【Python文本处理】基于运动路线记录GPX的文件解析，及对经纬度坐标的数学模型运动速度求解

解析

GPX文件格式

GPX文件本身其实就是坐标、海拔、时间、心率等综合性的xml文件
如图：

海拔：ele
时间：time
心率：heartrate
功率：power
踏频：cadence
距离：distance
一般不用距离distance 但可以根据距离求瞬时速度（前提是时间间隔均匀 最小精度不低于1s） 不过如果距离和坐标之差相差太远 则不太好确定 Strava等软件通过这个来计算瞬时速度和距离 但不用于计算赛段速度（赛段时间）

某一时刻的数据就看trkpt部分
以trkpt 为始 到 /trkpt 为止
比如：

<trkpt lat="30.3940883" lon="112.2400167"><ele>34</ele><time>2023-05-12T12:26:13Z</time><extensions><heartrate>167</heartrate><distance>26698</distance></extensions></trkpt>

代码实现

首先借助time库 求出每个时刻的参数 并且转换为"%Y-%m-%d %H:%M:%S"格式
而后对海拔 经纬度进行获取
最后获取关键词

import timekeywords_list=["heartrate","cadence","power","distance"]def read_gpx(gpx):first_time=0first_str_time=""trkpt_flag=0j=0num_list=[0]time_list=[None]ele_list=[None]lat_list=[None]lon_list=[None]key_list=[]gpx_dict={}key_dict={}for i in keywords_list:key_list.append([None])for i in range(len(gpx)):        try:ti=str((gpx[i].split("<time>")[1]).split("</time>")[0])now_time = time.mktime(time.strptime(ti, "%Y-%m-%dT%H:%M:%SZ"))first_time=now_time                first_str_time=time.strftime("%Y-%m-%d %H:%M:%S",time.localtime(first_time))  breakexcept:passtime_list[0]=first_str_timefor i in range(len(gpx)):if gpx[i].count('<trkpt'):trkpt_flag=1      j=j+1num_list.append(j)time_list.append(j)ele_list.append(j)lat_list.append(j)lon_list.append(j)            for k in range(len(keywords_list)):key_list[k].append(j)if trkpt_flag==1:try:ti=str((gpx[i].split("<time>")[1]).split("</time>")[0])now_time = time.mktime(time.strptime(ti, "%Y-%m-%dT%H:%M:%SZ"))now_str_time=time.strftime("%Y-%m-%d %H:%M:%S",time.localtime(now_time))  time_list[j]=now_str_timeexcept:passif gpx[i].count('<trkpt'):lat_list[j]=float(gpx[i].split('"')[1])lon_list[j]=float(gpx[i].split('"')[3])try:ele_list[j]=float(str((gpx[i].split("<ele>")[1]).split("</ele>")[0]))except:passfor k in range(len(keywords_list)):           try:dat=str((gpx[i].split("<"+keywords_list[k]+">")[1]).split("</"+keywords_list[k]+">")[0])key_list[k][j]=float(dat)except:passif gpx[i].count('</trkpt>'):trkpt_flag=0if gpx[i].count('</trkseg>'):breakgpx_dict["num"]=num_list    gpx_dict["time"]=time_list       gpx_dict["lat"]=lat_listgpx_dict["lon"]=lon_listgpx_dict["ele"]=ele_list for k in range(len(keywords_list)):key_dict[keywords_list[k]]=key_list[k]gpx_dict["key"]=key_dictreturn gpx_dict

