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NASA NTRS1974

Single-tone parameter estimation from discrete-time observations

Estimation of the parameters of a single-frequency complex tone from a finite number of noisy discrete-time observations is discussed. The appropriate Cramer-Rao bounds and maximum-likelihood (ML) estimation algorithms are derived. Some properties of the ML estimators are proved. The relationship of ML estimation to the discrete Fourier transform is exploited to obtain practial algorithms. The threshold effect of one algorithm is analyzed and compared to simulation results. Other simulation results verify other aspects of the analysis.

Rife, D. C.↗

NASA NTRSDate not supplied

Frequency Domain Quasi Maximum Likelihood Identification of Low Order Aeroservoelastic Models from Flight-Test Data

In this paper a quasi maximum likelihood method for estimating a low order model of a flexible vehicle has been developed and demonstrated. The quasi maximum likelihood method uses a large number of sensors to estimate the parameters and covariance in a method consistent with the maximum likelihood filter-error method. The cost function has been defined in a frequency domain to improve computational efficiency and to enable estimation of an unstable plant. The method has been demonstrated using flight data from the National Aeronautics and Space Administration X-56A Multi-Utility Technology Testbed flex wing tests, which include unstable flutter modes. The method was able to effectively estimate the frequency and damping of the dynamics of the aircraft and generate a transfer function that is useful for control system evaluations.

Jeffrey Ouellette↗

DOE OSTI2025

ASCR Workshop Position Paper: Challenges and Opportunities in High Energy Physics

High energy particle physics and cosmology concern themselves with estimating fundamental parameters of nature, such as the masses and interactions of fundamental particles like the Higgs boson and the rate of expansion of the universe. In doing so, they analyze exabyte-scale datasets, some of the largest in all of science, and face many challenges in subsequent data analysis. These challenges are shared between the two disciplines, but we focus on particle physics to highlight one specific domain. In particle physics, the standard method for estimating parameters involves performing Monte Carlo (MC) integration as a function of both parameters of interest and nuisance parameters using an expensive simulator, counting the number of observed collision events (i.i.d. samples) from an experiment in the corresponding integration domains, and forming a Poisson likelihood function. This likelihood function is then used in a Frequentist manner to construct a maximum likelihood point estimate (MLE) and confidence set for the parameters. To sufficiently populate the high-dimensional integration domains, simulators consume billions of CPU-hours annually and produce hundreds of petabytes of intermediate output data. Several techniques have been developed to: optimize definitions of the integration domains so as to be maximally sensitive to a particular subset of parameters, efficiently estimate the integrals, and build robust surrogate models by interpolating between integral evaluations at different parameter points. One can view this whole endeavor as classical Simulation-Based Inference (SBI).

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS1980

Development of advanced techniques for rotorcraft state estimation and parameter identification

An integrated methodology for rotorcraft system identification consists of rotorcraft mathematical modeling, three distinct data processing steps, and a technique for designing inputs to improve the identifiability of the data. These elements are as follows: (1) a Kalman filter smoother algorithm which estimates states and sensor errors from error corrupted data. Gust time histories and statistics may also be estimated; (2) a model structure estimation algorithm for isolating a model which adequately explains the data; (3) a maximum likelihood algorithm for estimating the parameters and estimates for the variance of these estimates; and (4) an input design algorithm, based on a maximum likelihood approach, which provides inputs to improve the accuracy of parameter estimates. Each step is discussed with examples to both flight and simulated data cases.

Hall, W. E., Jr.↗

DOE OSTI2026

Using PyBioNetFit to leverage qualitative and quantitative data in biological model parameterization and uncertainty quantification

Data generated in studies of cellular regulatory systems are often qualitative. For example, measurements of signaling readouts in the presence and absence of mutations may reveal a rank ordering of responses across conditions but not the precise extents of mutation-induced differences. Qualitative data are often ignored by mathematical modelers or are considered in an ad hoc manner, as in the study of Kocieniewski and Lipniacki (2013) [Phys Biol 10: 035006], which was focused on the roles of MEK isoforms in ERK activation. In this earlier study, model parameter values were tuned manually to obtain consistency with a combination of qualitative and quantitative data. This approach is not reproducible, nor does it provide insights into parametric or prediction uncertainties. Here, starting from the same data and the same ordinary differential equation (ODE) model structure, we generate formalized statements of qualitative observations, making these observations more reusable, and we improve the model parameterization procedure by applying a systematic and automated approach enabled by the software package PyBioNetFit. We also demonstrate uncertainty quantification (UQ), which was absent in the original study. Our results show that PyBioNetFit enables qualitative data to be leveraged, together with quantitative data, in parameterization of systems biology models and facilitates UQ. These capabilities are important for reliable estimation of model parameters and model analyses in studies of cellular regulatory systems and reproducibility.

