Fisher Information Calculator
Multi-channel optimal reconstruction of G(t) via Cramér–Rao bound
Model
Y_i(t) = Y0_i · (1 + c_i · G(t)) + noise_i noise ~ N(0, σ²_i)
G(t) = A_base + A_amp · cos(2πt)
Fisher Information: F = Σ_i [ Y0_i² · c_i² / σ_i² ]
Cramér–Rao bound: σ²_G ≥ 1 / F
Optimal estimate: Gˆ(t) = [Σ_i (c_i·Y0_i/σ²_i)(Y_i(t)-Y0_i)] / F
Measurement Streams
Add independent measurement channels. Each stream Yi(t) = Y0i·(1 + ci·G(t)) + εi. More streams → tighter Cramér–Rao bound.
Results
G(t) true
Gˆ(t) reconstructed
±σ_G bound