最后保存为字典集合
输出结果：

{'num': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184], 'time': ['2023-06-01 09:58:22', '2023-06-01 09:58:41', '2023-06-01 09:58:42', '2023-06-01 09:58:43', '2023-06-01 09:58:44', '2023-06-01 09:58:45', '2023-06-01 09:58:46', '2023-06-01 09:58:47', '2023-06-01 09:58:48', '2023-06-01 09:58:49', '2023-06-01 09:58:50', '2023-06-01 09:58:51', '2023-06-01 09:58:52', '2023-06-01 09:58:53', '2023-06-01 09:58:54', '2023-06-01 09:58:55', '2023-06-01 09:58:56', '2023-06-01 09:58:57', '2023-06-01 09:58:58', '2023-06-01 09:58:59', '2023-06-01 09:59:00', '2023-06-01 09:59:01', '2023-06-01 09:59:02', '2023-06-01 09:59:03', '2023-06-01 09:59:04', '2023-06-01 09:59:05', '2023-06-01 09:59:06', '2023-06-01 09:59:07', '2023-06-01 09:59:08', '2023-06-01 09:59:09', '2023-06-01 09:59:10', '2023-06-01 09:59:11', '2023-06-01 09:59:12', '2023-06-01 09:59:13', '2023-06-01 09:59:14', '2023-06-01 09:59:15', '2023-06-01 09:59:16', '2023-06-01 09:59:17', '2023-06-01 09:59:18', '2023-06-01 09:59:19', '2023-06-01 09:59:20', '2023-06-01 09:59:21', '2023-06-01 09:59:22', '2023-06-01 09:59:23', '2023-06-01 09:59:24', '2023-06-01 09:59:25', '2023-06-01 09:59:26', '2023-06-01 09:59:27', '2023-06-01 09:59:28', '2023-06-01 09:59:29', '2023-06-01 09:59:30', '2023-06-01 09:59:31', '2023-06-01 09:59:32', '2023-06-01 09:59:33', '2023-06-01 09:59:34', '2023-06-01 09:59:35', '2023-06-01 09:59:36', '2023-06-01 09:59:37', '2023-06-01 09:59:38', '2023-06-01 09:59:39', '2023-06-01 09:59:40', '2023-06-01 09:59:41', '2023-06-01 09:59:42', '2023-06-01 09:59:43', '2023-06-01 09:59:44', '2023-06-01 09:59:45', '2023-06-01 09:59:46', '2023-06-01 09:59:47', '2023-06-01 09:59:48', '2023-06-01 09:59:49', '2023-06-01 09:59:50', '2023-06-01 09:59:51', '2023-06-01 09:59:52', '2023-06-01 09:59:53', '2023-06-01 09:59:54', '2023-06-01 09:59:55', '2023-06-01 09:59:56', '2023-06-01 09:59:57', '2023-06-01 09:59:58', '2023-06-01 09:59:59', '2023-06-01 10:00:00', '2023-06-01 10:00:01', '2023-06-01 10:00:02', '2023-06-01 10:00:03', '2023-06-01 10:00:04', '2023-06-01 10:00:05', '2023-06-01 10:00:06', '2023-06-01 10:00:07', '2023-06-01 10:00:08', '2023-06-01 10:00:09', '2023-06-01 10:00:10', '2023-06-01 10:00:11', '2023-06-01 10:00:12', '2023-06-01 10:00:13', '2023-06-01 10:00:14', '2023-06-01 10:00:15', '2023-06-01 10:00:16', '2023-06-01 10:00:17', '2023-06-01 10:00:18', '2023-06-01 10:00:19', '2023-06-01 10:00:20', '2023-06-01 10:00:21', '2023-06-01 10:00:22', '2023-06-01 10:00:23', '2023-06-01 10:00:24', '2023-06-01 10:00:25', '2023-06-01 10:00:26', '2023-06-01 10:00:27', '2023-06-01 10:00:28', '2023-06-01 10:00:29', '2023-06-01 10:00:30', '2023-06-01 10:00:31', '2023-06-01 10:00:32', '2023-06-01 10:00:33', '2023-06-01 10:00:34', '2023-06-01 10:00:35', '2023-06-01 10:00:36', '2023-06-01 10:00:37', '2023-06-01 10:00:38', '2023-06-01 10:00:39', '2023-06-01 10:00:40', '2023-06-01 10:00:41', '2023-06-01 10:00:42', '2023-06-01 10:00:43', '2023-06-01 10:00:44', '2023-06-01 10:00:45', '2023-06-01 10:00:46', '2023-06-01 10:00:47', '2023-06-01 10:00:48', '2023-06-01 10:00:49', '2023-06-01 10:00:50', '2023-06-01 10:00:51', '2023-06-01 10:00:52', '2023-06-01 10:00:53', '2023-06-01 10:00:54', '2023-06-01 10:00:55', '2023-06-01 10:00:56', '2023-06-01 10:00:57', '2023-06-01 10:00:58', '2023-06-01 10:00:59', '2023-06-01 10:01:00', '2023-06-01 10:01:01', '2023-06-01 10:01:02', '2023-06-01 10:01:03', '2023-06-01 10:01:04', '2023-06-01 10:01:05', '2023-06-01 10:01:06', '2023-06-01 10:01:07', '2023-06-01 10:01:08', '2023-06-01 10:01:09', '2023-06-01 10:01:10', '2023-06-01 10:01:11', '2023-06-01 10:01:12', '2023-06-01 10:01:13', '2023-06-01 10:01:14', '2023-06-01 10:01:15', '2023-06-01 10:01:16', '2023-06-01 10:01:17', '2023-06-01 10:01:18', '2023-06-01 10:01:19', '2023-06-01 10:01:20', '2023-06-01 10:01:21', '2023-06-01 10:01:22', '2023-06-01 10:01:23', '2023-06-01 10:01:24', '2023-06-01 10:01:25', '2023-06-01 10:01:26', '2023-06-01 10:01:27', '2023-06-01 10:01:28', '2023-06-01 10:01:29', '2023-06-01 10:01:30', '2023-06-01 10:01:31', '2023-06-01 10:01:32', '2023-06-01 10:01:33', '2023-06-01 10:01:34', '2023-06-01 10:01:54', '2023-06-01 10:01:55', '2023-06-01 10:01:56', '2023-06-01 10:01:57', '2023-06-01 10:02:13', '2023-06-01 10:02:14', '2023-06-01 10:02:15', '2023-06-01 10:02:16', '2023-06-01 10:02:17', '2023-06-01 10:02:18'], 'lat': [None, 30.452805, 30.4528125, 30.4528189, 30.4528247, 30.4528287, 30.4528306, 30.4528274, 30.4528185, 30.4528061, 30.4527819, 30.4527605, 30.4527407, 30.4527255, 30.4527165, 30.4527105, 30.4527043, 30.4527002, 30.4526961, 30.4526878, 30.4526799, 30.4526724, 30.4526653, 30.4526585, 30.4526511, 30.4526432, 30.4526382, 30.4526364, 30.4526347, 30.4526313, 30.4526268, 30.4526225, 30.4526161, 30.4526085, 30.4526009, 30.4525931, 30.452585, 30.4525761, 30.4525672, 30.4525573, 30.4525471, 30.4525388, 30.4525315, 30.4525241, 30.4525176, 30.4525106, 30.4525042, 30.4524992, 30.4524957, 30.4524939, 30.4524964, 30.4525027, 30.4525095, 30.4525144, 30.4525146, 30.4525092, 30.4525001, 30.452491, 30.4524821, 30.4524735, 30.4524656, 30.4524585, 30.4524522, 30.4524467, 30.4524397, 30.4524306, 30.4524212, 30.4524128, 30.4524072, 30.4524037, 30.4523976, 30.452387, 30.4523743, 30.4523626, 30.4523544, 30.4523475, 30.4523411, 