59 BASIC BIOLOGICAL SCIENCES↗

NASA NTRS1973

Maximum likelihood synchronizer for binary overlapping PCM/NRZ signals.

A maximum likelihood parameter estimation technique for the self bit synchronization problem is investigated. The input sequence to the bit synchronizer is a sequence of binary overlapping PCM/NRZ signal in the presence of white Gaussian noise with zero mean and known variance. The resulting synchronizer consists of matched filters, a transition device and a weighting function. Finally, the performance is examined by Monte Carlo simulations.

Wang, C. D.↗

NASA NTRS1980

The sensitivity of a very long baseline interferometer

The theoretical sensitivity of various methods of acquiring and processing interferometer data are compared. It is shown that for a fixed digital recording capacity one bit quantization of single sideband data filtered with a rectangular bandpass and sampled at the Nyquist rate yields the optimum signal to noise ratio. The losses which result from imperfect bandpass, poor image rejection, approximate methods of fringe rotation, fractional bit correction, and loss of quadrature are discussed. Also discussed is the use of the complex delay function as a maximum likelihood fringe estimator.

Rogers, A. E. E.↗

NASA NTRS1983

Discrimination Relative to Measures of Non-Normality

The robustness of discriminant functions to nonnormality is investigated. The performance of procedures relative to measures of the difference between the actual distribution of the observations and the usual assumption of normal densities is assessed. For example, the two population, mixed distributions problem with equal costs of misclassification are considered. The parameters are estimated by maximum likelihood and recently proposed robust methods.

Smith, W. B.↗

NASA NTRS1985

On-orbit Systems Identification of Flexible Spacecraft Technol., 1984, Pt. 2 p 465-481

Future spacecraft include configurations which are too flexible to be adequately tested prior to flight and which will require on-orbit systems identification to ensure safe operation of the flight control system. The structural dynamics model will evolve and its accuracy will improve in stages as ground tests of full-scale components and replica-scale models are performed. State Space Modeling and Conditional Maximum Likelihood Parameter Estimation methodology can provide the formal probability-based framework for the process of upgrading a model as additional test results are obtained. Although the number of unknown parameters can be reduced by the use of canonical forms for the stability matrix, the number of unknown model parameters quickly becomes unmanageable unless advantage is taken of the relationship of a much fewer number of global model parameters. Distributed parameter systems or partial differential equation models are one way to take advantage of such global parameters to reduce the number of unknown model parameters.

Taylor, L.↗

NASA NTRS1985

Measurement of interaction cross section of cosmic ray Fe nuclei (E4 GeV/N) with Al target

Although the study of relatvistic heavy ion interaction encumbered by the low intensities of the incident heavy nuclei in cosmic ray experiments, however, one can use a suitable structure of detector to attain a result with a reasonable accuracy. A cross section value of Fe(E 4 GeV/N) with Al is presented. CR-39 was used as detector and Al as target. The cross section value is estimated using maximum likelihood method.

Ren, G. X.↗

NASA NTRS1985

On-orbit systems identification of flexible spacecraft

The process of on-orbit systems identification of flexible spacecraft is examined in terms of the difficulties that are expected because of the potentially unmanageable number of unknown model parameters due to the very high order system models involved. A Jordon block canonical form and global model parameters are used to reduce the number of unknown parameters to manageable numbers. A Bayesian approach is discussed which enables the merging of theoretical models with ground or on-orbit test results by using Unconditional Maximum Likelihood Parameter Estimation. A Modified Newton-Raphson technique is proposed for determining the model parameter estimates and an expected fit error criterion is recommended for the determination of the model structure and order reduction.

Taylor, L. W., Jr.↗

NASA NTRS1989

Multiple symbol differential detection of uncoded and trellis coded MPSK

A differential detection for MPSK, which uses a multiple symbol observation interval, is presented and its performance analyzed and simulated. The technique makes use of maximum-likelihood sequence estimation of the transmitted phases rather than symbol-by-symbol detection as in conventional differential detection. As such the performance of this multiple symbol detection scheme fills the gap between conventional (two-symbol observation) differentially coherent detection of MPSK and ideal coherent of MPSK with differential encoding. The amount of improvement gained over conventional differential detection depends on the number of phases, M, and the number of additional symbol intervals added to the observation. What is particularly interesting is that substantial performance improvement can be obtained for only one or two additional symbol intervals of observation. The analysis and simulation results presented are for uncoded and trellis coded MPSK.

