Orbital Analysis for matched events on 20210929_223330.500_UK

Summary for Event
-----------------
shower ID -1 spo
Lg 23.46° Bg 24.01° Vg 24.71km/s
mass 0.02907g, abs. mag 1.3
Path Details
------------
start 0.67° 53.54° 85.21km
end   0.61° 53.57° 74.66km

Orbit Details
-------------
Semimajor axis 1.38A.U., eccentricity 0.69, inclination 23.41°, Period 1.62Y, LA Sun 186.70°, last Perihelion 2020-04-05

Full details below
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Input measurement type: Azimuth +east of due north for meas1, Elevation angle above the horizon for meas2

Uncertainties type:
 Purely geometric uncertainties

Reference JD: 2459487.439936344046
Time: 2021-09-29 22:33:30.500126 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK0026 and UK002K
 Convergence angle = 39.25130 deg
 R.A. =  12.13878  Dec = +32.34240 deg
Intersection 2 - Stations: UK0026 and UK0032
 Convergence angle = 0.16811 deg
 R.A. =  70.75462  Dec = +65.67972 deg
Intersection 3 - Stations: UK002K and UK0032
 Convergence angle = 39.13905 deg
 R.A. =  11.92246  Dec = +32.26634 deg

Best intersection: Stations UK0026 and UK002K with Qconv = 39.25 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   3764407.54 +/- 51.91 m
 Y =   -803607.48 +/- 41.69 m
 Z =   5175063.33 +/- 56.59 m
 Vx =    22453.94 +/- 138.82 m/s
 Vy =     4411.40 +/- 126.83 m/s
 Vz =    14514.10 +/- 110.29 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+2.715279e+03, +2.041368e+03, +2.898787e+03, +8.618567e+02, +4.859129e+03, +4.770410e+03
+2.041368e+03, +1.759167e+03, +2.297398e+03, +8.108994e+02, +4.714259e+03, +4.115864e+03
+2.898787e+03, +2.297398e+03, +3.228544e+03, +1.017062e+03, +5.751266e+03, +5.627390e+03
+8.618567e+02, +8.108994e+02, +1.017062e+03, +4.164328e+02, +2.546669e+03, +2.107115e+03
+4.859129e+03, +4.714259e+03, +5.751266e+03, +2.546669e+03, +1.609954e+04, +1.277812e+04
+4.770410e+03, +4.115864e+03, +5.627390e+03, +2.107115e+03, +1.277812e+04, +1.200234e+04

Timing offsets (from input data):
    UK0026: -0.000043 s
    UK002K: 0.000000 s
    UK0032: -0.000031 s

Reference point on the trajectory:
  Time: 2021-09-29 22:33:30.500126 UTC
  Lon     = ++0.670905 +/- 0.0008 deg
  Lat     = +53.539707 +/- 0.0001 deg
  Lat geo = +53.358023 +/- 0.0001 deg
  Ht      =   85248.03 +/- 70.38 m

