updating a curve by reciving new points by using Kalman filter

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I want to estimate continuation parts of a curve by obtaining points online by using particle filter or Kalman filter.
For example in t=0 (time is zero) i have 5 points (p1,p2,p3,p4,p5). So, in t=0 i can estimate a curve by for example polyfit(p1,p2,p3,p4,p5). In t=1 i receive 3 new points (p6,p7,p8) and now i must estimate a better and accurate curve by using these 3 new points. One way is polyfit(p1,p2,p3,p4,p5,p6,p7,p8) but because of time saving in my program, i can not use that. Because polyfit consider all points from the first and i don't want to consider all points from the first (i have so many points and i want to write a code in C language). i want the available curve to be better and more accurate by using only 3 new points (p6, p7,p8) online. In this way i think "particle filter or Kalman filter" technique can be a suitable way to do that.
Please help me how can i use Kalman filter or particle filter for curve updating. thanks

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