Divsalar, Dariush↗

NASA NTRS1990

Multiple-symbol differential detection of MPSK

A differential detection technique for MPSK (multiple-phase shift keying), which uses a multiple-symbol observation interval, is presented, and its performance is analyzed and simulated. The technique makes use of maximum-likelihood sequence estimation of the transmitted phases rather than symbol-by-symbol detection as in conventional differential detection. Thus, the performance of this multiple-symbol detection scheme fills the gap between conventional (two-symbol observation) differentially coherent detection of MPSK and ideal coherent of MPSK with differential encoding. The amount of improvement gained over conventional differential detection depends on the number of phases M and the number of additional symbol intervals added to the observation. What is particularly interesting is that substantial performance improvement can be obtained for only one or two additional symbol intervals of observation. The analysis and simulation results presented are for uncoded MPSK.

Divsalar, Dariush↗

NASA NTRS1990

Maximum likelihood tuning of a vehicle motion filter

This paper describes the use of maximum likelihood parameter estimation unknown parameters appearing in a nonlinear vehicle motion filter. The filter uses the kinematic equations of motion of a rigid body in motion over a spherical earth. The nine states of the filter represent vehicle velocity, attitude, and position. The inputs to the filter are three components of translational acceleration and three components of angular rate. Measurements used to update states include air data, altitude, position, and attitude. Expressions are derived for the elements of filter matrices needed to use air data in a body-fixed frame with filter states expressed in a geographic frame. An expression for the likelihood functions of the data is given, along with accurate approximations for the function's gradient and Hessian with respect to unknown parameters. These are used by a numerical quasi-Newton algorithm for maximizing the likelihood function of the data in order to estimate the unknown parameters. The parameter estimation algorithm is useful for processing data from aircraft flight tests or for tuning inertial navigation systems.

Trankle, Thomas L.↗

NASA NTRS1994

Multiple-Symbol, Partially Coherent Detection of MPSK

Proposed method of reception of multiple-phase-shift-keyed (MPSK) radio signals involves multiple-symbol, partially coherent detection. Instead of attempting to determine phase of transmitted signal during each symbol period as in coherent detection, receiver acquires signal data during multiple-symbol observation interval, then produces maximum-likelihood-sequence estimate of phases transmitted during interval. Combination of coherent-reception and incoherent-reception decision rules are used.

Simon, Marvin K.↗

NASA NTRS1993

Pseudo-coherent demodulation for mobile satellite systems

This paper proposes three so-called pseudo-coherent demodulation schemes for use in land mobile satellite channels. The schemes are derived based on maximum likelihood (ML) estimation and detection of an N-symbol observation of the received signal. Simulation results for all three demodulators are presented to allow comparison with the performance of differential PSK (DPSK) and ideal coherent demodulation for various system parameter sets of practical interest.

Divsalar, Dariush↗

NASA NTRS1995

Comparison of 2- and 10-micron coherent Doppler lidar performance

The performance of 2- and 10-micron coherent Doppler lidar is presented in terms of the statistical distribution of the maximum-likelihood velocity estimator from simulations for fixed range resolution and fixed velocity search space as a function of the number of coherent photoelectrons per estimate. The wavelength dependence of the aerosol backscatter coefficient, the detector quantum efficiency, and the atmospheric extinction produce a simple shift of the performance curves. Results are presented for a typical boundary layer measurement and a space-based measurement for two regimes: the pulse-dominated regime where the signal statistics are determined by the transmitted pulse, and the atmospheric-dominated regime where the signal statistics are determined by the velocity fluctuations over the range gate. The optimal choice of wavelength depends on the problem under consideration.

Frehlich, Rod↗

NASA NTRS1997

Data Assimilation in the Ocean and in the Atmosphere: What Should be Next?

As part of the International Symposium on Assimilation of Observation in Meteorology and Oceanography, a panel discussion was held on the evening of 15 March 1995. The purpose of this panel discussion was focus on what the next major areas of research in data assimilation should be. The panelists had five minutes each for short presentations (Kalman filters, representers, etc.) and this was followed by an open discussion. This preprocessing will require a good understanding of the fine-scale phenomena. Least square methods such as Kalman filters and variational schemes are inefficient estimators of non-Gaussian field such as chemical traces. Regardless of the modeling technique employed (Lagrangian methods seem best), a least squares assimilation scheme will smear fine structure. The estimator of maximum likelihood must be sought, by examination of tracer probability distributions.

Kalnay, Eugenia↗