Signal Processing in Radar Systems

12 Estimation of Mathematical Expectation

12.1 Conditional Functional

Let the analyzed Gaussian stochastic process ξ(t) possess the mathematical expectation defined as

E(t)=E0s(t)⁢(12.1)

the correlation function R(t₁, t₂), and be observed within the limits of the finite time interval [0, T]. We assume that the law of variation of the mathematical expectation s(t) and correlation function R(t₁, t₂) are known. Thus, the received realization takes the following form:

x(t)=E(t)+x0(t)=E0s(t)+x0(t),0≤t≤T,⁢(12.2)

where

x0(t)=x(t)−E(t)⁢(12.3)

is the centered Gaussian stochastic process. The problem with estimating the mathematical expectation is correlated to the problem with estimating the amplitude E(t) of the deterministic signal in the additive ...