Hyperbolic tangent and Fibonacci numbers matter to nonlinear Beneš filtering: applications to drones

The hyperbolic tangent can be expressed in terms of Fibonacci hyperbolic functions, related to the Fibonacci sequence and the golden ratio φ≅1.618. This paper develops the necessary calculations and shows some applications of the results to the solutions of the Kalman filtering equations and the Riccati equation in the case of continuous-time scalar filtering. Applications to the continuous-time scalar nonlinear Beneš filter, to the estimation of the magnetic North onboard unmanned aerial vehicles (UAV) and to autonomous drone swarms are also shown.