Help with kalman filter problem


I have been using the 1 - dimensional kalman filter to estimate the steady state of time series data. The model used is random walk model.
x_(t+1)= x_t+ w_t and the error is w_t= x_(t+1)- x_t.

This works almost all the data if I ignore the process noise variance in the error update stage but not otherwise.
However, I am not sure if the model make any sense without the process noise.
Thanks in advance.
can someone help me to understand this, please?

What exactly is your problem. Please describe the setup carefully. And what do you mean with

The process you wrote down has a unit root. It will not have a steady state.