30.4523334, 30.4523246, 30.4523151, 30.4523058, 30.4522994, 30.4522931, 30.452284, 30.4522709, 30.4522573, 30.4522449, 30.4522331, 30.4522227, 30.4522135, 30.4522036, 30.4521941, 30.4521846, 30.4521749, 30.452165, 30.4521557, 30.4521475, 30.4521407, 30.452135, 30.4521298, 30.4521242, 30.4521187, 30.4521134, 30.4521077, 30.452099, 30.4520891, 30.4520801, 30.4520722, 30.4520656, 30.4520581, 30.4520494, 30.4520406, 30.4520326, 30.4520258, 30.4520207, 30.4520166, 30.4520156, 30.4520157, 30.4520148, 30.4520109, 30.4520021, 30.4519891, 30.451975, 30.4519647, 30.4519547, 30.4519429, 30.4519314, 30.4519224, 30.4519173, 30.4519121, 30.451905, 30.4518969, 30.4518886, 30.4518795, 30.45187, 30.4518607, 30.4518506, 30.451841, 30.451832, 30.4518227, 30.4518112, 30.4517992, 30.451789, 30.4517806, 30.4517714, 30.4517642, 30.4517577, 30.4517519, 30.4517441, 30.4517381, 30.4517355, 30.4517277, 30.4517154, 30.451696, 30.4516821, 30.4516804, 30.4516841, 30.4516871, 30.4516861, 30.4516817, 30.4516731, 30.4516592, 30.4516392, 30.4516241, 30.4515869, 30.4515576, 30.4515302, 30.4515145, 30.4514761, 30.4514449, 30.4514142, 30.4513832, 30.451353, 30.4513262, 30.4513047, 30.4512268, 30.4512039, 30.4511808, 30.4511591, 30.4510384, 30.4510348, 30.4510312, 30.4510243, 30.4510148, 30.4509683], 'lon': [None, 114.42341, 114.4234075, 114.4234007, 114.4233901, 114.4233757, 114.4233531, 114.4233333, 114.4233105, 114.4232842, 114.4232355, 114.4231986, 114.4231621, 114.4231234, 114.42308, 114.4230341, 114.4229862, 114.4229577, 114.4229293, 114.4228785, 114.4228315, 114.4227793, 114.4227282, 114.4226775, 114.4226272, 114.422577, 114.4225274, 114.4224779, 114.4224276, 114.4223772, 114.4223269, 114.4222768, 114.4222261, 114.4221743, 114.422121, 114.4220673, 114.4220143, 114.4219619, 114.4219094, 114.4218565, 114.4218039, 114.4217506, 114.421697, 114.4216435, 114.4215901, 114.4215373, 114.4214851, 114.4214326, 114.4213798, 114.4213273, 114.421277, 114.4212281, 114.4211797, 114.4211314, 114.4210826, 114.4210331, 114.4209821, 114.4209311, 114.4208804, 114.4208289, 114.420777, 114.4207252, 114.4206734, 114.4206211, 114.4205688, 114.4205168, 114.420465, 114.4204133, 114.4203623, 114.4203093, 114.4202557, 114.4202033, 114.4201521, 114.4201022, 114.4200552, 114.4200083, 114.419961, 114.4199125, 114.4198619, 114.4198099, 114.4197569, 114.4197042, 114.4196513, 114.4195989, 114.4195456, 114.4194927, 114.4194397, 114.4193878, 114.4193369, 114.419286, 114.4192341, 114.4191815, 114.419129, 114.4190763, 114.4190232, 114.4189688, 114.418915, 114.418861, 114.4188058, 114.4187511, 114.418697, 114.4186434, 114.4185905, 114.4185378, 114.4184854, 114.4184328, 114.4183798, 114.4183267, 114.4182727, 114.4182176, 114.4181623, 114.4181082, 114.4180579, 114.4180111, 114.4179664, 114.4179228, 114.4178808, 114.41784, 114.4177991, 114.4177536, 114.4177059, 114.4176574, 114.4176081, 114.4175565, 114.4175062, 114.4174569, 114.4174089, 114.4173598, 114.4173088, 114.4172565, 114.4172029, 114.4171484, 114.4170935, 114.4170372, 114.4169823, 114.4169284, 114.4168755, 114.4168227, 114.4167703, 114.416719, 114.4166684, 114.4166182, 114.4165688, 114.41652, 114.4164722, 114.4164238, 114.4163759, 114.4163279, 114.4162817, 114.4162345, 114.4161873, 114.416144, 114.4161079, 114.4160834, 114.4160621, 114.4160486, 114.4160213, 114.4159636, 114.4159197, 114.4158811, 114.415848, 114.4158204, 114.4157996, 114.4157916, 114.4157787, 114.4157734, 114.4157721, 114.4157722, 114.4157734, 114.4157742, 114.4157747, 114.4157775, 114.4157841, 114.4157923, 114.415801, 114.415851, 114.4158589, 114.4158646, 114.4158705, 114.4158796, 114.4158809, 114.4158822, 114.4158852, 114.4158888, 114.4159033], 'ele': [None, 19.0, 19.0, 19.0, 19.0, 19.0, 19.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 21.0, 21.0, 21.0, 21.0, 21.0, 21.0, 21.0, 21.0, 21.0, 21.0, 21.0, 21.0, 21.0, 21.0, 21.0, 21.0, 21.0, 21.0, 21.0, 21.0, 21.0, 21.0, 21.0, 21.0, 21.0, 21.0, 21.0, 21.0, 21.0, 21.0, 21.0, 21.0, 21.0, 21.0, 21.0, 21.0, 21.0, 21.0, 21.0, 21.0, 21.0, 21.0, 21.0, 21.0, 21.0, 21.0, 21.0, 21.0, 21.0, 21.0, 21.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 19.0, 19.0, 19.0, 19.0, 19.0, 19.0, 19.0, 19.0, 19.0, 19.0, 19.0, 19.0, 19.0, 19.0, 19.0, 19.0, 19.0, 19.0, 19.0, 19.0, 19.0, 19.0, 19.0, 19.0, 19.0, 19.0, 19.0, 19.0, 19.0, 19.0, 19.0, 19.0, 19.0, 19.0, 19.0, 19.0, 19.0, 19.0, 19.0, 19.0, 19.0, 19.0, 19.0, 19.0, 19.0, 19.0, 19.0, 19.0, 19.0, 19.0, 19.0, 19.0, 19.0, 19.0, 19.0, 19.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0], 'key': {'heartrate': [None, 99.0, 101.0, 101.0, 100.0, 100.0, 100.0, 100.0, 100.0, 100.0, 101.0, 101.0, 101.0, 101.0, 102.0, 102.0, 102.0, 102.0, 101.0, 101.0, 101.0, 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118.0, 118.0, 118.0, 117.0, 118.0, 118.0, 118.0, 118.0, 117.0, 117.0, 117.0, 112.0, 112.0, 112.0, 112.0, 113.0, 113.0, 113.0, 112.0, 112.0, 112.0], 'cadence': [None, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184], 'power': [None, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184], 'distance': [None, 0.0, 0.0, 0.0, 0.0, 4.0, 9.0, 12.0, 15.0, 19.0, 23.0, 27.0, 31.0, 36.0, 40.0, 44.0, 49.0, 54.0, 60.0, 65.0, 70.0, 75.0, 80.0, 84.0, 89.0, 94.0, 99.0, 104.0, 109.0, 114.0, 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速度求解

