⇦

PhD - I year (part 3)

In short, Λ:O is a model suitable to predict complex motions at the price of requiring accurate measurements. More in detail, Λ:O has the following characteristics.

Λ:O PROs

  • 1) Maneuvering object tracking
    Λ:O takes directly into account in its model that the object can maneuver during its motion, i.e. can move with a longitudinal and a steering speeds that can vary in time. In order to do that, Λ:O includes in its model not only the longitudinal and the steering speed, but also their time-derivatives (Λ derivatives for the longitudinal speed, O derivatives for the steering speed - where Λ and O are design parameters that can be arbitrarily choosen by the user);
  • 2) Extended object tracking
    Λ:O f‌its in a very natural manner in extended object tracking tanks to the heading angle: Λ:O exploit the heading angle to predict the future position of the object, the object extension provides to Λ:O an indirect observation of the heading angle;
  • 3) Interpretability
    Λ:O stresses the use of the longitudinal and steering speeds as state variables, which can be easily understood as the input commands ("gas pedal" and "steering wheel" command) choosen by the object driver. As a result, Λ:O points out clearly out when the object maneuvers. Moreover, the steering speed variable can be easily converted in centripetal acceleration or curvature radius, providing additional information about the object motion.

Λ:O CONs

  • 1) Information greediness
    Λ:O can employ a big number of state variables and each of them must be well estimated. If this is not the case, the ef‌f‌ect of using a lot of state variables becomes detrimental rather than benef‌icial. As a result, Λ:O is particularly sensitive to the measurement noise. If the noise covariance is too high, the problem can be mitigated by processing simultaneously multiple measurements (like in the extended object case) or by reducing the sampling time;
  • 2) Inertial ef‌fect
    As Λ and O grows, Λ:O slows down its response with respect to rapid variation in the object movement. This problem can be mitigated by adding white noise on each state variable (rather than just the Λth and Oth derivatives of the longitudinal and steering speeds);
  • 3) Inexact discretization
    The Tustin discretization introduces errors in the prediction, and such errors can be seen as a quantization noise that adds up to the measurement noise. This problem can be mitigated by employing exact discretization schemes (that are possible when Λ and O are small, e.g. up to the value 1) or semi-exact discretization schemes (one of my new ideas under development - coming soon!).

⇨