For the differential system characterized by its equations of state,specialization to invariance means that the system matrices A, B,C are constants

The quantity K2 is known as the Kalman gain. It is the optimum gain in the mean squared error sense. Substitute it into the expression for

If the system reaches a statistical steady state the covariance matrix would be constant. The system would have to be invariant

Prof vander Velde Use error between early and late indicator to lock onto signal. Error is a linear function of shift, within the range (-T,T) Return to the 1 st example process and take the case where the change points are Poisson distributed

Mean squared value: Higher order distribution and density functions. You can define these distributions of any order

The Poisson approximation to the binomial distribution The binomial distribution, like the Poisson, is that of a random variable taking only positive integral values. Since it involves factorials, the binomial distribution is not very convenient for numerical application

Summary of the subject (topics) 1. Brief review of probability a. Example applications 2. Brief review of random variables a. Example applications 3. Brief review of random processes a. Classical description b. State space description

This means that in the cascade of Ho(s) with F(s), the effect of the RHP zero on the amplitude of the product is cancelled out, but the effect on the phase is not In fact, the phase lag due to the RHP zero is doubled in the product. Note:

The estimate of x based on N data points can then be made without reprocessing the first N, points. Their effect can be included simply by starting with pseudo observation which is equal to the estimate based on the first N points having a variance equal to the variance of the estimate based on N The same is true of the variance of the estimate based on N

Special case: [(P)] is rational: In this solution formula we can carry out the indicated integrations in literal form in the case in which [(P)] is rational. In our work, we deal in practical way only with rational,sn, and, so this function will be rational if D(p)is rational This will be true of every desired operation except predictor. Thus except in the case of prediction, the above