ðɪs vˈɜːʒən ʌvðə sˌɛpɚɹˈeɪʃən pɹˈɪnsɪpəl ɪz ɐ spˈɛʃəl kˈeɪs ʌvðə sˌɛpɚɹˈeɪʃən pɹˈɪnsɪpəl ʌv stətʃˈæstɪk kəntɹˈoʊl wˌɪtʃ stˈeɪts ðæt ˈiːvən wɛn ðə pɹˈɑːsɛs ænd ˈaʊtpʊt nˈɔɪz sˈoːɹsᵻz ɑːɹ pˈɑːsᵻbli nˈɑːŋɡˈaʊʃən mˈɑːɹɾɪŋɡˌeɪlz, æz lˈɔŋ æz ðə sˈɪstəm daɪnˈæmɪks ɑːɹ lˈɪnɪɹ, ðɪ ˈɑːptɪməl kəntɹˈoʊl sˈɛpɚɹˌeɪts ˌɪntʊ ɐn ˈɑːptɪməl stˈeɪt ˈɛstᵻmˌeɪɾɚ wˌɪtʃ mˈeɪ nˌoʊ lˈɑːŋɡɚ biː ɐ kˈælmən fˈɪltɚ ænd ɐn ˌɛlkjˌuːˈɑːɹ ɹˈɛɡjʊlˌeɪɾɚ.
This version of the separation principle is a special case of the separation principle of stochastic control which states that even when the process and output noise sources are possibly non-Gaussian martingales, as long as the system dynamics are linear, the optimal control separates into an optimal state estimator (which may no longer be a Kalman filter) and an LQR regulator.