Principles of Modern Radar - Volume 2 1891121537

15.2 Multitarget Tracking 689Mode 1MixMode NFIGURE 15-9Steps in the IMMestimator.Propagate (xˆ1 k−1|k−1 , P1 k−1|k−1 )to (xˆ1 k|k−1 , P1 k|k−1 )Propagate (xˆN k−1|k−1 , PN k−1|k−1 )to (xˆN k|k−1 , PN k|k−1 )Measurement-to-trackassociationMeasurement-to-trackassociationUpdated (xˆ1 k|k−1 , P1 k|k−1 )with measurementto (xˆ1 k|k , P1 k|k )Updated (xˆN k|k−1 , PN k|k−1 )with measurementto (xˆN k|k , PN k|k )Update Mode ProbabilitiesBlendat t k−1 given that mode m is the best at t k . This probability is given byμ l,m p (l,m) μl= (15.21)¯c mwhere p(l,m) is the probability of switching from mode l to mode m (which is definedprior to the engagement and remains static), μ l is the probability of mode l at t k−1 , and¯c m is the probability of being in mode m at t k , given byN∑¯c m = p (l,m)μ l (15.22)l=1If the measurement time interval varies with sensors, then the transition probability matrix(TPM) {p(l,m)} can vary with time and can be calculated using the algorithm in [30].The mixed states and covariances are then propagated to the current time in each filter,using (15.9) and (15.10). Note that each of the N filters may have different propagationfunctions and process noise.Measurement-to-track association comes next. This step poses a challenge. If eachparallel filter independently conducted measurement-to-track association, they could arriveat different answers and begin to represent different objects. Since the goal is toassign the best measurement to this track, based on all the filter representations of it, thelikelihoods from (15.4) are combined in a weighted average viaN∑ ij = l ij μl (15.23)l=1where the weights are the mode probabilities [17]. The measurement-to-track cost matrixis then populated as a function of these combined likelihoods. As a result, each track is