Cramér-Rao bounds for particle size distribution estimation from multiangle dynamic light scattering
نویسندگان
چکیده
We derive the Cramér-Rao lower bounds (CRB) for parametric estimation of the number-weighted particle size distribution (PSD) from multiangle Dynamic Light Scattering (DLS) measurements. The CRB is a useful statistical tool to investigate the optimality of the PSD estimators. In the present paper, a Gaussian mixture (GM) model of the multimodal PSD is assumed and the associated Fisher information matrix (FIM) is determined. The usefulness of multiangle DLS in significantly decreasing the CRB is demonstrated. The mean square error (MSE) of the PSD GM model parameters estimation by the Bayesian inference method proposed in [1] is compared to the derived CRB for a simulated monomodal PSD. Results show that the MSE achieves the derived CRBs for the unbiased estimators of the PSD GM model parameters.
منابع مشابه
Assessment of an MCMC algorithm convergence for Bayesian estimation of the particle size distribution from multiangle dynamic light scattering measurements
Recovering the particle size distribution (PSD) from dynamic light scattering (DLS) measurements is known to be a highly ill-posed inverse problem. In a former study, we proposed a new Bayesian inference method applied directly to the multiangle DLS measurements to improve the estimation of multimodal PSDs. The posterior probability density of interest is sampled using a MCMC Metropolis-within-...
متن کاملDetermination of the size distribution of monodesperse and bidisperse mixtures of spherical particles in the nanometer and submicron size range by applying cumulant analysis and contin algorithm in dynamic light scattering
Determination of particle size is one of the major needs in the industry and biotechnology. Dynamic light scattering (DLS) is a widely used technique for determining size distribution of spherical particle in nanometer and submicron size range. In this method, there are different algorithms for determining the size and size distribution of particles, which are selected according to the required...
متن کاملVesicle size distributions measured by flow field-flow fractionation coupled with multiangle light scattering.
The separation method, flow field-flow fractionation (flow FFF), is coupled on-line with multiangle laser light scattering (MALLS) for simultaneous measurement of the size and concentration of vesicles eluting continuously from the fractionator. These size and concentration data, gathered as a function of elution time, may be used to construct both number- and mass-weighted vesicle size distrib...
متن کاملAnalytical Performance Bounds for Full and Reduced-order Distributed Bayesian Estimation
Motivated by the resource management problem in nonlinear multi-sensor tracking networks, the paper derives online, distributed estimation algorithms for computing the posterior Cramér-Rao lower bound (PCRLB) for full-order and reduced-order distributed Bayesian estimators without requiring a fusion centre and with nodal communications limited to local neighborhoods. For both cases, Riccati-typ...
متن کاملCramér-Rao Bounds for Estimation of Linear System Noise Covariances
The performance of Kalman filter depends directly on the noise covariances, which are usually not known and need to be estimated. Several estimation algorithms have been published in past decades, but the measure of estimation quality is missing. The Cramér-Rao bounds represent limitation of quality of parameter estimation that can be obtained from given data. In this article, The Cramér-Rao bo...
متن کامل