NMEA 0183 checksum validation
I believe this can be simplified quite a bit. My immediate reaction would be to write code something like this:

#include &lt;sstream&gt;
#include &lt;iostream&gt;
#include &lt;numeric&gt;

int main() { 
    std::istringstream in("$AIVDM,1,1,,A,13HOI:0P0000VOHLCnHQKwvL05Ip,0*23");

    std::string sentence;

    std::getline(in, sentence, '*');

    std::string received_checksum;

    // Save the checksum that was at the end of what we received.
    std::getline(in, received_checksum);

    // Re-compute the check-sum:
    char check = std::accumulate(sentence.begin()+1, sentence.end(), 0,
        [](char sum, char ch) { return sum ^ ch; });

    // Print out both the received and computed checksums:
    std::cout &lt;&lt; "received checksum: " &lt;&lt; received_checksum;
    std::cout &lt;&lt; "\ncomputed checksum: " &lt;&lt; std::hex &lt;&lt; (int)check &lt;&lt; "\n";
}


Looking at specific details of the code, I see a few things that even if you were going to preserve roughly your current implementation, you could still simplify and clarify. The first point would be to fix your indentation. Right now, it appears to be almost entirely arbitrary, and unrelated to the structure of the code.

Then you could clean up some of your loops. For example:

bool done = false;
while (!done)
{
    int h ( MsgLine.at (i) );
    i++;
    AsciiValues.push_back(h);

if ( i == j )
    done = true;
}


...can be turned into something like this:

for (int i=0; i&lt;j; i++)
    AsciiValues.push_back((int)MsgLine.at(i));


Or, you could just use std::copy. Likewise, your code for computing the checksum:

bool done = false;
while (!done)
{
    a = (AsciiValues[d]);
    b = c;
    c = a ^ b;
    d++;

if ( d == e )
    done = true;
}


...could be simplified down to something like this:

do {
    a = AsciiValues[d];
    b = c;
    c = a ^ b;
    ++d;
} while (d != e);


...or you could do something closer to the accumulate (it still seems a lot cleaner to me to use std::accumulate), as I showed to start with.