The following experiment takes an arbitrary GoldSequence and correlates that sequence with every other GoldSequence of GPS. There seems to be something special with sequence #37. It shows 2 peaks!

The java-program (with very little comments):

public void fillArray16() { // correlation experiments // construct a test-input with 1200 samples of Gold26 + noise // find the match-point with all other possible sequences // display peak in 3d int shift = 0; // display only most interesting part int inplen = 2500; double[] testinput = new double[inplen]; double[] bins = new double[inplen]; int prns = 37; // # PRN sequences double[][] plotData3d = new double[1268][prns]; Random r = new Random(); int noise = 3; GoldSequence gold26; gold26 = new GoldSequence(37); // find correlation with prn37 for (int i = 0; i < testinput.length; i++) { testinput[i] = gold26.nextan() + noise * r.nextGaussian(); } //implementation of a correlator for (int prn = 1; prn <= prns; prn++) { GoldSequence ref = new GoldSequence(prn); for (int i = 0; i < 1268; i++) { double acc = 0; for (int j = 0; j < 1023; j++) { if ((i + j) < inplen) { acc = acc + testinput[i + j] * ref.nextan(); } } bins[i] = acc; } for (int i = 0; i < 1268; i++) { plotData3d[i][prn - 1] = (bins[i + shift]) / 10.0; } } int id = 1; ShowPlot3d myPlot = new ShowPlot3d(id, plotData3d, "correlator"); myPlot.showFigure(); } |

The output shows 2 peaks:

I expect 2 peaks at the utmost (last) row. The test-pattern is #37, the very last PRN-sequence. However there are 2 more peaks. The explanation is in the numbers for the taps in GoldSequence: A snippet of the coding:

private int[][] magnum = { {2,6}, {3,7}, {4,8}, {5,9}, {1,9}, {2,10}, {1,8}, {2,9}, {3,10},{2,3}, {3,4}, {5,6}, {6,7}, {7,8}, {8,9}, {9,10},{1,4}, {2,5}, {3,6}, {4,7}, {5,8}, {6,9}, {1,3}, {4,6}, {5,7}, {6,8}, {7,9}, {8,10}, {1,6}, {2,7}, {3,8}, {4,9}, {5,10},{4,10}, {1,7}, {2,8}, {4,10} }; |

There are two pairs {4,10}. I don't know yet if that is perhaps an error in the book "a software defined gps and galileo receiver". Note: I asked the author and the pointed me to the original doc. This is intended.