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

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

1. 类木行星 2. 矮行星 3. 开珀带与奥尔特云 4. 小天体

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

The two middle terms are zero: fort>lo,n(t) and are uncorrelated becauset) is white(impulse correlation function) For=, n() has a finite effect on x()because n() is white. But the integral of a finite quantity over one point is zero

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

Solution in the Free Configuration Non-Real-Time Filter Case The applicable condition in this important case is:

Note n, s enter the system at the same place F is fixed. We design(and perhaps B). We must stabilize F if it is given as unstable

so if t is the current time in a real time situation, we cannot compute ()for which is necessary since w, () is nonzero only for>0. But we showed earlier that