golf contest analogy
--------------------

Suppose there is a contest involving two rounds of golf with 10 men and
10 women.  At the end, the best 3 total scores overall are declared
winners.  After one round, the best 3 scores, looking at the men and
women separately, are:

      Round 1

   M  Viterbi 40
      Kalman  50
      Kevin   60

   F  Jill    40
      Jane    45
      Joan    50

Obviously, to determine the best 3 scores after two rounds, we can not
just keep the best 3 scores after the first round and throw everyone else
out.  It may be that Shannon, who came in 4th in the first round in the
mens group, and isn't listed above, performs extra well in round 2 and
comes out the overall winner.

After two rounds, the best 3 total scores for the men and women are
shown in the "Round 1 + Round 2" column:

      Round 1		   Round 1 + Round 2

   M  Viterbi 40	M  Kevin   100
      Kalman  50	   Kalman  110
      Kevin   60	   Shannon 115

   F  Jill    40	F  Jill    105
      Jane    41	   Jane    106
      Joan    42	   Joan    107

The three overall winners are: Kevin, Jill, and Jane.

Comparing the total scores at the end with the scores from round 1,
Kevin must have scored 40 in round 2, and Kalman must have scored 60.
Viterbi, while in the lead after round 1, messed up in round 2 and
came out 4th or lower.  Shannon pulled up from behind and made it
to third place in the mens group.

In this example, each of the men listed had different scores in round 2.
But each of the 3-best women had the same score of 65.  The results
going from round 1 to the end for the men are similar to the effects
of using a Kalman cost function; each player (i.e. kalman filter)
at each time unit (i.e. round 1 or round 2) is unique and has a performance
that depends on their history (i.e. skill for the golf players; previous
track data used in the evolution for the kalman filters).

The results going from round 1 to the end for the women is similar
to the standard viterbi cost function, which depends only on the
state transition involved (i.e. cost going from state i to state k
is only a function of i and k, and is the same for all golf players).
Thus, regardless of their ranking after the initialization of round 1,
all of the women get the same incremental cost (65 in this case)
going from round 1 to round 2.  So the best 3 women after round 1
remain the same after round 2.

When applied to sports problems, the kalman filter cost function
makes more sense than the standard viterbi cost function.

The separation of scores into male and female groups in this example
was done just to make some analogy to states in a viterbi trellis.
So it's like there are two states, M and F, at each time unit.
In this example, transitions between states M and F are not shown,
and are a subject for further genetic research.