ROS melodic repro for https://answers.ros.org/question/341970/robot_localization-unusual-behavior-when-fusing-imu-orientation/

ekf_plus_transforms.launch

<launch>

  <node pkg="tf2_ros" type="static_transform_publisher" name="base_to_imu_tf_broadcaster"
        args="-0.5 0 0 1.5707963267948966 0 3.141592653589793 base_link imu_link"/>

  <node pkg="tf2_ros" type="static_transform_publisher" name="imu_to_ned_tf_broadcaster"
        args="0 0 0.2 0 0 0 imu_link ned_frame"/>

  <node pkg="robot_localization" type="ekf_localization_node" name="ekf_node">
    <param name="filter_type" value="ekf"/>
    <param name="frequency" value="10.0"/>
    <param name="two_d_mode" value="true"/>
    <param name="odom_frame" value="odom"/>
    <param name="base_link_frame" value="base_link"/>
    <param name="world_frame" value="odom"/>
    <param name="imu0" value="/imu"/>
    <rosparam param="imu0_config">
      [false, false, false,
      false, false, true,
      false, false, false,
      true, true, true,
      false, false, false]
    </rosparam>
    <param name="imu0_relative" value="true"/>
    <param name="odom0" value="/wheel/odom" />
    <rosparam param="odom0_config">
      [false, false, false,
      true, true, false,
      false, false, false,
      false, false, false,
      false, false, false]
    </rosparam>
    <param name="publish_tf" value="true"/>
  </node>
  
</launch>

repro.rviz

Panels:
  - Class: rviz/Displays
    Help Height: 78
    Name: Displays
    Property Tree Widget:
      Expanded:
        - /Global Options1
        - /Status1
        - /TF1
        - /TF1/Frames1
        - /Odometry1
        - /Odometry2
        - /Odometry2/Shape1
      Splitter Ratio: 0.5
    Tree Height: 734
  - Class: rviz/Selection
    Name: Selection
  - Class: rviz/Tool Properties
    Expanded:
      - /2D Pose Estimate1
      - /2D Nav Goal1
      - /Publish Point1
    Name: Tool Properties
    Splitter Ratio: 0.5886790156364441
  - Class: rviz/Views
    Expanded:
      - /Current View1
    Name: Views
    Splitter Ratio: 0.5
  - Class: rviz/Time
    Experimental: false
    Name: Time
    SyncMode: 0
    SyncSource: ""
Preferences:
  PromptSaveOnExit: true
Toolbars:
  toolButtonStyle: 2
Visualization Manager:
  Class: ""
  Displays:
    - Alpha: 0.5
      Cell Size: 1
      Class: rviz/Grid
      Color: 160; 160; 164
      Enabled: true
      Line Style:
        Line Width: 0.029999999329447746
        Value: Lines
      Name: Grid
      Normal Cell Count: 0
      Offset:
        X: 0
        Y: 0
        Z: 0
      Plane: XY
      Plane Cell Count: 10
      Reference Frame: <Fixed Frame>
      Value: true
    - Class: rviz/TF
      Enabled: true
      Frame Timeout: 15
      Frames:
        All Enabled: false
        base_link:
          Value: true
        imu_link:
          Value: true
        ned_frame:
          Value: false
        odom:
          Value: false
      Marker Scale: 0.800000011920929
      Name: TF
      Show Arrows: true
      Show Axes: true
      Show Names: true
      Tree:
        base_link:
          imu_link:
            ned_frame:
              {}
        odom:
          {}
      Update Interval: 0
      Value: true
    - Angle Tolerance: 0.10000000149011612
      Class: rviz/Odometry
      Covariance:
        Orientation:
          Alpha: 0.5
          Color: 255; 255; 127
          Color Style: Unique
          Frame: Local
          Offset: 1
          Scale: 1
          Value: true
        Position:
          Alpha: 0.30000001192092896
          Color: 204; 51; 204
          Scale: 1
          Value: true
        Value: false
      Enabled: true
      Keep: 1
      Name: Odometry
      Position Tolerance: 0.10000000149011612
      Shape:
        Alpha: 1
        Axes Length: 1
        Axes Radius: 0.10000000149011612
        Color: 255; 25; 0
        Head Length: 0.30000001192092896
        Head Radius: 0.10000000149011612
        Shaft Length: 1
        Shaft Radius: 0.05000000074505806
        Value: Arrow
      Topic: /odometry/filtered
      Unreliable: false
      Value: true
    - Angle Tolerance: 0.10000000149011612
      Class: rviz/Odometry
      Covariance:
        Orientation:
          Alpha: 0.5
          Color: 255; 255; 127
          Color Style: Unique
          Frame: Local
          Offset: 1
          Scale: 1
          Value: true
        Position:
          Alpha: 0.30000001192092896
          Color: 204; 51; 204
          Scale: 1
          Value: true
        Value: false
      Enabled: true
      Keep: 1
      Name: Odometry
      Position Tolerance: 0.10000000149011612
      Shape:
        Alpha: 1
        Axes Length: 1
        Axes Radius: 0.10000000149011612
        Color: 1; 255; 81
        Head Length: 0.30000001192092896
        Head Radius: 0.10000000149011612
        Shaft Length: 1
        Shaft Radius: 0.05000000074505806
        Value: Arrow
      Topic: /wheel/odom
      Unreliable: false
      Value: true
  Enabled: true
  Global Options:
    Background Color: 48; 48; 48
    Default Light: true
    Fixed Frame: odom
    Frame Rate: 30
  Name: root
  Tools:
    - Class: rviz/Interact
      Hide Inactive Objects: true
    - Class: rviz/MoveCamera
    - Class: rviz/Select
    - Class: rviz/FocusCamera
    - Class: rviz/Measure
    - Class: rviz/SetInitialPose
      Theta std deviation: 0.2617993950843811
      Topic: /initialpose
      X std deviation: 0.5
      Y std deviation: 0.5
    - Class: rviz/SetGoal
      Topic: /move_base_simple/goal
    - Class: rviz/PublishPoint
      Single click: true
      Topic: /clicked_point
  Value: true
  Views:
    Current:
      Class: rviz/Orbit
      Distance: 2.2010698318481445
      Enable Stereo Rendering:
        Stereo Eye Separation: 0.05999999865889549
        Stereo Focal Distance: 1
        Swap Stereo Eyes: false
        Value: false
      Focal Point:
        X: -0.12720155715942383
        Y: 0.03638945519924164
        Z: -0.06940260529518127
      Focal Shape Fixed Size: true
      Focal Shape Size: 0.05000000074505806
      Invert Z Axis: false
      Name: Current View
      Near Clip Distance: 0.009999999776482582
      Pitch: 0.69539874792099
      Target Frame: <Fixed Frame>
      Value: Orbit (rviz)
      Yaw: 4.1554059982299805
    Saved: ~
Window Geometry:
  Displays:
    collapsed: false
  Height: 1025
  Hide Left Dock: false
  Hide Right Dock: false
  QMainWindow State: 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
  Selection:
    collapsed: false
  Time:
    collapsed: false
  Tool Properties:
    collapsed: false
  Views:
    collapsed: false
  Width: 1853
  X: 67
  Y: 27

