Haversine 公式 - 数学略有偏差，不确定原因
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【中文标题】Haversine 公式 - 数学略有偏差，不确定原因【英文标题】：Haversine formula - Math is slightly off, unsure why 【发布时间】：2019-12-12 23:07:44 【问题描述】：我今天早些时候发布了这个问题并解决了这个问题。关于使用半正弦公式，我遇到了不同的问题。 我正在尝试计算两个经纬度点之间的距离。我有公式，我的计算非常接近我需要的输出，但有点偏离。我只需要正确的数字，而不是小数位。但有些计算距离太远，以至于它们不是同一只脚。
我已经完成并尝试从浮点数更改为双精度数，使用调试器比较我的 lat 和 long 以确保我正确地进行了从 DMS 到 Decimal 的计算。
我不知道发生了什么。我必须留下的所有 CONST，它们无法改变。
仅供参考，我没有对最后两列做任何事情。
我们将不胜感激任何有助于引导正确方向的帮助！谢谢！
代码：
//---------------------------------------------------------------------
//
// Input: $GPRMC sentence for add (A). Distance traveled (D).
// Average speed (S). Table of records (T).
//
// Output: Record added. Table of records. Distance traveled.
// Average speed.
//
//---------------------------------------------------------------------
#include<iostream>
#include<string>
#include<iomanip>
using namespace std;
const int MAX_RECS = 5;
const float EARTH_RADIUIS_MILES = 3959;
const int FEET_IN_MILE = 5280;
const float HALF_CIRCLE = 180;
const float PI = 3.14159f;
const int SECS_IN_HR = 3600;
const int SECS_IN_MIN = 60;
const float FPS_PER_KNOT = 1.68781f;
const int ID1 = 2234;
const int ID2 = 5327;
const int ID3 = 7741;
const int TABLEFIRSTSPACE = 51;
const int TABLESECONDSPACE = 6;
const int TABLE8 = 8;
const int TABLE10 = 10;
const int TABLE11 = 11;
const int TABLE13 = 13;
enum FitBitID_Type
ID_FITBIT1 = ID1, ID_FITBIT2 = ID2, ID_FITBIT3 = ID3
;
enum CommandType
ADD_CMD = 'A', DISTANCE_TRAVELED_CMD = 'D',
AVG_SPEED_CMD = 'S', TABLE_PRINT_CMD = 'T'
;
void ReadIn(string &time, string &latNum, string &longNum,
float &speedFloat);
//void timeBreakdown(int time, int &hours, int &minutes, int &seconds);
//void latLongCalc(float latNum, float longNum, float &latD, float &longD);
//float DegreesToRadians(float degrees);
class FitBit
private:
string strTime[MAX_RECS];
int totalSecs[MAX_RECS];
float latitude[MAX_RECS];
float longitude[MAX_RECS];
float speed[MAX_RECS];
int numRecs;//num of records currently stored in the parallel arrays
void timeBreakdown(string time, int &hours, int &minutes, int &seconds)
hours = stoi(time.substr(0, 2));
minutes = stoi(time.substr(2, 2));
seconds = stoi(time.substr(4, 2));
void latLongCalc(string latNum, string longNum, float &latD, float &longD)
float degreeLa = stof(latNum.substr(0, 2));
float minuteLa = stof(latNum.substr(2, 2));
float secondLa = stof(latNum.substr(5, 3));
latD = degreeLa + (minuteLa / SECS_IN_MIN) +
(((secondLa / 1000) * SECS_IN_MIN) / SECS_IN_HR);
float degreeLo = stof(longNum.substr(0, 3));
float minuteLo = stof(longNum.substr(3, 2));
float secondLo = stof(longNum.substr(6, 3));
longD = degreeLo + (minuteLo / SECS_IN_MIN) +
(((secondLo / 1000) * SECS_IN_MIN) / SECS_IN_HR); longD = -longD;
float DegreesToRadians(float degrees) const
return degrees * PI / HALF_CIRCLE;
public:
FitBit()
numRecs = 0;
void addRecord(string time, string latNum, string longNum,
float speedFloat)
int hours, minutes, seconds;
timeBreakdown(time, hours, minutes, seconds);
float latD, longD;
latLongCalc(latNum, longNum, latD, longD);
hours *= SECS_IN_MIN; minutes += hours; minutes *= SECS_IN_MIN;
seconds += minutes; speedFloat *= FPS_PER_KNOT;
if (numRecs < MAX_RECS)
strTime[numRecs] = time; totalSecs[numRecs] = seconds;
latitude[numRecs] = latD; longitude[numRecs] = longD;
speed[numRecs] = speedFloat;
numRecs++;
else
for (int i = 1; i < numRecs; i++)
