TurretController.cs

using UnityEngine;

public class TurretController : MonoBehaviour {

    public ShootingPoint shooter;

    public Transform pitchPivot;
    public Transform yawPivot;

    public float pitchTurnSpeed = 25;
    public float yawTurnSpeed = 25;
    public float aimAhead = 1;

    Vector3 lastTargetPosition = Vector3.zero;
    Transform _target;
    public Transform Target {
        get { return _target; }
        set {
            Transform old = _target;

            _target = value;

            if(old != Target && Target)
                lastTargetPosition = Target.position;
        }
    }

    public Vector3 AimPosition { get; private set; }

    public float yawSpeed;
    public float pitchSpeed;

    float TargetPitch {
        get {
            return Target ? Vector3.Dot(Vector3.Cross(pitchPivot.forward, (AimPosition - pitchPivot.position).normalized), pitchPivot.right) : 0;
        }
    }

    float TargetYaw {
        get {
            return Target ? Vector3.Dot(Vector3.Cross(yawPivot.forward, (AimPosition - yawPivot.position).normalized), yawPivot.up) : 0;
        }
    }

    void Update() {
        if(Target) {
            yawPivot.localRotation = yawPivot.localRotation * Quaternion.Euler(0, TargetYaw * yawTurnSpeed * Time.deltaTime, 0);
            pitchPivot.localRotation = pitchPivot.localRotation * Quaternion.Euler(TargetPitch * pitchTurnSpeed * Time.deltaTime, 0, 0);

            if(shooter.IsReady)
                shooter.Shoot();
        }
    }

    void LateUpdate() {
        if(Target) {
            AimPosition = Target.position + (Target.position - lastTargetPosition) * aimAhead;

            lastTargetPosition = Target.position;
        }
    }

    void OnDrawGizmos() {
        if(Target) {
            Gizmos.color = Color.red;
            Gizmos.DrawLine(shooter.transform.position, AimPosition);
        }
    }
}