Quantization Based Filtering Method Using First Order Approximation
SIAM Journal on Numerical Analysis
| Hi-index | 0.00 |
Methods of preprocessing the observations for nonlinear filters are investigated, the aim being to reduce the computational labor involved in their implementation. An example of preprocessing is quantization, which involves the replacement of real-valued observation samples by discrete values. Because the resulting likelihood functions have finite support, they can be held in "look-up" tables kept in some type of rapid access memory, which renders their "real-time" evaluation trivial. Preprocessed observations of this sort carry less information than raw observations. This loss of information is characterized here for filters with substantially noisy observation samples by means of a functional central limit theorem. Among other things, this supplies an asymptotic, effective signal-to-noise ratio for preprocessed filters.Methods of optimizing preprocessing operations with respect to this quantified information loss are developed. In particular, optimal quantization thresholds are found for observations that are contaminated by Gaussian noise, and it is shown that the loss of information for quite coarse quantization schemes is small; for example, the asymptotic, effective signal-to-noise ratio for a filter with one-bit quantized observations is $2/\pi$ times that for the same filter with raw observations. Simulations on two examples demonstrate the validity of the asymptotic characterization, even when the observation samples are only modestly contaminated by noise.