strTime[i - 1] = strTime[i]; totalSecs[i - 1] = totalSecs[i];
latitude[i - 1] = latitude[i];
longitude[i - 1] = longitude[i]; speed[i - 1] = speed[i];
strTime[numRecs] = time; totalSecs[numRecs] = seconds;
latitude[numRecs] = latD; longitude[numRecs] = longD;
speed[numRecs] = speedFloat;
float distanceBetweenEarthCoordinates(float lat1, float lon1,
float lat2, float lon2) const
float dLat, dLon, a, c;
lat1 = DegreesToRadians(lat1);
lon1 = DegreesToRadians(lon1);
lat2 = DegreesToRadians(lat2);
lon2 = DegreesToRadians(lon2);
lon1 = -lon1;
lon2 = -lon2;
dLat = (lat2 - lat1);
dLon = (lon2 - lon1);
a = (sin(dLat / 2) * sin(dLat / 2)) + cos(lat1) * cos(lat2)
* (sin(dLon / 2) * sin(dLon / 2));
c = 2 * atan2(sqrt(a), sqrt(1 - a));
//return ((EARTH_RADIUIS_MILES * c) * FEET_IN_MILE);
return EARTH_RADIUIS_MILES * c * FEET_IN_MILE;
float Distance()
if (!(numRecs <= 1))
float total = 0;
for (int i = 1; i < numRecs; i++)
float x = distanceBetweenEarthCoordinates(latitude[i-1],
longitude[i-1], latitude[i], longitude[i]);
total += x;
return total;
return 0;
float DistanceForTable(int i) const
if (!(i < 1))
return distanceBetweenEarthCoordinates(latitude[i - 1],
longitude[i - 1], latitude[i], longitude[i]);
return 0;
void PrintTable()
cout << left << setw(TABLE8) << "Time" << setw(TABLE10)
<< "Latitude" << setw(TABLE10) << "Longitude" << setw(TABLE11)
<< "Speed" << setw(TABLE13) << "Distance" << setw(TABLE10)
<< "Average" << setw(TABLE13) << "Acceleration" << endl << right
<< setw(TABLEFIRSTSPACE) << "Traveled(ft)"
<< setw(TABLESECONDSPACE) << "Speed" << endl;
if (numRecs > 0)
for (int i = 0; i < numRecs; i++)
cout << left << setw(TABLE8) << strTime[i];
cout << left << setw(TABLE10) << latitude[i];
cout << left << setw(TABLE10) << longitude[i];
cout << left << setw(TABLE11) << speed[i];
if (i < 1)
cout << left << setw(TABLE13) << " ";
else
cout << left << setw(TABLE13) << DistanceForTable(i);
cout << left << setw(TABLE10) << 200.0;
cout << left << setw(TABLE13) << 1.0101 << endl;
;
void ProcessCommandForFitBit(FitBit & bit, CommandType command,
FitBitID_Type FitBitID);
int main()
cout << fixed << showpoint << setprecision(4);
char cmd; int id;
FitBit bit1, bit2, bit3;
while (cin)
cin >> cmd >> id;
FitBitID_Type FitBitID = FitBitID_Type(id);
CommandType command = CommandType(cmd);
if (FitBitID == ID_FITBIT1)
ProcessCommandForFitBit(bit1, command, FitBitID);
else if (FitBitID == ID_FITBIT2)
ProcessCommandForFitBit(bit2, command, FitBitID);
else if (FitBitID == ID_FITBIT3)
ProcessCommandForFitBit(bit3, command, FitBitID);
cout << "Normal Termination of Program 5.";
return 0;
void ProcessCommandForFitBit(FitBit & bit, CommandType command,
FitBitID_Type FitBitID)
int returnedDistance = 0; float returnedAvgSpeed = 0;
string time, latNum, longNum; float speedFloat = 0;
switch (command)
case ADD_CMD:
ReadIn(time, latNum, longNum, speedFloat);
bit.addRecord(time, latNum, longNum, speedFloat);
cout << "Record added for FitBit with ID " << FitBitID << endl;
break;
case DISTANCE_TRAVELED_CMD:
returnedDistance = bit.Distance();
cout << "Distance Traveled in feet for FitBit with ID "
<< FitBitID << " is " << returnedDistance << endl;
break;
case AVG_SPEED_CMD:
cout << "Average Speed for FitBit with ID " << FitBitID
<< " is " << returnedAvgSpeed << endl;
break;
case TABLE_PRINT_CMD:
cout << "Records for FitBit with ID " << FitBitID << endl;
bit.PrintTable();
break;
void ReadIn(string &time, string &latNum, string &longNum, float &speedFloat)
