Robust Least-Squares Smoother

Smooths Noisy, Outlier-Infested Data by Minimizing a Cost Function

IRLSSMOOTH takes the same smoothing approach as LSSMOOTH (ID:49789) but adds Iterative Reweighting to deweight outliers, preventing them from swaying the smoothed output sequence. The user controls are the same, but IRLSSMOOTH typically makes 7 - 10 iterations, so it's less speedy. The cost function minimization idea, used in both LSSMOOTH and IRLSSMOOTH is credited to ID:48799.

The user specifies the smoother response time in units of samples, which translates to roughly the same bandwidth as a moving average of that many samples. The output is much smoother though, due to greater high-frequency attenuation.

Optionally, the user can specify the highest derivative not to penalize, which affects the smoother's transient response. The default is 2. Lower numbers produce more damping and higher numbers less. In practice the differences are usually subtle. More details about the inputs are found in the code header.

In IRLSSMOOTH , as in LSSMOOTH, the question of how to treat the ends of the sequence never arises. Every output sample is part of the vector solution to the cost minimization.

See also LSSMOOTH, ID:49789