C++ for Scientists - Technische Universität Dresden

284 CHAPTER 14. NUMERICAL EXERCISES
void step( T const& t, Base& base, F const& f ) {
...
}
public:
// Return the solution
typedef ... x type ;
x type const& x() const { ... }
private:
...
14.7.5 Test problems
We now solve the following test problems. First, consider the following expansion:
f(t) = ξ1 + ξ2 cos t + ξ3 sin t + ξ4cos2t + ξ5 sin 2t
We compute the coefficients following the least squares criterion for the function
f = (2 − 5 cos t)
Print the solution x for each step of the Kalman filter and see how it changes. It should be very
close to the function.
Then apply random noise with relative size 0.0001:
f = (2 − 5 cos t)(1 + 0.0001ɛ)
where ɛ is a random number in [−1, 1]. Print the solution x for each step of the Kalman filter
and see how it changes. It should be close to the solution of the function with ɛ ≡ 0.
Plot the results using gnuplot.