Example: Automotive Radar Tracking Systems
After filtering and conditioning the received baseband signal, the radar system then tests the signal upon a given detection threshold and then assembles the data into digital format for the tracking system. Where, the data structure is usually in the form of an array of detections for a given frame (or time step). In the case of an FMCW radar system, the detected beat frequencies would be converted into a set of range estimates for the tracking system.
The tracking system first must establish which detections are updates to existing tracks (i.e. from existing vehicles), and which detections are from new vehicles or clutter - where the latter usually presents the most challenging test. As an example, consider a tracking system with no established tracks: In order to assist the tracking system, a very logical hierarchy of track states is defined in order categorize a track's state:
In order to minimize the influence of detections from other vehicles (targets) or clutter and in essence associate the detections, all tracks have a target tracking gate. A target tracking gate can be thought of as an observation window in 2D space, which has its centre at the track’s predicted range and angle. Thus, all new detections that fall within the window or gate are considered to be valid detections for updating the given track.
There is rich variety of data association methods that exist depending on the application and available computing power. One of the most simplest methods referred to as GNN (global nearest neighbour) only uses the closest detection or ‘nearest neighbour’ within the gate in order to update the track. The term ‘global’ signifies that the association method looks at all tracks before making an optimal assignment. This means that only a single observation can be used to update a single track, rather than using one observation to update many tracks. The three most popular optimal assignment algorithms used with GNN are the Munkres, Auction and JVC algorithms.
Other more complicated but popular techniques include
JPDA (joint probability data association) and MHT (multiple hypotheses
testing) which use all neighbours within a gate to update a given track.
MHT is considered to be the most robust radar tracking algorithm on the
market today, as it has excellent tracking performance in heavy clutter,
where simpler techniques such as GNN perform badly. The MHT method is
based on branching, whereby a tracking filter is assigned to each new
detection in the tracking gate. As such, a final decision on difficult
data association situations can be postponed or resolved during
Two types of tracking filter are generally accepted as radar tracking filters:
Alpha-beta trackers on the other hand, are referred to as 'fixed gain' filters, as their gains are determined via a table in a textbook and then left unadjusted. As such, alpha-beta trackers do not perform as well as their Kalman brothers, but can be made to almost match the Kalman filter for non-manoeuvring targets if their gains are set to the Kalman gains at every time step. This usually achieved by pre-computing the Kalman gains and then storing them in a lookup table or via use of a first order exponential function. In many cases, setting the alpha-beta gains to the steady-state Kalman gains can lead to acceptable tracking performance for vehicles travelling in a straight line (i.e. non-manoeuvring) at a fraction of the computational power needed for a Kalman filter.
The plot shown on the right hand side illustrates the tracking performance of the alpha-beta tracker to that of the Kalman filter for an automotive application, where the alpha-beta gains are set to the Kalman's steady state gains. As seen, after approximately 1.5 seconds the tracking performance of the alpha-beta tracker is identical to that of the Kalman filter.
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