diff --git a/README.md b/README.md
index f014a8966..68d7e059f 100644
--- a/README.md
+++ b/README.md
@@ -244,6 +244,8 @@ The member types are optionally present according to the filter configuration.
 | `x` | Manages the state estimate column vector *X*. Gets or sets the value. The default value is the null column vector. |
 | `y` | Manages the innovation column vector *Y*. Gets the value last computed during the update. The default value is the null column vector. |
 | `z` | Manages the observation column vector *Z*. Gets the value last used during the update. The default value is the null column vector. |
+| `transition` | Manages the state transition function object *f*. Configures the callable object of expression `state(const state &, const input &, const PredictionTypes &...)` to compute the transition state value. The default value is the equivalent to *f(x) = F * X*. The default function is suitable for linear systems. For extended filters `transition` is a linearization of the state transition while *F* is the Jacobian of the transition function: *F = ∂f/∂X = ∂fj/∂xi* that is each row *i* contains the derivatives of the state transition function for every element *j* in the state column vector *X*. |
+| `observation` | Manages the state observation function object *h*. Configures the callable object of expression `output(const state &, const UpdateTypes &...arguments)` to compute the observation state value. The default value is the equivalent to *h(x) = H * X*. The default function is suitable for linear systems. For extended filters `observation` is a linearization of the state observation while *H* is the Jacobian of the observation function: *H = ∂h/∂X = ∂hj/∂xi* that is each row *i* contains the derivatives of the state observation function for every element *j* in the state vector *X*. |
 
 The characteristics are optionally present according to the filter configuration.
 
diff --git a/include/fcarouge/internal/kalman.tpp b/include/fcarouge/internal/kalman.tpp
index 14ee6f664..e99e4c865 100644
--- a/include/fcarouge/internal/kalman.tpp
+++ b/include/fcarouge/internal/kalman.tpp
@@ -224,6 +224,16 @@ kalman<Filter>::s() const -> const innovation_uncertainty & {
   return filter.s;
 }
 
+template <typename Filter>
+inline constexpr void kalman<Filter>::transition(const auto &callable) {
+  filter.transition = callable;
+}
+
+template <typename Filter>
+inline constexpr void kalman<Filter>::observation(const auto &callable) {
+  filter.observation = callable;
+}
+
 template <typename Filter>
 inline constexpr void kalman<Filter>::update(const auto &...arguments) {
   filter.update(arguments...);
diff --git a/include/fcarouge/kalman.hpp b/include/fcarouge/kalman.hpp
index 458553556..e6c4d8ed9 100644
--- a/include/fcarouge/kalman.hpp
+++ b/include/fcarouge/kalman.hpp
@@ -493,6 +493,34 @@ class kalman final : public internal::conditional_member_types<Filter> {
   inline constexpr auto s() const -> const innovation_uncertainty &;
   //! @}
 
+  //! @brief Sets the extended state transition function f(x).
+  //!
+  //! @param callable The copied target Callable object (function object,
+  //! pointer to function, reference to function, pointer to member function, or
+  //! pointer to data member) that will be called to compute the next state X on
+  //! prediction steps of expression `state(const state &, const input &, const
+  //! PredictionTypes &...)`. The default function `f(x) = F * X` is suitable
+  //! for linear systems. For non-linear system, or extended filter, implement a
+  //! linearization of the transition function f and the state transition F
+  //! matrix is the Jacobian of the state transition function.
+  //!
+  //! @complexity Constant.
+  inline constexpr void transition(const auto &callable);
+
+  //! @brief Sets the extended state observation function h(x).
+  //!
+  //! @param callable The copied target Callable object (function object,
+  //! pointer to function, reference to function, pointer to member function, or
+  //! pointer to data member) that will be called to compute the observation Z
+  //! on update steps of expression `output(const state &, const UpdateTypes
+  //! &...arguments)`. The default function `h(x) = H * X` is suitable for
+  //! linear systems. For non-linear system, or extended filter, the client
+  //! implements a linearization of the observation function hand the state
+  //! observation H matrix is the Jacobian of the state observation function.
+  //!
+  //! @complexity Constant.
+  inline constexpr void observation(const auto &callable);
+
   //! @name Public Filtering Member Functions
   //! @{