Doc fix, close #16

Author: mschauer

src/Kalman.jl

@@ -8,6 +8,7 @@ import DynamicIterators: evolve, dyniterate, @returnnothing
 import Base: iterate, IteratorSize, IteratorEltype, eltype, length
 
 import Random.rand
+import GaussianDistributions: ⊕
 
 meancov(G) = mean(G), cov(G)
 meancov(G::Tuple) = G

src/evolution.jl

@@ -1,8 +1,13 @@
 
 """
-    LinearEvolution(Φ, b, Q)
+    LinearEvolution(Φ, b, Q) <: Evolution
 
-Evolution of the law of `x -> Φ x + w` where ``w ~ N(0, Q)``
+Evolution of the law of `x -> Φ x + w` where ``w \\sim N(0, Q)``.
+
+# Examples
+```
+    evolve(LinearEvolution(Φ, b, Q), 0 => Gaussian(x, P))
+```
 """
 struct LinearEvolution{TΦ,TQ} <: Evolution
     Φ::TΦ # dxd
@@ -17,12 +22,8 @@ end
 evolve(M::LinearEvolution, u::Pair) = timelift_evolve(M, u)
 evolve(M::LinearEvolution, u::Pair, c) = timelift_evolve(M, u, c)
 
-function evolve(M::LinearEvolution, G::Gaussian)
-    Gaussian(M.Φ*mean(G) + mean(M.Q), M.Φ*cov(G)*M.Φ' + cov(M.Q))
-end
-
-function evolve(M::LinearEvolution, x)
-    Gaussian(M.Φ*x + mean(M.Q), cov(M.Q))
+function evolve(M::LinearEvolution, G)
+    M.Φ*G ⊕ M.Q
 end
 
 

src/observation.jl

@@ -6,7 +6,11 @@ end
 struct GenericLinearObservationModel <: Observation
 end
 
+"""
+    LinearObservationModel(H, R)
 
+Observe `y = Hx + v` where ``v \\sim N(0, R)``.
+"""
 struct LinearObservationModel{TH, TR} <: Observation
     H::TH # dxd
     R::TR # d
@@ -16,9 +20,15 @@ end
 (O::LinearObservationModel)((x, P)::Gaussian) = Gaussian(O.H*x, O.H*P*O.H' + O.R)
 
 """
-    LinearObservationModel(H, R)
+    LinearObservation(P, H, R)
+
+Observe the LinearEvolution `P` using `y = Hx + v`
+where ``v \\sim N(0, R)``.
 
-Observe `y = Hx + v` where ``v ~ N(0, R)``
+# Examples
+```
+    O = LinearObservation(LinearEvolution(Φ, Gaussian(b, Q)), H, R)
+```
 """
 struct LinearObservation{T, TH, TR} <: Observation
     P::T

src/statespacemodel.jl

@@ -24,7 +24,7 @@ LinearStateSpaceModel(sys, obs)
 Combines a linear system `sys` and an observations model `obs` and
 to a linear statespace model in a modular way.
 
-Evolves StateObs objects.
+Evolves `StateObs` objects.
 """
 struct LinearStateSpaceModel{Tsys,Tobs} <: StateSpaceModel
     sys::Tsys