Vector or multivariate approach given:
– XK : state multivector (n×1)
– xK : state vector of results
– YK : multivector of observations (m×1)
– yK : vector of observations and results
with A(K)= state matrix (n×n), deterministic matrix
and NK = process noise vector (l×1)
that we will choose centered, white and of correlation matrix (covariance matrix in the general case).
:correlation matrix of the process noise vector NK
: deterministic matrix
H(K): matrix of measurements or of observations (m×n), deterministic matrix;
WK : measurement noise vector of observations vector (p×1) that we choose, like NK, centered, white and of correlation matrix(covariance matrix in the general case);
correlation matrix of the measurement noise vector WK
G(K) : (m × p) : deterministic matrix
The noises NK and WK are independent, and, as they are centered:
∀K and j
We will suppose, in what follows, that WK ⊥ X0.
By iteration ...