diff --git a/nav_msgs/msg/Odometry.msg b/nav_msgs/msg/Odometry.msg
index dc62bc85..a7fee9b1 100644
--- a/nav_msgs/msg/Odometry.msg
+++ b/nav_msgs/msg/Odometry.msg
@@ -1,7 +1,18 @@
 # This represents an estimate of a position and velocity in free space.  
 # The pose in this message should be specified in the coordinate frame given by header.frame_id.
-# The velocity in this message should be specified in the coordinate frame given by the child_frame_id
+# The velocity in this message should be specified in the coordinate frame given by the child_frame_id.
+#
+# If the covariance of the measurement is known, it should be filled in (if all you know is the
+# variance of each measurement, e.g. from a datasheet, just put those along the diagonal).
+# A covariance matrix of all zeros will be interpreted as "covariance unknown", and to use the
+# data a covariance will have to be assumed or gotten from some other source.
+#
+# If you have no estimate for one of the data elements, please set _the respective diagonal_ element
+# of the associated covariance matrix to -1.
+# If you are interpreting this message, please check for a value of -1 in the _diagonal_ elements
+# of each covariance matrix, and disregard the associated estimates.
+
 Header header
 string child_frame_id
 geometry_msgs/PoseWithCovariance pose
-geometry_msgs/TwistWithCovariance twist # velocity but keeping name for backwards compatibility
+geometry_msgs/TwistWithCovariance twist
diff --git a/nav_msgs/msg/OdometryWithAcceleration.msg b/nav_msgs/msg/OdometryWithAcceleration.msg
index c221ae80..849b4aca 100644
--- a/nav_msgs/msg/OdometryWithAcceleration.msg
+++ b/nav_msgs/msg/OdometryWithAcceleration.msg
@@ -2,8 +2,19 @@
 # The pose in this message should be specified in the coordinate frame given by header.frame_id.
 # The velocity in this message should be specified in the coordinate frame given by the child_frame_id.
 # The acceleration in this message should be specified in the coordinate frame given by the child_frame_id.
+#
+# If the covariance of the measurement is known, it should be filled in (if all you know is the
+# variance of each measurement, e.g. from a datasheet, just put those along the diagonal).
+# A covariance matrix of all zeros will be interpreted as "covariance unknown", and to use the
+# data a covariance will have to be assumed or gotten from some other source.
+#
+# If you have no estimate for one of the data elements, please set _the respective diagonal_ element
+# of the associated covariance matrix to -1.
+# If you are interpreting this message, please check for a value of -1 in the _diagonal_ elements
+# of each covariance matrix, and disregard the associated estimates.
+
 Header header
 string child_frame_id
 geometry_msgs/PoseWithCovariance pose
-geometry_msgs/TwistWithCovariance velocity
-geometry_msgs/TwistWithCovariance acceleration
+geometry_msgs/TwistWithCovariance twist
+geometry_msgs/AccelWithCovariance accel