The form of MARSS models for users is "marxss", the MARSS models with inputs. See MARSS.marxss. In the internal algorithms (e.g. MARSSkem), the "marss" form is used and the D and d are incorporated into the A matrix and C and c are incorporated into the U matrix.
This is a MARSS(1) model of the marss form:
$$x(t+1) = B(t) x(t) + U(t) + G(t) w(t), where w(t) ~ MVN(0,Q(t))$$
$$y(t) = Z(t) x(t) + A(t) + H(t) v(t), where v(t) ~ MVN(0,R(t))$$
$$x(1) ~ MVN(x0, V0) or x(0) ~ MVN(x0, V0) $$
Note, by default \(V0\) is a matrix of all zeros and thus \(x(1)\) or \(x(0)\) is treated as an estimated parameter not a diffuse prior.
Note, "marss" is a model form. A model form is defined by a collection of form functions discussed in marssMODEL. These functions are not exported to the user, but are called by MARSS() using the argument form. These internal functions convert the users model list into the vec form of a MARSS model and do extensive error-checking.