string trash;
cin >> trash >> time >> trash >> latNum >> trash >> longNum
>> trash >> speedFloat >> trash >> trash >> trash >> trash;
输入文件：
A 2234 $GPRMC 204849 A 4243.636 N 09028.597 W 000.0 065.5 091297 000.2 W*7F
A 2234 $GPRMC 204851 A 4243.636 N 09028.594 W 006.4 074.4 091297 000.2 W*76
A 2234 $GPRMC 204853 A 4243.638 N 09028.586 W 011.7 067.9 091297 000.2 W*73
A 2234 $GPRMC 204855 A 4243.641 N 09028.574 W 014.2 067.5 091297 000.2 W*7A
T 2234
D 2234
S 2234
A 2234 $GPRMC 204903 A 4243.662 N 09028.593 W 018.7 066.2 090108 000.2 W*7A
T 2234
D 2234
S 2234
T 5327
D 5327
S 5327
A 5327 $GPRMC 204905 A 4273.667 N 09047.499 W 021.6 064.5 090108 000.2 W*78
T 5327
D 5327
S 5327
A 5327 $GPRMC 204907 A 4273.671 N 09047.480 W 027.3 065.4 090108 000.2 W*73
T 5327
D 5327
S 5327
A 7741 $GPRMC 204909 A 4273.679 N 09047.459 W 026.5 066.8 090108 000.2 W*77
A 7741 $GPRMC 204913 A 4273.689 N 09047.418 W 031.7 068.6 090108 000.2 W*7F
T 7741
D 7741
S 7741
我的输出：
Record added for FitBit with ID 2234
Record added for FitBit with ID 2234
Record added for FitBit with ID 2234
Record added for FitBit with ID 2234
Records for FitBit with ID 2234
Time Latitude Longitude Speed Distance Average Acceleration
Traveled(ft) Speed
204849 42.7273 -90.4766 0.0000 200.0000 1.0101
204851 42.7273 -90.4766 10.8020 12.8137 200.0000 1.0101
204853 42.7273 -90.4764 19.7474 37.9431 200.0000 1.0101
204855 42.7274 -90.4762 23.9669 54.9950 200.0000 1.0101
Distance Traveled in feet for FitBit with ID 2234 is 105
Average Speed for FitBit with ID 2234 is 0.0000
Record added for FitBit with ID 2234
Records for FitBit with ID 2234
Time Latitude Longitude Speed Distance Average Acceleration
Traveled(ft) Speed
204849 42.7273 -90.4766 0.0000 200.0000 1.0101
204851 42.7273 -90.4766 10.8020 12.8137 200.0000 1.0101
204853 42.7273 -90.4764 19.7474 37.9431 200.0000 1.0101
204855 42.7274 -90.4762 23.9669 54.9950 200.0000 1.0101
204903 42.7277 -90.4765 31.5620 151.4476 200.0000 1.0101
Distance Traveled in feet for FitBit with ID 2234 is 257
Average Speed for FitBit with ID 2234 is 0.0000
Records for FitBit with ID 5327
Time Latitude Longitude Speed Distance Average Acceleration
Traveled(ft) Speed
Distance Traveled in feet for FitBit with ID 5327 is 0
Average Speed for FitBit with ID 5327 is 0.0000
Record added for FitBit with ID 5327
Records for FitBit with ID 5327
Time Latitude Longitude Speed Distance Average Acceleration
Traveled(ft) Speed
204905 43.2278 -90.7916 36.4567 200.0000 1.0101
Distance Traveled in feet for FitBit with ID 5327 is 0
Average Speed for FitBit with ID 5327 is 0.0000
Record added for FitBit with ID 5327
Records for FitBit with ID 5327
Time Latitude Longitude Speed Distance Average Acceleration
Traveled(ft) Speed
204905 43.2278 -90.7916 36.4567 200.0000 1.0101
204907 43.2279 -90.7913 46.0772 87.9045 200.0000 1.0101
Distance Traveled in feet for FitBit with ID 5327 is 87
Average Speed for FitBit with ID 5327 is 0.0000
Record added for FitBit with ID 7741
Record added for FitBit with ID 7741
Records for FitBit with ID 7741
Time Latitude Longitude Speed Distance Average Acceleration
Traveled(ft) Speed
204909 43.2280 -90.7910 44.7270 200.0000 1.0101
204913 43.2281 -90.7903 53.5036 193.2789 200.0000 1.0101
Distance Traveled in feet for FitBit with ID 7741 is 193
Average Speed for FitBit with ID 7741 is 0.0000
Average Speed for FitBit with ID 7741 is 0.0000
Normal Termination of Program 5.