速度＝位移/时间
所以最先要做的就是算出两个经纬度坐标点的距离（弧长）

数学模型

首先 地球的平均半径为6371393米
近视地球为一个球体 则经纬度坐标就是一个球坐标方程

球坐标和直角坐标转换用到这两个方程组：

其中 φ为经度 90°-θ为纬度（这里有个坑需要注意）：
标准球坐标为：

可以看到 θ是90°-纬度
所以如果带入经纬度的话 就是：

（theta是经度 phi是纬度）

df['r'] = 6371393+df['ele']# radius of the Earth in meters
df['theta'] = np.deg2rad(df['lon'])
df['phi'] = np.deg2rad(df['lat'])
df['x'] = df['r']*np.cos(df['theta'])*np.cos(df['phi'])
df['y'] = df['r']*np.sin(df['theta'])*np.cos(df['phi'])
df['z'] = df['r']*np.sin(df['phi'])df['x2'] = df['x'].shift()
df['y2'] = df['y'].shift()
df['z2'] = df['z'].shift()df['distance'] = np.sqrt((df['x2']-df['x'])**2 + (df['y2']-df['y'])**2 + (df['z2']-df['z'])**2)df['central_angle'] = np.arccos((df['x']*df['x2'] + df['y']*df['y2'] + df['z']*df['z2'])/df['r']**2)df['arclength'] = df['central_angle']*df['r']df['elapsed_time'] = (df.index.to_series().diff() / pd.Timedelta(seconds=1))df['speed'] = df['arclength'] / df['elapsed_time']*3.6  # km/h
df = df[columns + ['speed']]

