Geoscience Reference
In-Depth Information
distribution considered previously for the noise should be substituted by the ones determined
in (24).
5. Radar tracking
In the basic section, we said that the proposed parameter estimation can be useful for the
tracking of a target. As mentioned, there are various methods for the target tracking which
present specific mathematical algorithms. These methods have different performance levels,
but most of them are recursive, so that at any time, the data is obtained by using previous
data and improving them. Now, some of the most common procedures and their problems
are expressed and then, the proposed moment method are described in detail.
5.1 Kalman filter
The Kalman filter is the central algorithm to the majority of all modern radar tracking systems.
The role of the filter is to take the current known state (i.e. position, heading, speed and
possibly acceleration) of the target and predict the new state of the target at the time of
the most recent radar measurement. In making this prediction, it also updates its estimate
of its own uncertainty (i.e. errors) in this prediction. It then forms a weighted average of
this prediction of state and the latest measurement of state, taking account of the known
measurement errors of the radar and its own uncertainty in the target motion models. Finally,
it updates its estimate of its uncertainty of the state estimate. A key assumption in the
mathematics of the Kalman filter is that measurement equations (i.e. the relationship between
the radar measurements and the target state) and the state equations (i.e. the equations for
predicting a future state based on the current state) are linear, i.e. can be expressed in the form
y
=
=
(
)
. The Kalman filter assumes that the
measurement errors of the radar, and the errors in its target motion model, and the errors in
its state estimate are all zero-mean Gaussian distributed. This means that all of these sources
of errors can be represented by a covariance matrix. The mathematics of the Kalman filter is
therefore concerned with propagating these covariance matrices and using them to form the
weighted sum of prediction and measurement [Ristic et al., 2004].
A
.
x
(where
A
is a constant), rather than
y
f
x
In situations where the target motion conforms well to the underlying model, there is a
tendency of the Kalman filter to become "over confident" of its own predictions and to start
to ignore the radar measurements. If the target then manoeuvres, the filter will fail to follow
the manoeuvre. It is therefore common practice when implementing the filter to arbitrarily
increase the magnitude of the state estimate covariance matrix slightly at each update to
prevent this.
5.2 Extended Kalman Filter (EKF)
This method is a class of nonlinear tracking algorithms that provides much better results than
the Kalman filter.
Nonlinear tracking algorithms use a nonlinear filter to cope with the following cases:
•
The relationship between the radar measurements and the track coordinates is nonlinear.
•
The errors are nonlinear.
•
The motion model, is non-linear.
