**Unscented Kalman Filter Arduino Code**
* The Unscented Kalman Filter (UKF) is a powerful tool for state variable estimation in highly nonlinear systems where the Extended Kalman Filter (EKF) may fail [1].
* Implementing the Unscented Kalman Filter (UKF) on an Arduino can be a challenging task due to limited computational resources and memory on typical Arduino boards. However, it's still possible to implement a simplified version of the UKF for simple state estimation tasks.
* Below is a basic outline of how you might implement a simple UKF on an Arduino, but keep in mind that this is a high-level conceptual guide, and you may need to adapt and optimize it for your specific use case and hardware constraints.
Here is a simplified example of an Unscented Kalman Filter in Arduino:

    #include <Arduino.h>

    // Define the state vector dimension and measurement dimension
    const int state_dim = 2;
    const int measurement_dim = 1;

    // State vector [position, velocity]
    double x[state_dim] = {0.0, 0.0};

    // State covariance matrix
    double P[state_dim][state_dim] = {
        {1.0, 0.0},
        {0.0, 1.0}
    };

    // Process noise covariance matrix
    double Q[state_dim][state_dim] = {
        {0.1, 0.0},
        {0.0, 0.1}
    };

    // Measurement noise covariance
    double R[measurement_dim][measurement_dim] = {
        {0.1}
    };

    void prediction() {
        // Implement the prediction step of the UKF
        // Update the state vector 'x' and covariance matrix 'P' based on the motion model
    }

    void update(double measurement) {
        // Implement the update step of the UKF
        // Update the state vector 'x' and covariance matrix 'P' based on the measurement
    }

    void setup() {
        // Initialization code
    }

    void loop() {
        // Your main loop
        // 1. Read sensor measurements
        double measurement = analogRead(A0);

        // 2. Prediction step
        prediction();

        // 3. Update step
        update(measurement);

        // 4. Access the estimated state:
        double estimated_position = x[0];
        double estimated_velocity = x[1];

        // Add a delay or other control logic here
    }

**Explanation**:
* State and Covariance Matrices: The state vector `x` represents the estimated state, while the matrices `P`, `Q`, and `R` represent the state covariance, process noise covariance, and measurement noise covariance, respectively.
* Prediction and Update Steps: The `prediction()` and `update()` functions are responsible for updating the state vector and covariance matrix based on the motion model and sensor measurements, respectively. The specific implementations of these steps are not provided and must be developed separately.
* `setup()` and `loop()`: The Arduino `setup()` function is for initialization, and the `loop()` function is the main loop where sensor measurements are read, prediction and update steps are called, and the estimated state is accessed.

Please note that this example is highly simplified and doesn't include key features like the unscented transform, process and measurement models, and the Kalman gain computation. Real-world applications typically require extensive mathematical calculations, and it's important to consider the computational limitations of an Arduino when implementing the UKF.

For complex state estimation tasks, it is often more suitable to use more powerful microcontrollers or embedded platforms that can handle the computational demands of a full-featured UKF implementation. Additionally, you may find existing libraries or resources designed for more capable hardware platforms to help with Kalman filtering tasks.