  JD dynamic   = 2459487.440737084951 
  LST apparent = 347.9496530418 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  11.11501 +/- 0.3016 deg
  Dec       = +32.38570 +/- 0.1475 deg
  Azimuth   = 132.66007 +/- 0.6309 deg
  Elevation = +63.14499 +/- 0.0660 deg
  Vavg      =  26.13637 +/- 0.1450 km/s
  Vinit     =  27.09795 +/- 0.0961 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  11.75802 +/- 0.3016 deg
  Dec       = +32.25945 +/- 0.1475 deg
  Azimuth   = 131.78461 +/- 0.6309 deg
  Elevation = +62.75424 +/- 0.0660 deg
  Vavg      =  26.23091 +/- 0.1450 km/s
  Vinit     =  27.19249 +/- 0.0961 km/s
Radiant (geocentric, J2000):
  R.A.   =  11.58732 +/- 0.3058 deg
  Dec    = +31.19548 +/- 0.1602 deg
  Vg     =  24.71232 +/- 0.1053 km/s
  Vinf   =  27.09795 +/- 0.0961 km/s
  Zc     =  26.73220 +/- 0.0664 deg
  Zg     =  27.98587 +/- 0.0689 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  23.45975 +/- 0.3258 deg
  Bg     = +24.00922 +/- 0.0723 deg
  Vh     =  33.60030 +/- 0.0566 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     = 320.27281 +/- 0.2501 deg
  Bh     = +17.41666 +/- 0.1339 deg
  Vh_x   = -24.65710 +/- 0.0308 km/s
  Vh_y   =  20.49049 +/- 0.1551 km/s
  Vh_z   = -10.05718 +/- 0.0614 km/s
Orbit:
  La Sun = 186.699334 +/- -0.0000 deg
  a      =   1.380851 +/- 0.0080 AU
  e      =   0.689461 +/- 0.0014
  i      =  23.411182 +/- 0.2559 deg
  peri   = 293.657819 +/- 0.5569 deg
  node   = 186.702656 +/- 0.0000 deg
  Pi     = 120.360476 +/- 0.5568 deg
  q      =   0.428809 +/- 0.0043 AU
  f      = 246.338920 +/- 0.5568 deg
  M      = 329.709184 +/- 0.2460 deg
  Q      =   2.332894 +/- 0.0117 AU
  n      =   0.607413 +/- 0.0054 deg/day
  T      =   1.622636 +/- 0.0140 years
  Last perihelion JD = 2458944.631247 (2020-04-05 03:08:59.703651) +/- 5.0780 days
  Tj     =   4.453655 +/- 0.0179
Shower association:
  IAU No.  =   -1
  IAU code =  ...

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +1.816545e-06, -5.679057e-06, +6.586120e-03, -8.064345e-10, +1.283710e-05, +5.793389e-06
q   , -5.679057e-06, +1.814713e-05, -2.140886e-02, +2.436468e-09, -4.118558e-05, -1.751070e-05
Tp  , +6.586120e-03, -2.140886e-02, +2.558582e+01, -2.747475e-06, +4.873798e-02, +1.975348e-02
node, -8.064345e-10, +2.436468e-09, -2.747475e-06, +3.841126e-13, -5.471998e-09, -2.757849e-09
peri, +1.283710e-05, -4.118558e-05, +4.873798e-02, -5.471998e-09, +9.354042e-05, +3.933051e-05
i   , +5.793389e-06, -1.751070e-05, +1.975348e-02, -2.757849e-09, +3.933051e-05, +1.980294e-05

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 0.093470
 a2 = 18.329433

Mean time residuals from time vs. length:
  Station with reference time: UK002K
  Avg. res. = 7.751e-06 s
  Stddev    = 2.78e-03 s

Begin point on the trajectory:
  Lon =     0.670687 +/- 0.0007 deg
  Lat =    53.539826 +/- 0.0000 deg
  Ht  = 85208.70 +/- 65.18 m
End point on the trajectory:
  Lon =     0.610210 +/- 0.0006 deg
  Lat =    53.571971 +/- 0.0001 deg
  Ht  = 74656.57 +/- 51.18 m

Stations
--------
        ID, Ignored, Lon +E (deg), Lat +N (deg),  Ht (m), Jacchia a1, Jacchia a2,  Beg Ht (m),  End Ht (m), +/- Obs ang (deg), +/- V (m), +/- H (m), Persp. angle (deg), Weight, FOV Beg, FOV End, Comment
    UK0026,   False,    -0.023645,    52.984073,    6.00,   0.030071,  20.850377,    84582.45,    74875.25,          0.018352,     21.94,     27.78,              50.22, 0.5906,    True,    True, {"ff_name": "FF_UK0026_20210929_223327_502_0386304.fits"}
    UK002K,   False,    -0.382860,    53.537770,   34.00,   0.079708,  17.934103,    85208.70,    74656.57,          0.006900,     10.66,      6.92,              24.67, 0.1743,    True,    True, {"ff_name": "FF_UK002K_20210929_223325_585_0384512.fits"}
    UK0032,   False,    -0.023645,    52.984073,    6.00,   0.000000,  67.225396,    81630.43,    75464.69,          0.017227,     20.85,     26.40,              50.22, 0.5906,    True,    True, {"ff_name": "FF_UK0032_20210929_223322_684_0387072.fits"}

