code: def test_simulation_smoothing_state_intercept():
      nobs = 10
      intercept = 100
      endog = np.ones(nobs) * intercept
  
      mod = sarimax.SARIMAX(
          endog, order=(0, 0, 0), trend="c", measurement_error=True
      )
      mod.initialize_known([100], [[0]])
      mod.update([intercept, 1.0, 1.0])
  
      sim = mod.simulation_smoother()
      sim.simulate(
          measurement_disturbance_variates=np.zeros(mod.nobs),
          state_disturbance_variates=np.zeros(mod.nobs),
          initial_state_variates=np.zeros(1),
      )
      assert_equal(sim.simulated_state[0], intercept)
  
imports: import os
  import numpy
  import pandas
  from numpy.testing import assert_allclose, assert_equal
  import pytest
  from statsmodels import datasets
  from statsmodels.tsa.statespace import mlemodel, sarimax, structural, varmax
  from statsmodels.tsa.statespace.simulation_smoother import SIMULATION_STATE, SIMULATION_DISTURBANCE, SIMULATION_ALL
label_desc: Use image node_id 3 for calling a global function with example usage: test_simulation_smoothing_state_intercept() without return types