Signal Processing in Radar Systems

14 Estimation of Probability Distribution and Density Functions of Stochastic Process

14.1 Main Estimation Regularities

Experimental definition of the one-dimensional probability distribution function F(x) and pdf p(x) is formed in the simplest way for ergodic stochastic processes and is based on an investigation of the stochastic process within the limits of the time interval [0, T]. Actually, a researcher observes the realization x(t) of a continuous ergodic process ξ(t). An example of the realization x(t) is shown in Figure 14.1a. According to the definition of ergodic stochastic process [1], the probability distribution function F(x) can be defined approximately in the following form (see Figure 14.1a):

F*(x)≈1T∑​i=1Nτi,⁢(14.1)

where ...