Points
------
 No, Station ID,  Ignore,  Time (s),                   JD,     meas1,     meas2, Azim +E of due N (deg), Alt (deg), Azim line (deg), Alt line (deg), RA obs (deg), Dec obs (deg), RA line (deg), Dec line (deg),       X (m),       Y (m),       Z (m), Latitude (deg), Longitude (deg), Height (m),  Range (m), Length (m), State vect dist (m),  Lag (m), Vel (m/s), Vel prev avg (m/s), H res (m), V res (m), Ang res (asec), AppMag, AbsMag
  0,     UK0026,       0,  0.031293, 2459487.439936737064,  76.95722,  66.18908,               36.32354,  47.03485,        36.32223,       47.03548,     76.95722,     +66.18908,      76.95701,      +66.19016,  3763789.35,  -803728.93,  5174663.74,      53.541732,       +0.667073,   84582.45,  114926.58,       0.00,              746.04,  -216.98,      0.00,           27962.31,      1.71,     -1.35,           3.92,  +3.39,  +3.09
  1,     UK0026,       0,  0.071697, 2459487.439937205054,  78.21836,  66.25238,               35.88896,  46.61752,        35.88449,       46.61967,     78.21836,     +66.25238,      78.21766,      +66.25611,  3762702.28,  -803942.50,  5173961.07,      53.545293,       +0.660413,   83412.07,  114100.64,    1311.90,             2057.94,     0.06,  32469.60,           27962.31,      5.86,     -4.63,          13.51,  +3.24,  +2.95
  2,     UK0026,       0,  0.152409, 2459487.439938139170,  80.43830,  66.31338,               35.17553,  45.87086,        35.13434,       45.89056,     80.43830,     +66.31338,      80.43261,      +66.34808,  3760841.27,  -804308.12,  5172758.12,      53.551393,       +0.648956,   81408.51,  112706.96,    3557.81,             4303.85,    58.84,  27826.25,           27962.31,     53.70,    -42.42,         125.24,  +2.82,  +2.56
  3,     UK0026,       0,  0.192705, 2459487.439938605297,  81.40064,  66.38118,               34.81030,  45.57314,        34.81288,       45.57191,     81.40064,     +66.38118,      81.40177,      +66.37899,  3760044.96,  -804464.57,  5172243.39,      53.554004,       +0.644027,   80551.22,  112118.49,    4518.83,             5264.87,   -72.09,  23848.84,           27962.31,     -3.36,      2.65,           7.87,  +2.83,  +2.58
  4,     UK0026,       0,  0.233097, 2459487.439939072821,  82.62027,  66.38633,               34.44217,  45.15859,        34.41670,       45.17070,     82.62027,     +66.38633,      82.61917,      +66.40797,  3759058.49,  -804658.38,  5171605.74,      53.557239,       +0.637958,   79489.25,  111397.85,    5709.32,             6455.36,    23.87,  29473.55,           27881.95,     33.05,    -26.10,          77.97,  +2.53,  +2.30
  5,     UK0026,       0,  0.273437, 2459487.439939539880,  83.71218,  66.42744,               34.06416,  44.81047,        34.06528,       44.80993,     83.71218,     +66.42744,      83.71338,      +66.42648,  3758184.30,  -804830.12,  5171040.67,      53.560106,       +0.632558,   78548.17,  110765.56,    6764.31,             7510.35,   -14.28,  26152.34,           27671.12,     -1.46,      1.15,           3.46,  +1.92,  +1.70
  6,     UK0026,       0,  0.313781, 2459487.439940006938,  84.78782,  66.42628,               33.73724,  44.44865,        33.72431,       44.45475,     84.78782,     +66.42628,      84.78903,      +66.43734,  3757335.55,  -804996.87,  5170492.04,      53.562891,       +0.627308,   77634.49,  110157.79,    7788.60,             8534.64,   -83.22,  25389.07,           27392.11,     16.69,    -13.18,          39.83,  +2.17,  +1.96
  7,     UK0026,       0,  0.354161, 2459487.439940473996,  85.99440,  66.44664,               33.34005,  44.05860,        33.34762,       44.05503,     85.99440,     +66.44664,      85.99565,      +66.44014,  3756394.76,  -805181.71,  5169883.92,      53.565978,       +0.621504,   76621.76,  109491.93,    8923.97,             9670.01,   -42.07,  28117.12,           27309.15,     -9.76,      7.70,          23.42,  +2.10,  +1.90
