n",
"\n",
"# фунция для формирования облака точек заданного цвета в виде графического объекта\n",
"def scatter_graph(points, sc_color):\n",
" x, y, z = [points[:,i] for i in [0,1,2]]\n",
" trace = go.Scatter3d(\n",
" x=x,\n",
" y=y,\n",
" z=z,\n",
" mode='markers',\n",
" marker=dict(\n",
" size=4,\n",
" line=dict(\n",
" color=sc_color,\n",
" width=0.01\n",
" ),\n",
" opacity=0.0\n",
" )\n",
" )\n",
" return trace\n",
"\n",
"###########################################################\n",
"\n",
"\n",
"# фунция для формирования сферы в виде графического объекта\n",
"def sphere_graph(x0,y0,z0,R):\n",
" theta = linspace(0,2*pi,100)\n",
" phi = linspace(0,pi,100)\n",
" x = R*outer(cos(theta),sin(phi))+x0\n",
" y = R*outer(sin(theta),sin(phi))+y0\n",
" z = R*outer(ones(100),cos(phi))+z0\n",
" spheredata = Data([\n",
" Surface(\n",
" x=x,\n",
" y=y,\n",
" z=z,\n",
" opacity=0.4\n",
" )\n",
" ])\n",
" return spheredata[0]\n",
"\n",
"###########################################################\n",
"\n",
"\n",
"# фунция для формирования эллипсоида в виде графического объекта\n",
"def ellipsoid_graph(x0,y0,z0,a,b,c):\n",
" theta = linspace(0,2*pi,100)\n",
" phi = linspace(0,pi,100)\n",
" x = a*outer(cos(theta),sin(phi))+x0\n",
" y = b*outer(sin(theta),sin(phi))+y0\n",
" z = c*outer(ones(100),cos(phi))+z0\n",
" ellipsoiddata = Data([\n",
" Surface(\n",
" x=x,\n",
" y=y,\n",
" z=z,\n",
" opacity=0.4\n",
" )\n",
" ])\n",
" return ellipsoiddata[0]\n",
"\n",
"###########################################################\n",
"\n",
"\n",
"# функция для отрисовки нескольких графических объектов вместе\n",
"def show_graphs(graphs_data):\n",
"# data = [trace1, spheredata[0]]\n",
" layout = go.Layout(\n",
" margin=dict(\n",
" l=0,\n",
" r=0,\n",
" b=0,\n",
" t=0\n",
" )\n",
" )\n",
" plotly.offline.init_notebook_mode(connected=True)\n",
" fig = go.Figure(data=graphs_data, layout=layout)\n",
" plotly.offline.iplot(fig, filename='simple-3d-scatter.html')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Отобразим данные в 3d\n",
"График можно вращать, приближать или отдалять."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<script>requirejs.config({paths: { 'plotly': ['https://cdn.plot.ly/plotly-latest.min']},});if(!window.Plotly) {{require(['plotly'],function(plotly) {window.Plotly=plotly;});}}</script>"
],
"text/vnd.plotly.v1+html": [
"<script>requirejs.config({paths: { 'plotly': ['https://cdn.plot.ly/plotly-latest.min']},});if(!window.Plotly) {{require(['plotly'],function(plotly) {window.Plotly=plotly;});}}</script>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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"source": [
"sc_color='rgb(50, 50, 50)'\n",
"show_graphs([scatter_graph(points_raw,sc_color)])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Обратите внимание!\n",
"Cкорее всего у вас несколько точек будут \"выбиваться из общей картины\" и будут расположены далеко от остальных измерений."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Удалим шумы и ошибки в данных\n",
"Как вы уже увидели выше из графика, иногда датчик может выдавать данные, которые явно являются ошибочными.\n",
"Ошибочные данные - те которые удалены от поверхности эллипсоида сформированной большинством измерений.\n",
"\n",
"Удалим 2% точек наиболее удаленных от начала координат, т.е. данные с самыми большими по модулю значениями. \n",
"\n",
"Удалим 2% точек внутри и 2% точек снаружи эллипсоида наиболее удаленных от поверхности эллипсоида.\n",
"\n",
"Красным цветом отмечены данные условно принятые шумом.\n",
"Вместе с данными отрисован эллипсоид, который наилучшим образом описывает множество данных измерений. Вращение не учитывается - главные оси эллипсоида параллельны осям системы координат."
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# Первый фильтр - уберем данные наиболее удаленные от начала координат\n",
"x, y, z = [points_raw[:,i] for i in [0,1,2]]\n",
"\n",
"zero_distances = x**2+y**2+z**2 # определим расстояние до начала координат для каждой точки\n",
"\n",
"# отсортируем по удаленности от начала координат\n",
"sorted_order = np.argsort(zero_distances)\n",
"points_temp_1 = points_raw[sorted_order]\n",
"\n",
"\n",
"length = points_temp_1.shape[0] # определим общее количество точек\n",
"start_filt1 = 0\n",
"end_filt1 = int(length*0.98) # 2% наиболее удаленных точек от начала координат не рассматриваем\n",
"\n",
"points_filtered_1 = points_temp_1[start_filt1:end_filt1]\n",
"noize_data_1 = points_temp_1[end_filt1:]\n",
"\n",
"\n",
"##############################################################\n",
"# Функция для определения параметров эллипсоида (без учета поворота)\n",
"def ellipsoid(params):\n",
" x0,y0,z0,a,b,c = params\n",
" deltas = ((x-x0)**2)/(a**2)+((y-y0)**2)/(b**2)+((z-z0)**2)/(c**2)-1\n",
" out = np.sum((np.sum(deltas**2))**2)\n",
" return out\n",
"\n",
"params0 = [0,0,0,1,1,1] #соответствует сфере с центром в начале координат единичного радиуса\n",
"bnds = ((None,None),(None,None),(None,None),(0,None),(0,None),(0,None)) #нет ограничения на координаты центра эллипсоида; a,b,c>0 \n",
"\n",
"##############################################################\n",
"# Второй фильтр - из оставшихся точек уберем точки наиболее удаленные от поверхности эллипсоида\n",
"\n",
"x, y, z = [points_filtered_1[:,i] for i in [0,1,2]]\n",
"\n",
"# Определим параметры эллипсоида\n",
"ellipsoid_res = minimize(ellipsoid, params0, tol=1e-3, bounds = bnds)\n",
"x0,y0,z0,a,b,c = ellipsoid_res.x\n",
"\n",
"# Определим степень удаленности каждой точки от поверхности эллипсоида\n",
"deltas = (((x-x0)**2)/(a**2)+((y-y0)**2)/(b**2)+((z-z0)**2)/(c**2)-1)**2\n",
"# Отсортируем данные по степени удаленности от поверхности эллипсоида\n",
"sorted_order = np.argsort(deltas)\n",
"points_temp_2 = points_filtered_1[sorted_order]\n",
"length = points_filtered_1.shape[0]\n",
"\n",
"# Отбросим 2% точек сначала и 2% точек с конца списка - наиболее удаленные точки от поверхности эллипсоида\n",
"start_filt2 = int(length*0.02)\n",
"end_filt2 = int(length*0.98)\n",
"\n",
"points_filtered = points_temp_2[start_filt2:end_filt2]\n",
"noize_data_2 = np.append(points_temp_2[:start_filt2],points_temp_2[end_filt2:],axis=0)\n",
"noize_data = np.append(noize_data_1,noize_data_2,axis=0)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
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