Library
Mitosis.AffineMap
— TypeAffineMap(B, β)
Represents a function f = AffineMap(B, β)
such that f(x) == B*x + β
.
Mitosis.BF
— TypeBF()
Backward filter for linear Gaussian systems parametrized by mean and covariance of the backward filtered marginal distribution.
Mitosis.BFFG
— TypeBFFG()
Backward filter forward guiding context for non-linear Gaussian systems with h
parametrized by WGaussian{(:F,:Γ,:c)}
` (see Theorem 7.1 [Automatic BFFG].)
Mitosis.ConstantMap
— TypeConstantMap(β)
Represents a function f = ConstantMap(β)
such that f(x) == β
.
Mitosis.Gaussian
— TypeGaussian{(:μ,:Σ)}
Gaussian{(:F,:Γ)}
Mitosis provides the measure Gaussian
based on MeasureTheory.jl, with a mean μ
and covariance Σ
parametrization, or parametrised by natural parameters F = Γ μ
, Γ = Σ⁻¹
.
Usage:
Gaussian(μ=m, Σ=C)
p = Gaussian{(:μ,:Σ)}(m, C)
Gaussian(F=C\m, Γ=inv(C))
convert(Gaussian{(:F,:Γ)}, p)
rand(rng, p)
Mitosis.LinearMap
— TypeLinearMap(B)
Represents a function f = LinearMap(B)
such that f(x) == B*x
.
MeasureTheory.kernel
— Functionkernel(f, M)
kernel((f1, f2, ...), M)
A kernel κ = kernel(f, M)
returns a wrapper around a function f
giving the parameters for a measure of type M
, such that κ(x) = M(f(x)...)
respective κ(x) = M(f1(x), f2(x), ...)
.
If the argument is a named tuple (;a=f1, b=f1)
, κ(x)
is defined as M(;a=f(x),b=g(x))
.
Reference
- https://en.wikipedia.org/wiki/Markov_kernel
Mitosis.conditional
— Methodconditional(p::Gaussian, A, B, xB)
Conditional distribution of X[i for i in A]
given X[i for i in B] == xB
if $X ~ P$.
Mitosis.correct
— Methodcorrect(prior, obskernel, obs) = u, yres, S
Joseph form correction step of a Kalman filter with prior
state and obs
the observation with observation kernel obskernel = kernel(Gaussian; μ=LinearMap(H), Σ=ConstantMap(R))
H
is the observation operator and R
the observation covariance. Returns corrected/conditional distribution u
, the residual and the innovation covariance. See https://en.wikipedia.org/wiki/Kalman_filter#Update.