通过三角函数计算出两个坐标点的弧长，则可以算出该时间段的速度

但物理里面学过：
若要精确计算速度 则应该求两个连续弧长/两个经过的时间

但也可以不这么麻烦：

弧长公式在球坐标中更容易求得 而且如果转成直角坐标 则可能把角度弄错（我第一次就把90°-θ踩坑了 导致我的弧长求反三角函数时 居然大于1）

计算经纬度坐标距离的原理就是就算球面两点间的距离，经纬度表示法实际是用角度描述的坐标。纬度上下一共180度，经度360度。

假设地球是标准的球形，计算距离就等于计算一个截面圆的弧长。计算弧长的话需要先求出两点相对于球芯的夹角。然后根据半径就可以求出弧长了，也就是距离。

假设A点纬度lat1，精度lng1.B点纬度lat2， 经度lng2， 地球半径为R

求这个夹角之前，先把坐标转换为直角空间坐标系的点，并让地心为坐标中心点，即
A（Rcos(lat1)cos(lng1),  Rcos(lat1)sin(lng1), Rsin(lat1)）
B（Rcos(lat2)cos(lng2),  Rcos(lat2)sin(lng2), Rsin(lat2)）

然后算夹角，这里用向量的夹角计算方法,可以求出夹角余弦值，那么夹角COS为
COS = (向量A*向量B) / (向量A的模 * 向量B的模)

令A为（x,y,z）,B(a,b,c)
COS = (xa+yb+zc)/[√(x2+y2+z2)*√(a2+b2+c2)]

把经纬度的坐标代进去
COS = cos(lat2) * cos(lat1) * cos(lng1-lng2) + sin(lat2)*sin(lat1)

得到夹角的余弦值可得角度，然后就可以算出弧长了，即得距离(arccos 为反余弦函数，这里反余弦的结果得到的是弧度)
d = 2PI*R * (arccos(COS) / 2 * PI)
d = R * arccos(COS)
最终
d = R * arccos( cos(lat2) * cos(lat1) * cos(lng2-lng1) + sin(lat2)*sin(lat1))

代码：

df['arclength'] = df['r'] * np.arccos(np.cos(df['phi']) * np.cos(df['phi2']) * np.cos(df['theta2']-df['theta']) + np.sin(df['phi'])*np.sin(df['phi2']))

加上物理中求速度的公式 运动速度求解就成了：
其中elapsed_time_list为经过的时间列表

try:speed_list.append((df['arclength'][i]+df['arclength'][i+1])/ (elapsed_time_list[i]+elapsed_time_list[i+1]))  # km/h
except:speed_list.append(df['arclength'][i]/ elapsed_time_list[i])  # m/s

