If you want to add specially noise you can change your odom topic with the another name maybe old_odom and than subscribe this topic. After that you can add what ever want and publish your odom.

https://blog.lxsang.me/post/id/16

#! /usr/bin/env python
import rospy
from math import *
import numpy as np
from nav_msgs.msg import Odometry
import tf

last_odom = None
pose = [0.0,0.0,0.0]
a1 = 0.0
a2 = 0.0
a3 = 0.0
a4 = 0.0
base_frame = ""

# a callback for Gazebo odometry data
def callback(data):
    global last_odom
    global base_frame
    global pose
    global a1
    global a2
    global a3
    global a4

    if(last_odom == None):
        last_odom = data
        pose[0] = data.pose.pose.position.x
        pose[1] = data.pose.pose.position.y
        q = [ data.pose.pose.orientation.x,
                data.pose.pose.orientation.y,
                data.pose.pose.orientation.z,
                data.pose.pose.orientation.w ]
        (r, p, y) = tf.transformations.euler_from_quaternion(q)
        pose[2] = y
    else:
        # calculate new odometry pose using the motion model
        dx = data.pose.pose.position.x - last_odom.pose.pose.position.x
        dy = data.pose.pose.position.y - last_odom.pose.pose.position.y
        trans = sqrt(dx*dx + dy*dy)
        q = [ last_odom.pose.pose.orientation.x,
                last_odom.pose.pose.orientation.y,
                last_odom.pose.pose.orientation.z,
                last_odom.pose.pose.orientation.w ]
        (r,p, theta1) = tf.transformations.euler_from_quaternion(q)
        q = [ data.pose.pose.orientation.x,
                data.pose.pose.orientation.y,
                data.pose.pose.orientation.z,
                data.pose.pose.orientation.w ]
        (r,p, theta2) = tf.transformations.euler_from_quaternion(q)
        rot1 = atan2(dy, dx) - theta1
        rot2 = theta2-theta1-rot1

        sd_rot1 = a1*abs(rot1) + a2*trans
        sd_rot2 = a1*abs(rot2) + a2*trans
        sd_trans = a3*trans + a4*(abs(rot1) + abs(rot2))

        trans +=  np.random.normal(0,sd_trans*sd_trans)
        rot1 += np.random.normal(0, sd_rot1*sd_rot1)
        rot2 += np.random.normal(0, sd_rot2*sd_rot2)

        pose[0] += trans*cos(theta1+rot1)
        pose[1] += trans*sin(theta1+rot1)
        pose[2] = theta1 + rot1 + rot2
        last_odom = data

    # publish the tf
    br = tf.TransformBroadcaster()
    br.sendTransform((pose[0], pose[1], 0),
                     tf.transformations.quaternion_from_euler(0, 0, pose[2]),
                     data.header.stamp,
                     base_frame,
                     "odom")

if __name__ == '__main__':
    rospy.init_node('noisy_odometry', anonymous=True)
    # alpha 1 is degree/degree
    if rospy.has_param("~alpha1"):
        a1 = rospy.get_param("~alpha1")
    else:
        rospy.logwarn("alpha1 is set to default")
        a1 = 15.0*pi/180.0
    # alpha 2 is degree/m
    if rospy.has_param("~alpha2"):
        a2 = rospy.get_param("~alpha2")
    else:
        a2 = 15.0*pi/180.0
        rospy.logwarn("alpha2 is set to default")
    # alpha 3 is m/meter
    if rospy.has_param("~alpha3"):
        a3 = rospy.get_param("~alpha3")
    else:
        a3 = 0.2
        rospy.logwarn("alpha3 is set to default")
    # alpha 4 is m/degree
    if rospy.has_param("~alpha4"):
        a4 = rospy.get_param("~alpha4")
    else:
        a4 = 0.01
        rospy.logwarn("alpha4 is set to default")
    # get odom topic
    if rospy.has_param("~old_odom_topic"):
        odom_topic = rospy.get_param("~old_odom_topic")
    else:
        odom_topic = "/odom"
    # get base frame
    if rospy.has_param("~base_frame"):
        base_frame = rospy.get_param("~base_frame")
    else:
        base_frame = "/base_footprint"

    rospy.Subscriber(odom_topic, Odometry, callback)

    rospy.spin()