Principles of Modern Radar - Volume 2 1891121537

15.2 Multitarget Tracking 677state are in the same coordinate systems. In this simplified 1-D example, the Kalman gainreduces toK (1−D)k =P (1−D)k|k−1P (1−D)k|k−1+ R(1−D) k(15.17)If the propagated track covariance, P (1−D)k|k−1 , is much larger than the measurement covariance,R (1−D)k , then the Kalman gain approaches one. Subsequently, the state updatesimplifies tox k|k = x k|k−1 + ( z k − x k|k−1) = zk (15.18)which effectively sets the updated state equal to the state of the new measurement. Thismakes intuitive sense. If the measurement’s uncertainty is much smaller than that of thepropagated track state, then it should be trusted much more heavily. Similarly, if the propagatedtrack covariance is much smaller than the measurement covariance (in this simple1-D example), then the Kalman gain approaches zero and the measurement does not affectthe propagated state and covariance. Again, this makes intuitive sense. If the measurementis much less trustworthy than the propagated state, its impact on the propagated stateshould be minimal. If the track and measurement covariances are relatively similar in size,then the Kalman gain is between zero and one and the updated state lands along the lineconnecting the states of the predicted track and measurement.15.2 MULTITARGET TRACKINGThe more objects observed by the radar, the greater the potential for performance degradationin the tracker. Measurement-to-track association (from Section 15.1.2) is clearly moredifficult when many objects are observed in a similar locale. Generally speaking, the morethe measurement covariances overlap, the more ambiguous this process becomes. Trackfiltering (from Section 15.1.3) can also be adversely affected by the presence of manytargets. In the standard EKF, the same propagation function (denoted by f in (15.9)) isapplied to all tracks. However, the more objects in the scene, the more likely it becomesthat some of them will exhibit different target dynamics. A single propagation functionmay be inadequate to reliably track a large number of (potentially) disparate classes ofobjects.Fortunately, target tracking literature is full of sophisticated techniques intended tomitigate these problems. A thorough treatise on all of these techniques would require aseparate textbook. Hence, this section is limited to some of the more common techniquesfor mitigating the complications that multi-target tracking poses to measurement-to-trackassociation and track filtering. With that in mind, Section 15.2.1 covers approaches tomulti-target measurement-to-track data association that incorporate features, track clusters,or use multiple-hypothesis tracking. Section 15.2.2 then presents state-of-the-artalternatives for addressing disparate sets of target dynamics, such as VS-IMM estimators.15.2.1 Measurement-to-track Data AssociationMeasurement-to-track data association is significantly harder when multiple targets arepresent. The resulting ambiguity is the rationale for more sophisticated techniques.