如果还想更加精确 则再延伸两个时间段 并且求出来的速度按权重去求平均值 这里就需要经验值了

代码实现

这里用到了numpy和pandas做数学计算
同时也要引入状态机考虑如果时间戳相同的结果（一般GPX是一秒钟更新一次 所以也没啥影响）

def calculate_speed(time_list,lat_list,lon_list,ele_list):if len(time_list)==len(lat_list) and len(time_list)==len(lon_list) and len(time_list)==len(ele_list):passelse:return df = pd.DataFrame({'time': time_list, 'lat': lat_list, 'lon': lon_list, 'ele': ele_list})columns = df.columns.tolist()df['r'] = 6371393+df['ele'] # radius of the Earth in metersdf['theta'] = np.deg2rad(df['lon'])df['phi'] = np.deg2rad(df['lat'])df['theta2']=df['theta'].shift()df['phi2']=df['phi'].shift()df['arclength'] = df['r'] * np.arccos(np.cos(df['phi']) * np.cos(df['phi2']) * np.cos(df['theta2']-df['theta']) + np.sin(df['phi'])*np.sin(df['phi2']))elapsed_time_list=[]stamp_list=[]speed_list=[]stamp_same_list=[]same_flag=0enable_flag=0exit_same_list=[]for i in range(len(time_list)):try:stamp_list.append(time.mktime(time.strptime(time_list[i], "%Y-%m-%d %H:%M:%S")))enable_flag=1if i>0 and enable_flag==1:if stamp_list[i]>stamp_list[i-1]:elapsed_time_list.append(stamp_list[i]-stamp_list[i-1]) if same_flag==1:same_flag=0exit_same_list.append(i)else:if same_flag==0:stamp_same_list.append(i)same_flag=1elapsed_time_list.append(0.0)else:elapsed_time_list.append(None)except:if enable_flag==0:elapsed_time_list.append(None)else:if same_flag==0:stamp_same_list.append(i)same_flag=1elapsed_time_list.append(0.0)if len(stamp_same_list)>len(exit_same_list):exit_same_list.append(0)  j=0displacement=0.0displacement_time=0.0end_displacement=0.0same_flag=0end_elapsed_time=0.0stamp_same_in_1st_flag=0if len(stamp_same_list)==0:for i in range(len(elapsed_time_list)):try:try:speed_list.append((df['arclength'][i]+df['arclength'][i+1])/ (elapsed_time_list[i]+elapsed_time_list[i+1]))  # km/hexcept:speed_list.append(df['arclength'][i]/ elapsed_time_list[i])  # m/sexcept:speed_list.append(None)else:  for i in range(len(elapsed_time_list)):try:if i>0:try:if i==stamp_same_list[j]-1:same_flag=1if stamp_same_list[0]==1 and stamp_same_in_1st_flag==0:stamp_same_in_1st_flag=1same_flag=1except:passif same_flag==0:try:speed_list.append((df['arclength'][i]+df['arclength'][i+1])/ (elapsed_time_list[i]+elapsed_time_list[i+1]))  # m/sexcept:speed_list.append(df['arclength'][i]/ elapsed_time_list[i])  # m/selse:   try:displacement=displacement+df['arclength'][i]except:displacement=displacement+0.0try:displacement_time=displacement_time+elapsed_time_list[i]except:displacement_time=displacement_time+0.0if j==len(stamp_same_list)-1 and exit_same_list[j]==0:if end_elapsed_time==0.0:end_elapsed_time=elapsed_time_list[i]                                end_displacement=end_displacement+df['arclength'][i]if end_elapsed_time>0.0:speed_list.append(end_displacement/end_elapsed_time)else:speed_list.append(end_displacement/1.0)else:speed_list.append(None)if i==exit_same_list[j]: avg_speed=displacement/displacement_timefor k in range(stamp_same_list[j]-1,i+1):speed_list[k]=avg_speed       j=j+1try:if elapsed_time_list[j]-end_elapsed_time[j-1]<=1:passelse:same_flag=0displacement=0.0displacement_time=0.0except:same_flag=0displacement=0.0displacement_time=0.0else:speed_list.append(None)except:speed_list.append(None)df['elapsed_time'] = elapsed_time_listdf['speed'] = speed_list  # m/sdf['speed'] = 3.6*df['speed'] # km/hdf = df[columns + ['arclength']+['speed']]return df

