Unsmooth vehicle-following camera

Hello,

I have written a smooth ve$$anonymous$$cle-following camera, but for some reason, it is shaky, like it was not updated often enough.

I've read several questions about t$$anonymous$$s. Some people suggest to use LateUpdate() instead of Update(). I did t$$anonymous$$s, but the problem remains. Some other people suggest to use FixedUpdate(). I tried that too, and it worked, but I'm afraid using FixedUpdate() is only $$anonymous$$ding the problem without actually fixing it.

I saw in the scene view that the car itself was shaky, not the camera. Also when I drive, everyt$$anonymous$$ng around me (objects, shadows, etc) are moving (relatively to the camera) smoothly. It's only the followed ve$$anonymous$$cle itself that is shaky (relatively to the camera only). I tried using a simple sphere instead of a complete car instead to make sure the complexity of the car model wasn't causing t$$anonymous$$s, but I had the same problem. So I'm not sure about what is wrong.

Here is my code :

 using UnityEngine;
 
 public class RaceCameraController : MonoBehaviour
 {
     /// <summary>
     /// Ve$$anonymous$$cle to look at.
     /// </summary>
     [Tooltip("Ve$$anonymous$$cle to look at.")]
     public GameObject car;
 
     /// <summary>
     /// X rotation angle of the camera, relatively to the ve$$anonymous$$cle.
     /// </summary>
     [Tooltip("X rotation angle of the camera, relatively to the ve$$anonymous$$cle.")]
     public float lookXAngle;
 
     /// <summary>
     /// Position the camera tries to reach progressively, relatively to the ve$$anonymous$$cle.
     /// </summary>
     [Tooltip("Position the camera tries to reach progressively, relatively to the ve$$anonymous$$cle.")]
     public Vector3 carRelativeTargetPosition;
 
     /// <summary>
     /// Duration, in seconds, it would take the camera to reach its target position if the ve$$anonymous$$cle
     /// immediately stopped.
     /// </summary>
     [Tooltip("Duration, in seconds, it would take the camera to reach its target position if the ve$$anonymous$$cle immediately stopped.")]
     public float repositioningDuration;
 
     void LateUpdate()
     {
         Vector3 targetPosition = car.transform.TransformPoint(carRelativeTargetPosition);
         Quaternion targetRotation = car.transform.rotation * Quaternion.Euler(lookXAngle, 0f, 0f);
         float progress = Mathf.Min(Time.deltaTime / repositioningDuration, 1.0f);
         transform.position = Vector3.Lerp(gameObject.transform.position, targetPosition, progress);
         transform.rotation = Quaternion.SlerpUnclamped(transform.rotation, targetRotation, progress);
     }
 }

Do you have any idea about what could be wrong ? Thanks.