simplify exposition

Author: baggepinnen

docs/src/examples/lpv.md

@@ -10,10 +10,10 @@ on a *known, measured* scalar scheduling variable ``\lambda(t)``:
 
 ```math
 \begin{aligned}
-A(\lambda) &= \sum_{k} \theta^A_k\, \varphi_k(\lambda),\\
-B(\lambda) &= \sum_{k} \theta^B_k\, \varphi_k(\lambda),\\
-C(\lambda) &= \sum_{k} \theta^C_k\, \varphi_k(\lambda),\\
-D(\lambda) &= \sum_{k} \theta^D_k\, \varphi_k(\lambda),
+A(\lambda) &= \sum_{k} A_k\, \varphi_k(\lambda),\\
+B(\lambda) &= \sum_{k} B_k\, \varphi_k(\lambda),\\
+C(\lambda) &= \sum_{k} C_k\, \varphi_k(\lambda),\\
+D(\lambda) &= \sum_{k} D_k\, \varphi_k(\lambda),
 \end{aligned}
 ```
 

docs/src/nonlinear.md

@@ -259,7 +259,7 @@ DisplayAs.PNG(current()) # hide
 
 [`lpv_pem`](@ref) fits a state-space model whose matrices depend on a measured
 scheduling variable ``\lambda(t)`` through a user-supplied basis expansion,
-``A(\lambda) = \sum_k \theta^A_k\, \varphi_k(\lambda)`` and likewise for
+``A(\lambda) = \sum_k A_k\, \varphi_k(\lambda)`` and likewise for
 ``B,C,D``. The returned [`LPVStateSpace`](@ref) is callable: `sys(λ)` returns
 a plain `StateSpace` frozen at that operating point.
 

src/lpv.jl

@@ -3,7 +3,7 @@
 # The user supplies a scheduling-variable trajectory λ(t) and a basis {φ_k} in λ.
 # The estimated model has matrices
 #
-#     A(λ) = Σ_k θ^A_k φ_k(λ),    similarly for B(λ), C(λ), D(λ),
+#     A(λ) = Σ_k A_k φ_k(λ),    similarly for B(λ), C(λ), D(λ),
 #
 # i.e. a single shared state-space realization whose entries depend smoothly on λ.
 # Estimation uses the same prediction-error scaffolding (Optim + ForwardDiff) as
@@ -355,7 +355,7 @@ Linear Parameter-Varying (LPV) state-space identification using PEM.
 The model has matrices that vary as a basis expansion in a measured scalar
 scheduling variable `λ(t)`:
 
-    A(λ) = Σ_k θ^A_k φ_k(λ),     ...,     D(λ) = Σ_k θ^D_k φ_k(λ).
+    A(λ) = Σ_k A_k φ_k(λ),     ...,     D(λ) = Σ_k D_k φ_k(λ).
 
 A constant Kalman gain `K` is also estimated (when `focus = :prediction`).
 Estimation minimizes one-step prediction error over the full dataset; the