Haversine Formula in Python Bearing and Distance between two GPS points

Question

Problem  I would like to know how to get the distance and bearing between 2 GPS points  I have researched on the haversine formula  Someone told me that I could also find the bearing using the same data   Edit  Everything is working fine but the bearing doesn t quite work right yet  The bearing outputs negative but should be between 0 - 360 degrees  The set data should make the horizontal bearing 96 02166666666666 and is   Start point  53 32055555555556   -1 7297222222222221    Bearing   96 02166666666666   Distance  2 km   Destination point  53 31861111111111  -1 6997222222222223   Final bearing  96 04555555555555   Here is my new code   from math import    Aaltitude   2000 Oppsite    20000  lat1   53 32055555555556 lat2   53 31861111111111 lon1   -1 7297222222222221 lon2   -1 6997222222222223  lon1  lat1  lon2  lat2   map radians   lon1  lat1  lon2  lat2    dlon   lon2 - lon1 dlat   lat2 - lat1 a   sin dlat 2   2   cos lat1    cos lat2    sin dlon 2   2 c   2   atan2 sqrt a   sqrt 1-a   Base   6371   c   Bearing  atan2 cos lat1  sin lat2 -sin lat1  cos lat2  cos lon2-lon1   sin lon2-lon1  cos lat2     Bearing   degrees Bearing  print    print    print  --------------------  print  Horizontal Distance   print Base print  --------------------  print  Bearing   print Bearing print  --------------------    Base2   Base   1000 distance   Base   2   Oppsite   2   2 Caltitude   Oppsite - Aaltitude  a   Oppsite Base b   atan a  c   degrees b   distance   distance   1000  print  The degree of vertical angle is   print c print  --------------------  print  The distance between the Balloon GPS and the Antenna GPS is   print distance print  --------------------

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There is also a vectorized implementation  which allows to use 4 numpy arrays instead of scalar values for coordinates   def distance s lat  s lng  e lat  e lng         approximate radius of earth in km    R   6373 0     s lat   s lat np pi 180 0                          s lng   np deg2rad s lng          e lat   np deg2rad e lat                            e lng   np deg2rad e lng        d   np sin  e lat - s lat  2   2   np cos s lat  np cos e lat    np sin  e lng - s lng  2   2     return 2   R   np arcsin np sqrt d

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Here s a numpy vectorized implementation of the Haversine Formula given by  Michael Dunn  gives a 10-50 times improvement over large vectors   from numpy import radians  cos  sin  arcsin  sqrt  def haversine lon1  lat1  lon2  lat2               Calculate the great circle distance between two points      on the earth  specified in decimal degrees                Convert decimal degrees to Radians      lon1   np radians lon1 values      lat1   np radians lat1 values      lon2   np radians lon2 values      lat2   np radians lat2 values        Implementing Haversine Formula       dlon   np subtract lon2  lon1      dlat   np subtract lat2  lat1       a   np add np power np sin np divide dlat  2    2                               np multiply np cos lat1                                          np multiply np cos lat2                                                      np power np sin np divide dlon  2    2         c   np multiply 2  np arcsin np sqrt a        r   6371      return c r

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Most of these answers are  rounding  the radius of the earth   If you check these against other distance calculators  such as geopy   these functions will be off   This works well   from math import radians  cos  sin  asin  sqrt  def haversine lat1  lon1  lat2  lon2          R   3959 87433   this is in miles   For Earth radius in kilometers use 6372 8 km        dLat   radians lat2 - lat1        dLon   radians lon2 - lon1        lat1   radians lat1        lat2   radians lat2         a   sin dLat 2   2   cos lat1  cos lat2  sin dLon 2   2       c   2 asin sqrt a          return R   c    Usage lon1   -103 548851 lat1   32 0004311 lon2   -103 6041946 lat2   33 374939  print haversine lat1  lon1  lat2  lon2

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You can try the following   from haversine import haversine haversine  45 7597  4 8422   48 8567  2 3508   unit  mi   243 71209416020253

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The Y in atan2 is  by default  the first parameter  Here is the documentation  You will need to switch your inputs to get the correct bearing angle   bearing   atan2 sin lon2-lon1  cos lat2   cos lat1  sin lat2 in lat1  cos lat2  cos lon2-lon1   bearing   degrees bearing  bearing    bearing   360    360

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The bearing calculation is incorrect  you need to swap the inputs to atan2       bearing   atan2 sin long2-long1  cos lat2   cos lat1  sin lat2 -sin lat1  cos lat2  cos long2-long1       bearing   degrees bearing      bearing    bearing   360    360   This will give you the correct bearing

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Here are two functions to calculate distance and bearing  which are based on the code in previous messages and https   gist github com jeromer 2005586  added tuple type for geographical points in lat  lon format for both functions for clarity   I tested both functions and they seem to work right    coding UTF-8 from math import radians  cos  sin  asin  sqrt  atan2  degrees  def haversine pointA  pointB        if  type pointA     tuple  or  type pointB     tuple           raise TypeError  Only tuples are supported as arguments        lat1   pointA 0      lon1   pointA 1       lat2   pointB 0      lon2   pointB 1         convert decimal degrees to radians      lat1  lon1  lat2  lon2   map radians   lat1  lon1  lat2  lon2           haversine formula      dlon   lon2 - lon1      dlat   lat2 - lat1      a   sin dlat 2   2   cos lat1    cos lat2    sin dlon 2   2     c   2   asin sqrt a        r   6371   Radius of earth in kilometers  Use 3956 for miles     return c   r   def initial bearing pointA  pointB        if  type pointA     tuple  or  type pointB     tuple           raise TypeError  Only tuples are supported as arguments        lat1   radians pointA 0       lat2   radians pointB 0        diffLong   radians pointB 1  - pointA 1        x   sin diffLong    cos lat2      y   cos lat1    sin lat2  -  sin lat1                cos lat2    cos diffLong        initial bearing   atan2 x  y         Now we have the initial bearing but math atan2 return values       from -180   to   180   which is not what we want for a compass bearing       The solution is to normalize the initial bearing as shown below     initial bearing   degrees initial bearing      compass bearing    initial bearing   360    360      return compass bearing  pA    46 2038 6 1530  pB    46 449  30 690   print haversine pA  pB   print initial bearing pA  pB

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Here s a Python version   from math import radians  cos  sin  asin  sqrt  def haversine lon1  lat1  lon2  lat2               Calculate the great circle distance between two points      on the earth  specified in decimal degrees                convert decimal degrees to radians      lon1  lat1  lon2  lat2   map radians   lon1  lat1  lon2  lat2          haversine formula      dlon   lon2 - lon1      dlat   lat2 - lat1      a   sin dlat 2   2   cos lat1    cos lat2    sin dlon 2   2     c   2   asin sqrt a        r   6371   Radius of earth in kilometers  Use 3956 for miles     return c   r

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Refer to this link  https   gis stackexchange com questions 84885 whats-the-difference-between-vincenty-and-great-circle-distance-calculations  this actually gives two ways of getting distance  They are Haversine and Vincentys  From my research I came to know that Vincentys is relatively accurate  Also use import statement to make the implementation

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You can solve the negative bearing problem by adding 360     Unfortunately  this might result in bearings larger than 360   for positive bearings  This is a good candidate for the modulo operator  so all in all you should add the line   Bearing    Bearing   360    360   at the end of your method

[python] Haversine Formula in Python (Bearing and Distance between two GPS points)

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