Improving accuracy of mercator meters conversion to lat/lon?

Question

My question is an extention to Converting mercator meters without UTM zone?

While the answer in the previous Q&A got me so far, I've now come to an impass. While the conversion I do from Mercator metres to lat/long works, I don't get the accuracy that I've seen possible with other programs. I've posted this query on a more dedicated forum (http://forums.sideimagingsoft.com/index.php?topic=7785.0) but haven't had any feedback so would like to see if the wider community may be able to help.

Here is the basic post I had on the other forum:

I've been working on extracting the header information from the raw SON files from a 998c SI unit. I have hundreds of recordings so I'm aiming to create a batch extraction of depth and coordinate information. I've been successful at getting out the information from the SON files but the final stumbling block is once again the handling of the coordinates. I now know that the Sonar writes the coordinates in World Mercator metres (EPGS: 3395). Unfortunately when I use some spatial transformation libraries (GDAL and ProjNet) the conversion to lat/lon is never accurate enough. I know it is possible to get a very accurate conversion as HumViewer and HBSI Sonar File Converter both produce accurate points with HumViewer the most accurate. Here is a graphic of the various coordinates converted from the same Mercator Meter coordinates 16044360, -4228674.

So my question is, what is being done to the raw data to improve its accuracy? According to 'hydrograph' in this thread http://bb.sideimageforums.com/viewtopic.php?t=118&highlight=source+code there probably is some independent axis shift calculation being used. Anyone have an idea what this might be? I don't mind going back to basics and coding my own transformation function but I'm not keen if I'm going to get the same result as other transformation libraries without incorporating the independent shift, if required.

If it's any help to anyone I've attached the header structure from the 998c SI.

Here are a couple of lines data from B000.SON but I don't think the adjustment needed is in it.

Answer 1

The conversion code was supplied by peterv6i in this thread.

http://forums.sideimagingsoft.com/index.php?topic=7785.msg48682#msg48682

  public static double MMtoEllipsiodDegLatitude(double Lat_m)
  {
    if (Math.abs(Lat_m) < 15433199.0D)
    {
      if (Lat_m != 0.0D) {
        return Math.atan(Math.tan(Math.atan(Math.exp(Lat_m / 6378388.0D)) * 2.0D - 1.570796326794897D) * 1.0067642927D) * 57.295779513082302D;
      }
      return 0.0D;
    }
    return 0.0D;
  }

  public static double MMtoEllipsiodDegLongitude(double Lon_m)
  {
    if (Math.abs(Lon_m) <= 20038300.0D)
    {
      double d;
      if ((d = Lon_m * 57.295779513082302D / 6378388.0D) > 180.0D) {
        d = 180.0D;
      } else if (d < -180.0D) {
        d = -180.0D;
      }
      return d;
    }
    return 0.0D;
  }