  8,     UK0026,       0,  0.394517, 2459487.439940941054,  87.12907,  66.45335,               32.97621,  43.68877,        32.99788,       43.67858,     87.12907,     +66.45335,      87.12919,      +66.43467,  3755521.22,  -805353.33,  5169319.27,      53.568845,       +0.616101,   75681.44,  108880.37,    9978.18,            10724.22,   -81.43,  26122.60,           27200.19,    -27.88,     22.01,          67.30,  +2.62,  +2.44
  9,     UK0026,       0,  0.434821, 2459487.439941407647,  88.11316,  66.45797,               32.65821,  43.37034,        32.69746,       43.35193,     88.11316,     +66.45797,      88.11089,      +66.42405,  3754772.30,  -805500.46,  5168835.17,      53.571304,       +0.611443,   74875.25,  108360.88,   10882.00,            11628.04,  -269.76,  22425.15,           26916.53,    -50.42,     39.80,         122.27,  +4.37,  +4.20
  0,     UK002K,       0,  0.000000, 2459487.439936344046,  41.77536,  38.41432,               89.39833,  50.13914,        89.38861,       50.14534,     41.77536,     +38.41432,      41.77454,      +38.42309,  3764371.01,  -803614.66,  5175039.72,      53.539826,       +0.670687,   85208.70,  110445.97,       0.00,               44.09,   -70.96,      0.00,           26732.96,      9.22,     14.22,          31.65,  +3.10,  +2.88
  1,     UK002K,       0,  0.040080, 2459487.439936807845,  42.07850,  38.43890,               89.12827,  49.97502,        89.12319,       49.97824,     42.07850,     +38.43890,      42.07826,      +38.44348,  3763484.14,  -803788.90,  5174466.46,      53.542732,       +0.665226,   84253.85,  109474.43,    1070.29,             1114.38,   -86.75,  26703.84,           26732.96,      4.77,      7.36,          16.52,  +2.55,  +2.35
  2,     UK002K,       0,  0.080164, 2459487.439937271643,  42.40286,  38.46394,               88.84196,  49.79859,        88.84163,       49.79881,     42.40286,     +38.46394,      42.40317,      +38.46424,  3762553.59,  -803971.72,  5173864.95,      53.545781,       +0.659501,   83251.98,  108457.45,    2193.31,             2237.40,   -49.93,  28016.65,           26732.96,      0.31,      0.48,           1.09,  +2.53,  +2.35
  3,     UK002K,       0,  0.120248, 2459487.439937735908,  42.69846,  38.47812,               88.59223,  49.63220,        88.58717,       49.63539,     42.69846,     +38.47812,      42.69859,      +38.48269,  3761721.55,  -804135.18,  5173327.12,      53.548507,       +0.654363,   82356.19,  107549.21,    3197.43,             3241.52,  -132.00,  25050.49,           26732.96,      4.67,      7.21,          16.48,  +2.57,  +2.41
  4,     UK002K,       0,  0.160344, 2459487.439938199706,  43.08703,  38.51866,               88.23978,  49.42775,        88.25499,       49.41818,     43.08703,     +38.51866,      43.08877,      +38.50492,  3760647.73,  -804346.15,  5172633.01,      53.552027,       +0.647778,   81200.15,  106381.81,    4493.34,             4537.43,    77.39,  32320.18,           27725.31,    -13.92,    -21.44,          49.56,  +2.33,  +2.20
  5,     UK002K,       0,  0.200440, 2459487.439938663971,  43.38971,  38.51832,               88.00362,  49.24776,        87.99953,       49.25032,     43.38971,     +38.51832,      43.39028,      +38.52201,  3759831.44,  -804506.52,  5172105.37,      53.554704,       +0.642729,   80321.36,  105494.70,    5478.45,             5522.54,   -24.02,  24568.81,           27557.73,      3.70,      5.71,          13.30,  +2.32,  +2.20
  6,     UK002K,       0,  0.240524, 2459487.439939127769,  43.72689,  38.55014,               87.70418,  49.06821,        87.71548,       49.06115,     43.72689,     +38.55014,      43.72860,      +38.53992,  3758933.11,  -804683.01,  5171524.69,      53.557650,       +0.637188,   79354.27,  104521.26,    6562.59,             6606.67,   -26.08,  27046.49,           27443.12,    -10.17,    -15.65,          36.83,  +2.15,  +2.05