我需要匹配的输出：
Record added for FitBit with ID 2234
Record added for FitBit with ID 2234
Record added for FitBit with ID 2234
Record added for FitBit with ID 2234
Records for FitBit with ID 2234
Time Latitude Longitude Speed Distance Average Acceleration
Traveled(ft) Speed
204849 42.7273 -90.4766 0.0000
204851 42.7273 -90.4766 10.8020 12 5.4010 5.4010
204853 42.7273 -90.4764 19.7474 36 10.1831 4.4727
204855 42.7274 -90.4762 23.9669 56 13.6291 2.1098
Distance Traveled in feet for FitBit with ID 2234 is 104
Average Speed for FitBit with ID 2234 is 13.6291
Record added for FitBit with ID 2234
Records for FitBit with ID 2234
Time Latitude Longitude Speed Distance Average Acceleration
Traveled(ft) Speed
204849 42.7273 -90.4766 0.0000
204851 42.7273 -90.4766 10.8020 12 5.4010 5.4010
204853 42.7273 -90.4764 19.7474 36 10.1831 4.4727
204855 42.7274 -90.4762 23.9669 56 13.6291 2.1098
204903 42.7277 -90.4765 31.5620 153 17.2157 0.9494
Distance Traveled in feet for FitBit with ID 2234 is 257
Average Speed for FitBit with ID 2234 is 17.2157
Records for FitBit with ID 5327
Time Latitude Longitude Speed Distance Average Acceleration
Traveled(ft) Speed
Distance Traveled in feet for FitBit with ID 5327 is 0
Average Speed for FitBit with ID 5327 is 0.0000
Record added for FitBit with ID 5327
Records for FitBit with ID 5327
Time Latitude Longitude Speed Distance Average Acceleration
Traveled(ft) Speed
204905 43.2278 -90.7916 36.4567
Distance Traveled in feet for FitBit with ID 5327 is 0
Average Speed for FitBit with ID 5327 is 36.4567
Record added for FitBit with ID 5327
Records for FitBit with ID 5327
Time Latitude Longitude Speed Distance Average Acceleration
Traveled(ft) Speed
204905 43.2278 -90.7916 36.4567
204907 43.2278 -90.7913 46.0772 84 41.2670 4.8103
Distance Traveled in feet for FitBit with ID 5327 is 84
Average Speed for FitBit with ID 5327 is 41.2670
Record added for FitBit with ID 7741
Record added for FitBit with ID 7741
Records for FitBit with ID 7741
Time Latitude Longitude Speed Distance Average Acceleration
Traveled(ft) Speed
204909 43.2280 -90.7910 44.7270
204913 43.2281 -90.7903 53.5036 192 49.1153 2.1942
Distance Traveled in feet for FitBit with ID 7741 is 192
Average Speed for FitBit with ID 7741 is 49.1153
Normal Termination of Program 5.
【问题讨论】：
嗨。您是否尝试过为 PI 使用更精确的常数？我没有检查你所有的代码，但 5 位数对我来说似乎真的很低。 @AlexG，我做到了，但这让这些数字甚至变得很糟糕。我得到的 PI 必须使用，所以我不能再精确了。 看起来您的输入程序可能有点不对劲。查看您的输入很难看出您如何将 ID2234 与 42.7273 和 -90.4766 的纬度/经度联系起来。根据您的输入，看起来那些经纬度与 ID 5327??
@DavidC.Rankin 我刚刚经历并从我的输入文件中删除了另一个 id。输出是相同的，数学只是略有偏差。这是一个学校项目，所以他们严格要求不传递身份。
可以在this question 中找到另一种选择。
【参考方案1】：
解决了
我不得不重用一段我们的教授从未告诉我们需要复制的旧代码。这是度分秒转换器的不同实现，与半正弦公式无关。
感谢大家的帮助！
【讨论】：
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