The diagonal Bernoulli differential estimation equation

Abstract

The Bernoulli Differential Equation traditionally applies a linearization procedure instead of solving the direct form, and viewed in state space has unknown parametres, focusing all attention on it. This equation viewed in state space with unknown matrix parametres had a natural transformation and introduced a diagonal description. In this case, the problem is to know the matrix parametres. This procedure is a new technique for solving the state space Bernoulli Differential Equation without using linearization into diagonal filtering application. Diagonal filtering is a kind of quadratic estimation. This is a procedure which uses observed signals with noises and produces the best estimation for unknown matrix parametres. More formally, diagonal filtering operates recursively on streams of noisy input signals to produce an optimal estimation of the underlying state system. The recursive nature allows running in Real-time bounded temporally using the present input signal and the previously calculated state and no additional past information. From a theoretical standpoint, the diagonal filtering assumption considered that the black-box system model includes all error terms and signals having a Gaussian distribution, described as a recursive system in a Lebesgue sense. Diagonal filtering has numerous applications in science and pure solutions, but generally, the applications are in tracking and performing the stochastic system.