Kalman Filter (1D)

Implement a 1D Kalman filter for state estimation given measurement z, previous estimate x, estimate covariance P, measurement noise R, and process noise Q. Output updated state and covariance.

Constraints

• Use standard Kalman update equations.
• Measurements are scalar.
• No loops allowed.
• Must compute Kalman gain K.
• Output variables: x_out and P_out.
• Assume Q and R are positive.