state_reconstruction.jl

using LinearAlgebra
using Convex, SCS

# --> Direct resolution of the measurement equation.
lstsq(Θ, y) = Θ \ y

# --> Constrained least-squares formulation.
function cstrnd_lstsq(Θ, y, Σ)
        # --> Optimization variable.
        a = Convex.Variable(length(Σ))
        
        # --> Objective function to be minimized.
        prob = minimize( sumsquares(Θ * a - y) )
        
        # --> Linear inequality constraints.
        prob.constraints += abs(a) <= 2Σ
        
        # --> Solve the problem using the SCS solver.
        solve!(prob, SCS.Optimizer())
        
        return Convex.evaluate(a)
end