Variable

Explanation

Variable

Explanation

$a$

Gram right-hand-side vector

$G$

union of data kernels

${\widehat{a}}_i$

Thomas right-hand-side vector at time, i

$G^{\left(i\right)}$

data kernel at time, i

${\tilde{a}}_i$

Kalman right-hand-side vector at time, i

$G^{-g}$

generalized inverse

$A$

Gram matrix

$h$

prior right-hand-side vector

$A_i$

th diagonal element of Gram matrix

$H$

union of prior information

${\widehat{A}}_i$

Thomas matrix at time, i

$f$

GLS right-hand-side vector

${\tilde{A}}_i$

Kalman matrix at time, i

$F$

GLS matrix

$B$

Off-main-diagonal of Gram matrix

K

number of time steps

$C_{A1}$

prior covariance of initial condition

$m$

union of states

$C_d$

covariance of data at time, i

$m^{\left(i\right)}$

state at time, i

$C_h$

union of prior covariances

$m_A^{\left(1\right)}$

initial condition

$C_m$

posterior covariance of state

$m_G$

GLS estimate of state

$C_o$

union of data covariances

$m_K$

Kalman estimate of state

$C_s$

prior covariance of source

M

length of state vector

$d$

union of data

N

number of data at time, i

$d^{\left(i\right)}$

data at time, i

$N$

data resolution matrix

$D$

dynamics matrix

$R$

model resolution matrix

${\Delta }_2$

second difference matrix

$s^{\left(i\right)}$

source at time, i