  7,     UK002K,       0,  0.280628, 2459487.439939592034,  44.08755,  38.56011,               87.41308,  48.86056,        87.41567,       48.85894,     44.08755,     +38.56011,      44.08888,      +38.55776,  3757995.44,  -804867.23,  5170918.59,      53.560726,       +0.631408,   78344.86,  103507.94,    7694.19,             7738.28,    18.79,  28216.75,           27459.87,     -2.31,     -3.56,           8.46,  +1.91,  +1.84
  8,     UK002K,       0,  0.320724, 2459487.439940056298,  44.44194,  38.58209,               87.11422,  48.66450,        87.12275,       48.65920,     44.44194,     +38.58209,      44.44373,      +38.57437,  3757089.53,  -805045.21,  5170333.01,      53.563698,       +0.625816,   77369.66,  102531.11,    8787.46,             8831.55,    25.54,  27266.40,           27454.78,     -7.54,    -11.60,          27.83,  +2.14,  +2.09
  9,     UK002K,       0,  0.360816, 2459487.439940520097,  44.75573,  38.59082,               86.86292,  48.48395,        86.86539,       48.48243,     44.75573,     +38.59082,      44.75736,      +38.58859,  3756301.91,  -805199.95,  5169823.90,      53.566283,       +0.620931,   76521.80,  101682.85,    9737.98,             9782.07,  -110.35,  23708.44,           27247.83,     -2.16,     -3.32,           8.04,  +2.09,  +2.05
 10,     UK002K,       0,  0.400912, 2459487.439940984361,  45.11982,  38.61068,               86.56138,  48.28086,        86.56921,       48.27603,     45.11982,     +38.61068,      45.12185,      +38.60358,  3755404.59,  -805376.24,  5169243.88,      53.569228,       +0.615387,   75555.89,  100719.79,   10820.89,            10864.97,  -113.97,  27007.73,           27124.04,     -6.81,    -10.47,          25.58,  +2.27,  +2.25
 11,     UK002K,       0,  0.441016, 2459487.439941448625,  45.46573,  38.61217,               86.29580,  48.07665,        86.29048,       48.07992,     45.46573,     +38.61217,      45.46736,      +38.61699,  3754569.12,  -805540.38,  5168703.84,      53.571971,       +0.610210,   74656.57,   99824.87,   11829.15,            11873.23,  -192.44,  25141.20,           26976.34,      4.58,      7.05,          17.38,  +2.67,  +2.67
 12,     UK002K,       1,  0.481084, 2459487.439941911958,  45.75214,  38.63914,               86.04749,  47.92438,        86.05976,       47.91686,     45.75214,     +38.63914,      45.75461,      +38.62800,  3753884.19,  -805674.94,  5168261.10,      53.574220,       +0.605935,   73919.27,   99091.53,   12655.74,            12699.82,  -451.61,  20629.65,           26677.98,    -10.51,    -16.16,          40.12,  +6.00,  +6.02
  0,     UK0032,       0,  0.136958, 2459487.439937959891,  80.18019,  66.35352,               35.20058,  45.98060,        35.21844,       45.97205,     80.18019,     +66.35352,      80.18370,      +66.33850,  3761047.40,  -804267.63,  5172891.36,      53.550717,       +0.650253,   81630.43,  112860.70,       0.00,             4055.09,   228.76,      0.00,           24873.34,    -23.29,     18.40,          54.25,  +2.94,  +2.68
  1,     UK0032,       0,  0.177094, 2459487.439938424621,  81.07862,  66.32935,               34.96857,  45.65746,        34.92170,       45.67983,     81.07862,     +66.32935,      81.07316,      +66.36893,  3760313.78,  -804411.76,  5172417.15,      53.553122,       +0.645700,   80840.62,  112316.80,     885.36,             4940.45,    26.51,  22058.89,           24873.34,     61.01,    -48.20,         142.78,  +3.02,  +2.77
