Free Access

Table 1

Index of mathematical symbols.

np number of exposures
nd number of detectors (data) per exposure
N number of parameters (to determine)
L number of data points in a time series
M number of data points
Dp data recorded during the exposure (pointing) p
Dp is a vector of length nd(p)
y data sorted in sequential order (vector of length M)
y ≡ (D1,D2,...,Dnp) where Dp are the data points
accumulated during exposure p.
x solution of the equation Hx = y (vector of length N).
Also time series (“image space”) x ≡ x1:L = (x1,...,xL)
where xi are supposed sequentially ordered in time
H real rectangular matrix of size M × N
H (J) the submatrix (columns of H) related to source named or
numbered J, such that H ≡  [H(1),···   ,H(N)]
A square real symmetric matrix of order N (A = HTH)
ε measurement errors on x (time series vector of length L)
assumed to have zero mean, to be independent and normally
distributed with a known variance Σ ( )
T ti is the time where the data point xi is measured with
measurement error ϵi. T = (t1,...,tL).
f(ti) the model of a series, this is a piecewise constant function.
m number of change points that defined the m + 1 segments such
that f(t) is constant between two successive change points
nseg(J) number of segments to describe source named or numbered J
τ change points such that τ0 = min(T) and τm + 1 = max(T)
or in point number units, τ0 = 1 and τm + 1 = L + 1
(τ0 < τ1 < ... < τm + 1).τ denotes the last found change point
s sk is the value of the model f(t) for the segment defined by
τk − 1 ≤ t < τk (vector of length m + 1)
F(τ) recursive function to be minimized with respect to τ
β penalty to prevent overfitting
x (τi − 1 + 1):τi subset of the vector x, x(τi − 1 + 1):τi = (xτi − 1 + 1,...,xτi)
Cost function or effective fitness for the
vector x subset x(τi − 1 + 1):τi
n Iteration number which corresponds to time tn

Notes.Initial state is denoted with the upper subscript 0: (H0,N0,...). The temporary state, with the upper subscript : (). The time t is sometimes replaced by the iteration number n.

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.