Reason for 0.5 factor in the error

[nkhedekar]

In the IntegratedMatchingCostFactor (and others), the error is evaluated as const double error = 0.5 * residual.transpose() * residual; . This error is then used to create the HessianFactor as new gtsam::HessianFactor(keys()[0], H_source, -b_source, error).

As per the documentation of the HessianFactor, the constant term that needs to be provided to the constructor is $f = b^Tb$ where $b = \Sigma^{-1/2} (z - h(x_0))$ is the whitened negative error at the linearization point $x_0$.

Maybe I am misunderstanding something but I don't follow the reason for the factor of 0.5 in the code?

[koide3]

Hmmm, maybe I added that constant for some reasons (consistency with GTSAM factors?), but I'm not very confident now. While the error value itself does not affect the optimization as long as H and b are correct, I'll re-check whether 0.5 is necessary.