  2,     UK0032,       0,  0.217170, 2459487.439938888419,  82.10959,  66.39160,               34.58803,  45.33556,        34.58151,       45.33867,     82.10959,     +66.39160,      82.10986,      +66.39713,  3759469.39,  -804577.65,  5171871.34,      53.555891,       +0.640482,   79931.59,  111696.94,    1904.39,             5959.48,   -40.43,  25427.51,           24873.34,      8.47,     -6.69,          19.94,  +2.23,  +1.99
  3,     UK0032,       0,  0.257294, 2459487.439939352684,  83.22496,  66.40186,               34.24191,  44.96145,        34.22131,       44.97123,     83.22496,     +66.40186,      83.22477,      +66.41940,  3758573.33,  -804753.70,  5171292.13,      53.558830,       +0.634953,   78966.96,  111045.94,    2985.77,             7040.86,   -46.33,  26951.02,           24873.34,     26.68,    -21.08,          63.16,  +1.73,  +1.50
  4,     UK0032,       0,  0.297398, 2459487.439939816948,  84.40810,  66.43848,               33.83930,  44.58245,        33.84447,       44.58000,     84.40810,     +66.43848,      84.40946,      +66.43406,  3757633.83,  -804938.27,  5170684.84,      53.561912,       +0.629162,   77955.59,  110370.92,    4119.59,             8174.68,     0.75,  28271.87,           25779.30,     -6.68,      5.28,          15.91,  +1.51,  +1.30
  5,     UK0032,       0,  0.337526, 2459487.439940281678,  85.60602,  66.43636,               33.47276,  44.18159,        33.46879,       44.18346,     85.60602,     +66.43636,      85.60751,      +66.43976,  3756695.97,  -805122.53,  5170078.62,      53.564989,       +0.623378,   76946.02,  109704.69,    5251.41,             9306.50,    45.19,  28205.29,           26384.91,      5.12,     -4.04,          12.26,  +1.78,  +1.58
  6,     UK0032,       0,  0.377626, 2459487.439940745477,  86.68148,  66.44909,               33.12213,  43.83330,        33.13541,       43.82705,     86.68148,     +66.44909,      86.68233,      +66.43767,  3755864.42,  -805285.90,  5169541.11,      53.567719,       +0.618229,   76050.88,  109119.95,    6254.95,            10310.04,   -37.90,  25025.87,           26455.57,    -17.09,     13.49,          41.16,  +1.97,  +1.78
  7,     UK0032,       0,  0.417714, 2459487.439941209741,  87.39047,  66.42550,               32.92494,  43.58719,        32.91499,       43.59187,     87.39047,     +66.42550,      87.39303,      +66.43408,  3755319.92,  -805392.87,  5169189.15,      53.569506,       +0.614798,   75464.69,  108738.84,    6912.07,            10967.16,  -467.09,  16391.95,           25646.90,     12.79,    -10.10,          30.91,  +4.41,  +4.23

Notes
-----
- Points that have not been taken into consideration when computing the trajectory have '1' in the 'Ignore' column.
- The time already has time offsets applied to it.
- 'meas1' and 'meas2' are given input points.
- X, Y, Z are ECI (Earth-Centered Inertial) positions of projected lines of sight on the radiant line.
- Zc is the observed zenith distance of the entry angle, while the Zg is the entry zenith distance corrected for Earth's gravity.
- Latitude (deg) and Longitude (deg) are in WGS84 coordinates, while Height (m) is in the EGM96 datum. There values are coordinates of each point on the radiant line.
- Jacchia (1955) deceleration equation fit was done on the lag.
- Right ascension and declination in the table are given in the epoch of date for the corresponding JD, per every point.
- 'RA and Dec obs' are the right ascension and declination calculated from the observed values, while the 'RA and Dec line' are coordinates of the lines of sight projected on the fitted radiant line. The coordinates are in the epoch of date, and NOT J2000!. 'Azim and alt line' are thus corresponding azimuthal coordinates.
- 'Vel prev avg' is the average velocity including all previous points up to the given point. For the first 4 points this velocity is computed as the average velocity of those 4 points.