Maximum A posteriori interval estimation
Maximum a posteriori estimate of random process state vector in interval
RANDOM PROCESS↗
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Maximum a posteriori decoder for digital communications
A system and method for decoding by identification of the most likely phase coded signal corresponding to received data. The present invention has particular application to communication with signals that experience spurious random phase perturbations. The generalized estimator-correlator uses a maximum a posteriori (MAP) estimator to generate phase estimates for correlation with incoming data samples and for correlation with mean phases indicative of unique hypothesized signals. The result is a MAP likelihood statistic for each hypothesized transmission, wherein the highest value statistic identifies the transmitted signal.
Altes, Richard A.↗
Maximum a posteriori interval estimation.
Maximum a posteriori /MAP/ interval estimation for state vector of random process, solving fixed delay filtering and deriving error matrix
RANDOM PROCESS↗
A generalization of the near-optimum binary coherent state receiver concept
The structure of a maximum a posteriori decoder is derived for binary optical fields processed according to Kennedy's near-optimum scheme, but operating in the presence of random optical phase-error and interfering background fields. An exact expression is found for the error probability, and examples to illustrate decoder performance under various operating conditions of interest are provided.
Vilnrotter, V. A.↗
On the design of turbo codes
In this article, we design new turbo codes that can achieve near-Shannon-limit performance. The design criterion for random interleavers is based on maximizing the effective free distance of the turbo code, i.e., the minimum output weight of codewords due to weight-2 input sequences. An upper bound on the effective free distance of a turbo code is derived. This upper bound can be achieved if the feedback connection of convolutional codes uses primitive polynomials. We review multiple turbo codes (parallel concatenation of q convolutional codes), which increase the so-called 'interleaving gain' as q and the interleaver size increase, and a suitable decoder structure derived from an approximation to the maximum a posteriori probability decision rule. We develop new rate 1/3, 2/3, 3/4, and 4/5 constituent codes to be used in the turbo encoder structure. These codes, for from 2 to 32 states, are designed by using primitive polynomials. The resulting turbo codes have rates b/n (b = 1, 2, 3, 4 and n = 2, 3, 4, 5, 6), and include random interleavers for better asymptotic performance. These codes are suitable for deep-space communications with low throughput and for near-Earth communications where high throughput is desirable. The performance of these codes is within 1 dB of the Shannon limit at a bit-error rate of 10(exp -6) for throughputs from 1/15 up to 4 bits/s/Hz.
Divsalar, D.↗
Maximum a posteriori classification of multifrequency, multilook, synthetic aperture radar intensity data
We present a maximum a posteriori (MAP) classifier for classifying multifrequency, multilook, single polarization SAR intensity data into regions or ensembles of pixels of homogeneous and similar radar backscatter characteristics. A model for the prior joint distribution of the multifrequency SAR intensity data is combined with a Markov random field for representing the interactions between region labels to obtain an expression for the posterior distribution of the region labels given the multifrequency SAR observations. The maximization of the posterior distribution yields Bayes's optimum region labeling or classification of the SAR data or its MAP estimate. The performance of the MAP classifier is evaluated by using computer-simulated multilook SAR intensity data as a function of the parameters in the classification process. Multilook SAR intensity data are shown to yield higher classification accuracies than one-look SAR complex amplitude data. The MAP classifier is extended to the case in which the radar backscatter from the remotely sensed surface varies within the SAR image because of incidence angle effects. The results obtained illustrate the practicality of the method for combining SAR intensity observations acquired at two different frequencies and for improving classification accuracy of SAR data.
Rignot, E.↗
Combined Uncertainty and A-Posteriori Error Bound Estimates for General CFD Calculations: Theory and Software Implementation
This workshop presentation discusses the design and implementation of numerical methods for the quantification of statistical uncertainty, including a-posteriori error bounds, for output quantities computed using CFD methods. Hydrodynamic realizations often contain numerical error arising from finite-dimensional approximation (e.g. numerical methods using grids, basis functions, particles) and statistical uncertainty arising from incomplete information and/or statistical characterization of model parameters and random fields. The first task at hand is to derive formal error bounds for statistics given realizations containing finite-dimensional numerical error [1]. The error in computed output statistics contains contributions from both realization error and the error resulting from the calculation of statistics integrals using a numerical method. A second task is to devise computable a-posteriori error bounds by numerically approximating all terms arising in the error bound estimates. For the same reason that CFD calculations including error bounds but omitting uncertainty modeling are only of limited value, CFD calculations including uncertainty modeling but omitting error bounds are only of limited value. To gain maximum value from CFD calculations, a general software package for uncertainty quantification with quantified error bounds has been developed at NASA. The package provides implementations for a suite of numerical methods used in uncertainty quantification: Dense tensorization basis methods [3] and a subscale recovery variant [1] for non-smooth data, Sparse tensorization methods[2] utilizing node-nested hierarchies, Sampling methods[4] for high-dimensional random variable spaces.
CFD↗
On estimating the phase of a periodic waveform in additive Gaussian noise, part 1
Motivated by recent advances in technology, a new look is taken at the problem of estimating the phase of a periodic waveform in additive Gaussian noise. The maximum a posteriori probability criterion with signal space interpretation is used to obtain the structures of optimum and some suboptimum phase estimators for the following cases: (1) known constant frequency and unknown constant phase with an a priori distribution; (2) unknown constant frequency and phase with a joint a priori distribution; (3) frequency a parameterized function of time with a joint a priori distribution on parameters and phase and (4) frequency a Gaussian random process.
Rauch, L. L.↗