Playing movement animations without tracking inputs

I'm developing an online first person multiplayer game. When other players move around in the game, I would like them to be visible and animating with a walk. I do not send their movement inputs, but instead track their movement in the world. Here is what I am currently using, it is called every fixedupdate:

     public void AnimateModel(bool isJump, bool isGrounded)
     {
         if (lastPosition.x > transform.position.x) modelAnim.SetFloat("XMovement", 1); //moving right
         else if(lastPosition.x < transform.position.x) modelAnim.SetFloat("XMovement", -1);
         else modelAnim.SetFloat("XMovement", 0);
 
         if (lastPosition.z > transform.position.z) modelAnim.SetFloat("YMovement", -1); //moving back
         else if (lastPosition.z < transform.position.z) modelAnim.SetFloat("YMovement", 1);
         else modelAnim.SetFloat("YMovement", 0);
 
         modelAnim.SetBool("Jump", isJump);
         modelAnim.SetBool("Grounded", isGrounded);

         lastPosition = transform.position;
     }

The issue with this is it uses world space, so when a player is looking up the Z axis and walks forward, everything is fine, but when they look down the Z axis and walk forward, they play the walking backward animation.

What way could I track the movement correctly with the direction the player is facing? I tried creating a separate game object that lagged behind the player every frame, then tried calculating the movement based on where the player moved from the lagging gameobject, but it did not seem to work.