WSF_ALPHA_BETA_GAMMA_FILTER¶

filter WSF_ALPHA_BETA_GAMMA_FILTER¶

filter <name> WSF_ALPHA_BETA_GAMMA_FILTER
   ... Commands ...
end_filter

Overview¶

Defines an alpha-beta-gamma filter for filtering tracks.

Commands¶

alpha <value>¶: Defines the filter’s alpha (position) parameter.

beta <value>¶: Defines the filter’s beta (velocity) parameter.

gamma <value>¶: Defines the filter’s gamma (acceleration) parameter.

debug¶: Writes debugging information to the standard output.

Methodology¶

The alpha-beta-gamma filter operates using the following algorithm:

$X_f = X'_p + \alpha \times (X_m - X'_p)$

$V_f = V'_f + dT \times A'_f + \frac{\beta}{dT} \times (X_m - X'_p)$

$A_f = A'_f + \frac{\gamma}{dT^2} \times (X_m - X'_p)$

$X_p = X_f + dT \times V_f + \frac{dT^2}{2} \times A_f$

Where:

$\alpha$

The value of alpha

$\beta$

The value of beta

$\gamma$

The value of gamma

$X_m$

The measured position

$X_f$

The filtered position

$X_p$

The predicted position

$V_f$

The filtered velocity

$A_f$

The filtered acceleration

$dT$

The time since the last filter update

The primed values are the filtered values from the last filter update.