swinging_base_node.py

import math

import rospy

from sensor_msgs.msg import Imu
from nav_msgs.msg import Odometry

import tf.transformations as tft


if __name__ == '__main__':
    rospy.init_node('swinging_base_node')
    imu_pub = rospy.Publisher('/imu', Imu, queue_size=10)
    odom_pub = rospy.Publisher('/wheel/odom', Odometry, queue_size=10)

    rate = rospy.Rate(50)
    start_time = rospy.get_rostime()
    while not rospy.is_shutdown():
        current_time = rospy.get_rostime()
        yaw_angle = math.pi/2 * math.sin(2 * math.pi * (current_time - start_time).to_sec() / 20)
        yaw_velocity = math.pi/40 * math.cos(2 * math.pi * (current_time - start_time).to_sec() / 20)

        imu_quat = tft.quaternion_about_axis(-yaw_angle, (0, 0, 1))

        # NED -> ENU conversion
        imu_quat = tft.quaternion_multiply(
            imu_quat, tft.quaternion_from_euler(math.pi, 0, math.pi/2, 'sxyz')
        )

        odom_quat = tft.quaternion_about_axis(yaw_angle, (0, 0, 1))

        imu_msg = Imu()
        imu_msg.header.stamp = current_time
        imu_msg.header.frame_id = 'imu_link'
        imu_msg.angular_velocity.z = -yaw_velocity
        imu_msg.linear_acceleration.z = -9.8
        (imu_msg.orientation.x,
         imu_msg.orientation.y,
         imu_msg.orientation.z,
         imu_msg.orientation.w) = imu_quat
        imu_pub.publish(imu_msg)

        odom_msg = Odometry()
        odom_msg.header.stamp = current_time
        odom_msg.header.frame_id = 'odom'
        odom_msg.child_frame_id = 'base_link'
        odom_msg.twist.twist.angular.z = yaw_velocity
        (odom_msg.pose.pose.orientation.x,
         odom_msg.pose.pose.orientation.y,
         odom_msg.pose.pose.orientation.z,
         odom_msg.pose.pose.orientation.w) = odom_quat
        odom_pub.publish(odom_msg)

        rate.sleep()