Simplex-directed partitioned adaptive filters

Survey of maneuvering target tracking. part v: multiple-model methods

“…Magill's results were further extended by Lainiotis, et al [315,183,179,182,180] to a recursive form, with an exact error covariance form, for vector measurements and arbitrary continuous and discrete parameters. Early works dealt only with estimation for systems with a time-invariant mode that is unknown (a nonrandom constant) or uncertain (a random variable, but not a random process), which led to the autonomous operations of conditional filtering [315,308,118,185]. Many reinventions, extensions, and applications of this generation can be found in the literature under various names, including the "partition (partitioned or partitioning) filter" [179,182,180,347], the "multiple model adaptive filter" [179,182], the "parallel processing algorithm" [7], the "multiple model adaptive estimator" [242], the "static multiple-model algorithm" [18,216], the "filter bank method" [65], the "self-tuning estimator" [65], the "operating regime approach" [156], and in the same spirit the "mixture of experts" [254,73].…”

“…Many practical schemes for adaptation of the grid are possible. The algorithms/designs of [185], [120], [244], [271], [105], [150], [344], [306], [114], and [288] are examples of this structure, where illustrations of their superior cost effectiveness to the FS-IMM algorithm were also given.…”

“…Reference [274] reported simulation results of automatic adjusting model parameters by an if-then rule for process noise covariance and heuristic estimation of turn rate based on kinematics. Reference [185] proposed a simplex-directed mathematical programming scheme for an AMM algorithm, where the grid is formed by the vertices of a simplex and updated by certain rules (e.g., replacement of worst vertices by their mirror images and scaling up or down of the simplex) based on mode (vertex) probabilities. Other programming schemes are of course possible here, as discussed next.…”

“…Other generally applicable optimization techniques (see, e.g., the survey of [175]), such as the popular simulated annealing and tabu search, are potentially applicable here as well. The simplex-directed scheme of [185] and the recursive quadratic programming of [72], [73] also belong to this class in some sense.…”

Moving-Bank Multiple Model Adaptive Estimation and Control Algorithms: An Evaluation

“…Another approach has been to match each elemental filter to a time history of parameter values rather than to just one constant value [4][5][6]8,14]. Various approaches to reducing the computational burden of the algorithm have been taken, including the use of Markov models for parameter variation [4,14,15], "pruning" and "merging" of branches in a "tree" of possible parameter time histories [5,6,8,16], hierarchical structuring [17], and dynamic coarse-to-finer rediscretization [18]. Various approaches to reducing the computational burden of the algorithm have been taken, including the use of Markov models for parameter variation [4,14,15], "pruning" and "merging" of branches in a "tree" of possible parameter time histories [5,6,8,16], hierarchical structuring [17], and dynamic coarse-to-finer rediscretization [18].…”