On the optimal and suboptimal nonlinear filtering problem for discrete-time systems

Survey of maneuvering target tracking: III. Measurement models

“…There are reports that the relinearization iteration degrades the performance. The reader is referred to [57] for some insight that substantiates this warning.…”

“…The scaling factors ½ ¾ ¿ are chosen such that Þ £ Ü Ô ¼, leading to the following [16,17], in the form of (52), (55) under the assumption that the measurement errors in spherical coordinates have a symmetric distribution with independent components that is independent of the ideal measurement Þ. For Gaussian and uniform measurement errors, they are given by ÜÔ ¾ ¾ · ¾ ¾ ¡ ÜÔ ¾ ¾ ¡ (for Gaussian errors) (56) × Ò × Ò´¾ µ ´¾ µ (for uniform errors over ) (57) This conversion is truly unbiased (i.e., Þ £ Ü Ô ¼) regardless whether the true Ü Ô is fixed or random. The corresponding cov´Ú £ Þµ was also derived in [17] without the Gaussian distribution assumption and formulas of ´Ú £ Ú ¼ £ Þµ Þ (less desirable) can be found in [16,19].…”

${\cal H}_{2}$ Filtering for Discrete-Time Nonlinear Singularly Perturbed Systems

“…Under Assumption 3.1, we obtain the reduced-order slow subsystem (32) and a boundary-layer (or quasi-steady-state) subsystem as (33) where is a stretched-time parameter. This subsystem is guaranteed to be asymptotically stable for (see [25,Th.…”

“…In general, statistical discrete-time nonlinear filtering techniques developed using minimum-variance, Bayesian, and maximum-likelihood criteria [10], [30], [33] are too complicated, and approximations [20], [32] are still computationally intensive to implement. These filters require the solution of infinite-dimensional evolution equations such as the Kolmogorov equation, the Stratonovitch-Kushner equation or the Wong-Zakai equation [23].…”

Recursive Filtering for Log-Rice Signals

“…For instance, in the field of avionics communications, the need for a wide dynamic range is a crucial issue that is commonly solved by means of a logarithmic compression of the envelope of the received signal [9]. It is well known that when noisy signals undergo a nonlinear transformation the problem of optimal filtering becomes not tractable, because the minimum error variance estimate requires the computation of the conditional probability density, a difficult infinite-dimensional problem in the general case [1,2,3]. For this reason suboptimal filters, often based on heuristics, are proposed in the literature.…”