输出结果：

                    time        lat    ...      arclength      speed
0    2023-06-01 09:58:22        NaN    ...            NaN        NaN
1    2023-06-01 09:58:41  30.452805    ...            NaN        NaN
2    2023-06-01 09:58:42  30.452813    ...       0.870153   3.309064
3    2023-06-01 09:58:43  30.452819    ...       0.968216   3.904454
4    2023-06-01 09:58:44  30.452825    ...       1.200925   4.775849
5    2023-06-01 09:58:45  30.452829    ...       1.452325   6.533599
6    2023-06-01 09:58:46  30.452831    ...       2.177452   7.392403
7    2023-06-01 09:58:47  30.452827    ...       1.929438   7.792940
8    2023-06-01 09:58:48  30.452818    ...       2.399973   9.492160
9    2023-06-01 09:58:49  30.452806    ...       2.873450  14.872643
10   2023-06-01 09:58:50  30.452782    ...       5.389130  17.373583
11   2023-06-01 09:58:51  30.452761    ...       4.262861  15.114427
12   2023-06-01 09:58:52  30.452741    ...       4.134043  14.777814
13   2023-06-01 09:58:53  30.452725    ...       4.075853  15.040074
14   2023-06-01 09:58:54  30.452717    ...       4.279743  15.715562
15   2023-06-01 09:58:55  30.452710    ...       4.451124  16.370151
16   2023-06-01 09:58:56  30.452704    ...       4.643404  13.346376
17   2023-06-01 09:58:57  30.452700    ...       2.771250   9.955965
18   2023-06-01 09:58:58  30.452696    ...       2.759842  13.890313
19   2023-06-01 09:58:59  30.452688    ...       4.956999  17.185842
20   2023-06-01 09:59:00  30.452680    ...       4.590692  17.396119
21   2023-06-01 09:59:01  30.452672    ...       5.073819  18.063651
22   2023-06-01 09:59:02  30.452665    ...       4.961543  17.782722
23   2023-06-01 09:59:03  30.452658    ...       4.917747  17.655921
24   2023-06-01 09:59:04  30.452651    ...       4.891098  17.607951
25   2023-06-01 09:59:05  30.452643    ...       4.891098  17.420183
26   2023-06-01 09:59:06  30.452638    ...       4.786782  17.164355
27   2023-06-01 09:59:07  30.452636    ...       4.748971  17.231882
28   2023-06-01 09:59:08  30.452635    ...       4.824296  17.407732
29   2023-06-01 09:59:09  30.452631    ...       4.846666  17.447997
..                   ...        ...    ...            ...        ...
155  2023-06-01 10:01:15  30.451680    ...       1.308677   7.122322
156  2023-06-01 10:01:16  30.451684    ...       2.648168  14.741737
157  2023-06-01 10:01:17  30.451687    ...       5.541685  17.552431
158  2023-06-01 10:01:18  30.451686    ...       4.209665  14.294663
159  2023-06-01 10:01:19  30.451682    ...       3.731814  12.683910
160  2023-06-01 10:01:20  30.451673    ...       3.314802  11.483126
161  2023-06-01 10:01:21  30.451659    ...       3.064712  10.890838
162  2023-06-01 10:01:22  30.451639    ...       2.985753   8.692529
163  2023-06-01 10:01:23  30.451624    ...       1.843429  11.085891
164  2023-06-01 10:01:24  30.451587    ...       4.315399  13.704922
165  2023-06-01 10:01:25  30.451558    ...       3.298446  11.427151
166  2023-06-01 10:01:26  30.451530    ...       3.049971   8.631806
167  2023-06-01 10:01:27  30.451514    ...       1.745477  10.830216
168  2023-06-01 10:01:28  30.451476    ...       4.271310  13.934782
169  2023-06-01 10:01:29  30.451445    ...       3.470236  12.391505
170  2023-06-01 10:01:30  30.451414    ...       3.413934  12.368084
171  2023-06-01 10:01:31  30.451383    ...       3.457224  12.377582
172  2023-06-01 10:01:32  30.451353    ...       3.419210  11.702734
173  2023-06-01 10:01:33  30.451326    ...       3.082309  10.101783
174  2023-06-01 10:01:34  30.451305    ...       2.529793   2.130881
175  2023-06-01 10:01:54  30.451227    ...       9.900348   2.152631
176  2023-06-01 10:01:55  30.451204    ...       2.656664   9.511795
177  2023-06-01 10:01:56  30.451181    ...       2.627666   9.192733
178  2023-06-01 10:01:57  30.451159    ...       2.479408   3.373405
179  2023-06-01 10:02:13  30.451038    ...      13.450560   2.933653
180  2023-06-01 10:02:14  30.451035    ...       0.402802   1.450089
181  2023-06-01 10:02:15  30.451031    ...       0.402802   2.195135
182  2023-06-01 10:02:16  30.451024    ...       0.816717   3.477648
183  2023-06-01 10:02:17  30.451015    ...       1.115310  11.646074
184  2023-06-01 10:02:18  30.450968    ...       5.354732  19.277034[185 rows x 6 columns]

