16.322 Stochastic Estimation and Control, Fall 2004 Prof vander velde Choosing P=0.5, c=1.177 CPE=0.588(0x+,) This approximation is good to an ellipticity of around 3 Random processes A random process is an ensemble of functions of time which occur at random x(t) x(t) In most instances we have to imagine a non-countable infinity of possible functions in the ensemble There is also a probability law which determines the chances of selecting the different members of the ensemble We generally characterize random processes only partially One important descriptor- the first order distribution This is the classical description of random processes. We will also give the state space description later Page 7 of 816.322 Stochastic Estimation and Control, Fall 2004 Prof. Vander Velde Page 7 of 8 1 ( ) 2 σ = + σ σ x y Choosing P=0.5, c=1.177 0.588( ) CPE = + σ x y σ This approximation is good to an ellipticity of around 3. Random Processes A random process is an ensemble of functions of time which occur at random. In most instances we have to imagine a non-countable infinity of possible functions in the ensemble. There is also a probability law which determines the chances of selecting the different members of the ensemble. We generally characterize random processes only partially. One important descriptor – the first order distribution. This is the classical description of random processes. We will also give the state space description later