Principles of Modern Radar - Volume 2 1891121537

690 CHAPTER 15 Multitarget, Multisensor Trackingstill represented in the cost matrix with a single row, regardless of the number of modesrunning in parallel in the IMM estimator.Once a measurement is assigned to the track, each of the filters in the IMM estimatoris updated using the measurement via (15.11) through (15.16). The mode probabilities arealso updated at this point, based on the measurement-to-track likelihoods, viaμ l = l ¯c l¯cwhere ¯c l comes from (15.22) and ¯c is given by(15.24)¯c =N∑ l ¯c l (15.25)l=1The updated states and covariances from each filter then become inputs to the mixingfunction during the next IMM cycle. Should a single estimate be needed from the IMM,it comes from blending the various mode states and covariances together viaandP k =N∑l=1ˆx k =N∑˜x k|k l μl (15.26)l=1[)( ) ] Tμ l ˜P k|k(˜x l + k|k l − ˆx k ˜x k|k l − ˆx k(15.27)To ensure good track accuracy across the spectrum of possible target behaviors, theIMM designer may be tempted to include a large number of modes. Increasing the numberof modes is not always advantageous, though. Each mode influences the track state duringthe mixing and blending steps. Even though the degree of influence for a given (poorlymatching)mode may be small, the cumulative influence of several poorly-matching modesmay be significant enough to noticeably degrade track accuracy. As a result, the IMMdesigner is faced with a tradeoff between overall track accuracy and the ability to maintaintracks during different dynamic modes. As a rule of thumb, IMM estimators are typicallydesigned with as few modes as possible to achieve adequate track maintenance. They ofteninclude filters precisely tuned to the small set of most-likely target dynamics, as well asone generic mode intended to preserve the track when the target dynamics don’t matchany of the more focused filters.15.2.3 VS-IMM EstimatorsThe VS-IMM estimator mitigates the negative impact of this tradeoff by allowing the setof candidate modes to vary adaptively for each track over time [26]. The equations fromSection 15.2.2.1 still apply to the VS-IMM. The only difference is that the l modes usedat any point in time for a given track are based on that track’s current dynamics. As aresult, more filters are available to accommodate a broad range of target dynamics. Theleast-likely filters do not contribute to the mixed or blended states if they are not partof the currently selected set for that track. Given the large number of modes needed tocharacterize realistic target dynamics in some applications, use of the VS-IMM can benecessary to achieve both satisfactory track accuracy and track maintenance.