整体代码

# -*- coding: utf-8 -*-
"""
Created on Tue Jun  6 13:58:42 2023@author: ZHOU
"""import numpy as np
import pandas as pd
import timekeywords_list=["heartrate","cadence","power","distance"]def read_gpx(gpx):first_time=0first_str_time=""trkpt_flag=0j=0num_list=[0]time_list=[None]ele_list=[None]lat_list=[None]lon_list=[None]key_list=[]gpx_dict={}key_dict={}for i in keywords_list:key_list.append([None])for i in range(len(gpx)):        try:ti=str((gpx[i].split("<time>")[1]).split("</time>")[0])now_time = time.mktime(time.strptime(ti, "%Y-%m-%dT%H:%M:%SZ"))first_time=now_time                first_str_time=time.strftime("%Y-%m-%d %H:%M:%S",time.localtime(first_time))  breakexcept:passtime_list[0]=first_str_timefor i in range(len(gpx)):if gpx[i].count('<trkpt'):trkpt_flag=1      j=j+1num_list.append(j)time_list.append(j)ele_list.append(j)lat_list.append(j)lon_list.append(j)            for k in range(len(keywords_list)):key_list[k].append(j)if trkpt_flag==1:try:ti=str((gpx[i].split("<time>")[1]).split("</time>")[0])now_time = time.mktime(time.strptime(ti, "%Y-%m-%dT%H:%M:%SZ"))now_str_time=time.strftime("%Y-%m-%d %H:%M:%S",time.localtime(now_time))  time_list[j]=now_str_timeexcept:passif gpx[i].count('<trkpt'):lat_list[j]=float(gpx[i].split('"')[1])lon_list[j]=float(gpx[i].split('"')[3])try:ele_list[j]=float(str((gpx[i].split("<ele>")[1]).split("</ele>")[0]))except:passfor k in range(len(keywords_list)):           try:dat=str((gpx[i].split("<"+keywords_list[k]+">")[1]).split("</"+keywords_list[k]+">")[0])key_list[k][j]=float(dat)except:passif gpx[i].count('</trkpt>'):trkpt_flag=0if gpx[i].count('</trkseg>'):breakgpx_dict["num"]=num_list    gpx_dict["time"]=time_list       gpx_dict["lat"]=lat_listgpx_dict["lon"]=lon_listgpx_dict["ele"]=ele_list for k in range(len(keywords_list)):key_dict[keywords_list[k]]=key_list[k]gpx_dict["key"]=key_dictreturn gpx_dictdef calculate_speed(time_list,lat_list,lon_list,ele_list):if len(time_list)==len(lat_list) and len(time_list)==len(lon_list) and len(time_list)==len(ele_list):passelse:return df = pd.DataFrame({'time': time_list, 'lat': lat_list, 'lon': lon_list, 'ele': ele_list})columns = df.columns.tolist()df['r'] = 6371393+df['ele'] # radius of the Earth in metersdf['theta'] = np.deg2rad(df['lon'])df['phi'] = np.deg2rad(df['lat'])df['theta2']=df['theta'].shift()df['phi2']=df['phi'].shift()df['arclength'] = df['r'] * np.arccos(np.cos(df['phi']) * np.cos(df['phi2']) * np.cos(df['theta2']-df['theta']) + np.sin(df['phi'])*np.sin(df['phi2']))elapsed_time_list=[]stamp_list=[]speed_list=[]stamp_same_list=[]same_flag=0enable_flag=0exit_same_list=[]for i in range(len(time_list)):try:stamp_list.append(time.mktime(time.strptime(time_list[i], "%Y-%m-%d %H:%M:%S")))enable_flag=1if i>0 and enable_flag==1:if stamp_list[i]>stamp_list[i-1]:elapsed_time_list.append(stamp_list[i]-stamp_list[i-1]) if same_flag==1:same_flag=0exit_same_list.append(i)else:if same_flag==0:stamp_same_list.append(i)same_flag=1elapsed_time_list.append(0.0)else:elapsed_time_list.append(None)except:if enable_flag==0:elapsed_time_list.append(None)else:if same_flag==0:stamp_same_list.append(i)same_flag=1elapsed_time_list.append(0.0)if len(stamp_same_list)>len(exit_same_list):exit_same_list.append(0)  j=0displacement=0.0displacement_time=0.0end_displacement=0.0same_flag=0end_elapsed_time=0.0stamp_same_in_1st_flag=0if len(stamp_same_list)==0:for i in range(len(elapsed_time_list)):try:try:speed_list.append((df['arclength'][i]+df['arclength'][i+1])/ (elapsed_time_list[i]+elapsed_time_list[i+1]))  # km/hexcept:speed_list.append(df['arclength'][i]/ elapsed_time_list[i])  # m/sexcept:speed_list.append(None)else:  for i in range(len(elapsed_time_list)):try:if i>0:try:if i==stamp_same_list[j]-1:same_flag=1if stamp_same_list[0]==1 and stamp_same_in_1st_flag==0:stamp_same_in_1st_flag=1same_flag=1except:passif same_flag==0:try:speed_list.append((df['arclength'][i]+df['arclength'][i+1])/ (elapsed_time_list[i]+elapsed_time_list[i+1]))  # m/sexcept:speed_list.append(df['arclength'][i]/ elapsed_time_list[i])  # m/selse:   try:displacement=displacement+df['arclength'][i]except:displacement=displacement+0.0try:displacement_time=displacement_time+elapsed_time_list[i]except:displacement_time=displacement_time+0.0if j==len(stamp_same_list)-1 and exit_same_list[j]==0:if end_elapsed_time==0.0:end_elapsed_time=elapsed_time_list[i]                                end_displacement=end_displacement+df['arclength'][i]if end_elapsed_time>0.0:speed_list.append(end_displacement/end_elapsed_time)else:speed_list.append(end_displacement/1.0)else:speed_list.append(None)if i==exit_same_list[j]: avg_speed=displacement/displacement_timefor k in range(stamp_same_list[j]-1,i+1):speed_list[k]=avg_speed       j=j+1try:if elapsed_time_list[j]-end_elapsed_time[j-1]<=1:passelse:same_flag=0displacement=0.0displacement_time=0.0except:same_flag=0displacement=0.0displacement_time=0.0else:speed_list.append(None)except:speed_list.append(None)df['elapsed_time'] = elapsed_time_listdf['speed'] = speed_list  # m/sdf['speed'] = 3.6*df['speed'] # km/hdf = df[columns + ['arclength']+['speed']]return dfif __name__ == '__main__':calculate_speed(['2017-07-08 22:05:45', '2017-07-08 22:05:46', '2017-07-08 22:05:47', '2017-07-08 22:05:48', '2017-07-08 22:05:49','2017-07-08 22:05:50'],[-33.81612, -33.81615, -33.816117, -33.816082, -33.816043,-33.816001],[150.871031, 150.871035, 150.87104399999998, 150.87105400000002, 150.871069,150.871080],[74.0, 73.0, 74.0, 75.0, 73.0,75.0])path="./2.gpx"f=open(path, 'r', encoding="utf-8")gpx=f.readlines()f.close()  gpx=read_gpx(gpx)print(gpx)df=calculate_speed(gpx["time"],gpx["lat"],gpx["lon"],gpx["ele"])print(df)