How can I get my character to move forward in the direction of the camera?

I currently have the following class. The class is supposed to be a custom character controller that allows the player to walk on non-horizontal surfaces, and so far most of it has been working, except for direction-based movement.

 using UnityEngine;
 using System.Collections;
 
 namespace Normal
 {
     /// <summary>
     /// This class is responsible for managing the various aspects of the player,
     /// from simple movement to mesh alignment.
     /// </summary>
     [RequireComponent(typeof(Rigidbody))]
     public class PlayerController : MonoBehaviour
     {
         public float RotationTransitionSpeed = 1.0f;
         public float Sensitivity = 2.0f;
         public float MovementSpeed = 5.0f;
         public float RaycastDistance = 10.0f;
         public float GravityForce = 9.8f;
         public Vector3 GravityVector = new Vector3(0, -1, 0);
 
         private Quaternion _TargetRotation;
         private float _VerticalCameraRotation;
         private Vector3 _MovementDistance;
         private Vector3 _MovementVelocity;
         private Rigidbody _Rigidbody;
 
         /// <summary>
         /// Apply movement to the player object based on specific key inputs. The player can currently
         /// move forwards, backwards, left and right.
         /// </summary>
         public void ApplyMovement()
         {
             Vector3 movementDirection = new Vector3(Input.GetAxis("Horizontal"), 0, Input.GetAxis("Vertical")).normalized;
             Vector3 movementVector = movementDirection * this.MovementSpeed * Time.deltaTime;
             this.transform.Translate(movementVector);
         }
 
         /// <summary>
         /// Apply rotation to the player based on the normal of the face they're
         /// "above". This function will also set the gravity of the player accordingly.
         /// </summary>
         public void ApplyRotation()
         {
             // Apply rotation to the player and the camera objects based on the movement of
             // the mouse cursor.
             Camera.main.transform.Rotate(Vector3.up * Input.GetAxis("Mouse X") * this.Sensitivity);
             this._VerticalCameraRotation += Input.GetAxis("Mouse Y") * this.Sensitivity;
             this._VerticalCameraRotation = Mathf.Clamp(this._VerticalCameraRotation, -60, 60);
             Camera.main.transform.localEulerAngles = new Vector3(
                 Vector3.left.x * this._VerticalCameraRotation,
                 Camera.main.transform.localEulerAngles.y,
                 0
             );
 
             // Apply rotation to the entire player object based on where they are walking
             // on a specific mesh.
             RaycastHit raycastHit;
             if(Physics.Raycast(this.transform.position, -this.transform.up, out raycastHit))
             {
                 this._TargetRotation = Quaternion.FromToRotation(Vector3.up, raycastHit.normal);
                 this.GravityVector = -raycastHit.normal;
             }
 
             this.transform.rotation = Quaternion.Lerp(
                 this.transform.rotation, 
                 this._TargetRotation, 
                 Time.deltaTime * this.RotationTransitionSpeed
             );
         }
 
         /// <summary>
         /// Apply a gravity force to the player based on the currently set gravitational
         /// force. Gravitational force direction is determined based on the normal that
         /// the player is "above".
         /// </summary>
         public void ApplyGravity()
         {
             this._Rigidbody.AddForce(this.GravityVector * this.GravityForce * this._Rigidbody.mass);
         }
 
         /// <summary>
         /// FixedUpdate is called a set amount of times per frame in sync with the physics engine.
         /// </summary>
         public void FixedUpdate()
         {
             this.ApplyGravity();
         }
 
         /// <summary>
         /// Update is called once per frame.
         /// </summary>
         public void Update()
         {
             this.ApplyRotation();
             this.ApplyMovement();
         }
 
         /// <summary>
         /// Start is called once.
         /// </summary>
         public void Start()
         {
             this._Rigidbody = this.GetComponent<Rigidbody>();
         }
     }
 }

Ideally, I'd like to have the player move forward relative to the direction the camera is facing, but I cannot for the life of me figure out how to do this. Is it possible?