# GPS P code construction
#
# Copyright 2014 Peter Monta
import numpy as np
chip_rate = 10230000
code_length = chip_rate*86400*7
def x1a_shift(x):
return [x[11]^x[10]^x[7]^x[5]] + x[0:11]
def x1b_shift(x):
return [x[11]^x[10]^x[9]^x[8]^x[7]^x[4]^x[1]^x[0]] + x[0:11]
def x2a_shift(x):
return [x[11]^x[10]^x[9]^x[8]^x[7]^x[6]^x[4]^x[3]^x[2]^x[0]] + x[0:11]
def x2b_shift(x):
return [x[11]^x[8]^x[7]^x[3]^x[2]^x[1]] + x[0:11]
def make_12bit(reg_shift,reg_initial,n):
x = reg_initial
s = np.zeros(n)
for i in range(n):
s[i] = x[11]
x = reg_shift(x)
return s
x1a = make_12bit(x1a_shift,[0,0,0,1,0,0,1,0,0,1,0,0],4092)
x1b = make_12bit(x1b_shift,[0,0,1,0,1,0,1,0,1,0,1,0],4093)
x2a = make_12bit(x2a_shift,[1,0,1,0,0,1,0,0,1,0,0,1],4092)
x2b = make_12bit(x2b_shift,[0,0,1,0,1,0,1,0,1,0,1,0],4093)
def x1(prn,start,len):
idx = start + np.arange(len)
idx = idx % 15345000
p_x1a = x1a[idx % 4092]
hold = idx>=(15345000-343)
idx[hold] = 4092
p_x1b = x1b[idx % 4093]
return np.logical_xor(p_x1a,p_x1b)
def x2(prn,start,len):
idx = start + np.arange(len)
idx = idx % 15345037
idx_a = idx.copy()
hold = idx_a>=(15345037-37)
idx_a[hold] = 4091
p_x2a = x2a[idx_a % 4092]
idx_b = idx.copy()
hold = idx_b>=(15345037-37-343)
idx_b[hold] = 4092
p_x2b = x2b[idx_b % 4093]
return np.logical_xor(p_x2a,p_x2b)
def last_x2(prn,start,len):
idx = start + np.arange(len)
idx_x2 = idx % 15345037
idx_a = idx % 15345000
hold = idx_a>=(15345000-1069)
idx_x2_a = idx_x2.copy()
idx_x2_a[hold] = 4091
p_x2a = x2a[idx_x2_a % 4092]
idx_b = idx % 15345000
hold = idx_b>=(15345000-965)
idx_x2_b = idx_x2.copy()
idx_x2_b[hold] = 4092
p_x2b = x2b[idx_x2_b % 4093]
return np.logical_xor(p_x2a,p_x2b)
def p_code(prn,start,len):
day = (prn-1)//37
prn = prn - 37*day
start += chip_rate*86400*day
start = start%code_length
p_x1 = x1(prn,start,len)
p_x2 = x2(prn,start-prn,len)
p_last_x2 = last_x2(prn,(start-prn)%code_length,len)
idx_x2 = (start - prn + np.arange(len)) % code_length
idx_last_x2 = idx_x2>=(code_length-4092)
p_x2[idx_last_x2] = p_last_x2[idx_last_x2]
return np.logical_xor(p_x1,p_x2)
def code(prn,chips,frac,incr,n):
len = np.int(np.floor(n*incr)+5)
c = p_code(prn,chips,len).astype('int')
idx = frac + incr*np.arange(n)
idx = np.floor(idx).astype('int')
x = c[idx]
return 1.0 - 2.0*x
# test vectors in IS-GPS-200J
def first_12_chips(prn):
c = p_code(prn,0,12)
r = 0
for i in range(12):
r = 2*r + c[i]
return r
def binary(s):
n = s.shape[0]
r = 0
for i in range(n):
r += s[i]*2**((n-1)-i)
return r
def hex_digit(s):
return "%x"%binary(s)
def chips2hex(c):
n = c.shape[0]//4
r = c.shape[0]%4
if r!=0:
s = octal_digit(c[0:r])
else:
s = ""
for i in range(n):
s += hex_digit(c[r+4*i:r+4*(i+1)])
return s
def first_256_chips_hex(prn):
start = 0
len = 256
c = p_code(prn,start,len)
return chips2hex(c)
def last_1024_chips_hex(prn):
start = (7*86400*10230000) - 1024
len = 1024
c = p_code(prn,start,len)
return chips2hex(c)
def print_first_12_chips():
for prn in range(1,211):
print('%3d: %04o' % (prn,first_12_chips(prn)))
def print_first_256_chips():
for prn in [1,2,37,38,74,75,111,112,148,149,185,186,210]:
print('%3d: %s' % (prn,first_256_chips_hex(prn)))
def print_last_1024_chips():
for prn in [1,2,37,38,74,75,111,112,148,149,185,186,210]:
print('%3d: %s' % (prn,last_1024_chips_hex(prn)))
if __name__=='__main__':
print_first_12_chips()
print_first_256_chips()
print_last_1024_chips()
