Bridging the ensemble Kalman and particle filter

In many applications of Monte Carlo nonlinear filtering, the propagation step is computationally expensive, and hence, the sample size is limited. With small sample sizes, the update step becomes crucial. Particle filtering suffers from the well-known problem of sample degeneracy. Ensemble Kalman filtering avoids this, at the expense of treating non-Gaussian features of the forecast distribution incorrectly. Here we introduce a procedure which makes a continuous transition indexed by gamma in [0,1] between the ensemble and the particle filter update. We propose automatic choices of the parameter gamma such that the update stays as close as possible to the particle filter update subject to avoiding degeneracy. In various examples, we show that this procedure leads to updates which are able to handle non-Gaussian features of the prediction sample even in high-dimensional situations

Optimal analog wavelet bases construction using hybrid optimization algorithm

An approach for the construction of optimal analog wavelet bases is presented. First, the definition of an analog wavelet is given. Based on the definition and the least-squares error criterion, a general framework for designing optimal analog wavelet bases is established, which is one of difficult nonlinear constrained optimization problems. Then, to solve this problem, a hybrid algorithm by combining chaotic map particle swarm optimization (CPSO) with local sequential quadratic programming (SQP) is proposed. CPSO is an improved PSO in which the saw tooth chaotic map is used to raise its global search ability. CPSO is a global optimizer to search the estimates of the global solution, while the SQP is employed for the local search and refining the estimates. Benefiting from good global search ability of CPSO and powerful local search ability of SQP, a high-precision global optimum in this problem can be gained. Finally, a series of optimal analog wavelet bases are constructed using the hybrid algorithm. The proposed method is tested for various wavelet bases and the improved performance is compared with previous works.Peer reviewedFinal Published versio

Fast Monte-Carlo Localization on Aerial Vehicles using Approximate Continuous Belief Representations

Size, weight, and power constrained platforms impose constraints on computational resources that introduce unique challenges in implementing localization algorithms. We present a framework to perform fast localization on such platforms enabled by the compressive capabilities of Gaussian Mixture Model representations of point cloud data. Given raw structural data from a depth sensor and pitch and roll estimates from an on-board attitude reference system, a multi-hypothesis particle filter localizes the vehicle by exploiting the likelihood of the data originating from the mixture model. We demonstrate analysis of this likelihood in the vicinity of the ground truth pose and detail its utilization in a particle filter-based vehicle localization strategy, and later present results of real-time implementations on a desktop system and an off-the-shelf embedded platform that outperform localization results from running a state-of-the-art algorithm on the same environment

Analysis of error propagation in particle filters with approximation

This paper examines the impact of approximation steps that become necessary when particle filters are implemented on resource-constrained platforms. We consider particle filters that perform intermittent approximation, either by subsampling the particles or by generating a parametric approximation. For such algorithms, we derive time-uniform bounds on the weak-sense $L_p$ error and present associated exponential inequalities. We motivate the theoretical analysis by considering the leader node particle filter and present numerical experiments exploring its performance and the relationship to the error bounds.Comment: Published in at http://dx.doi.org/10.1214/11-AAP760 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Multiobjective optimization of electromagnetic structures based on self-organizing migration

Práce se zabývá popisem nového stochastického vícekriteriálního optimalizačního algoritmu MOSOMA (Multiobjective Self-Organizing Migrating Algorithm). Je zde ukázáno, že algoritmus je schopen řešit nejrůznější typy optimalizačních úloh (s jakýmkoli počtem kritérií, s i bez omezujících podmínek, se spojitým i diskrétním stavovým prostorem). Výsledky algoritmu jsou srovnány s dalšími běžně používanými metodami pro vícekriteriální optimalizaci na velké sadě testovacích úloh. Uvedli jsme novou techniku pro výpočet metriky rozprostření (spread) založené na hledání minimální kostry grafu (Minimum Spanning Tree) pro problémy mající více než dvě kritéria. Doporučené hodnoty pro parametry řídící běh algoritmu byly určeny na základě výsledků jejich citlivostní analýzy. Algoritmus MOSOMA je dále úspěšně použit pro řešení různých návrhových úloh z oblasti elektromagnetismu (návrh Yagi-Uda antény a dielektrických filtrů, adaptivní řízení vyzařovaného svazku v časové oblasti…).This thesis describes a novel stochastic multi-objective optimization algorithm called MOSOMA (Multi-Objective Self-Organizing Migrating Algorithm). It is shown that MOSOMA is able to solve various types of multi-objective optimization problems (with any number of objectives, unconstrained or constrained problems, with continuous or discrete decision space). The efficiency of MOSOMA is compared with other commonly used optimization techniques on a large suite of test problems. The new procedure based on finding of minimum spanning tree for computing the spread metric for problems with more than two objectives is proposed. Recommended values of parameters controlling the run of MOSOMA are derived according to their sensitivity analysis. The ability of MOSOMA to solve real-life problems from electromagnetics is shown in a few examples (Yagi-Uda and dielectric filters design, adaptive beam forming in time domain…).

Ensemble Transport Adaptive Importance Sampling

Markov chain Monte Carlo methods are a powerful and commonly used family of numerical methods for sampling from complex probability distributions. As applications of these methods increase in size and complexity, the need for efficient methods increases. In this paper, we present a particle ensemble algorithm. At each iteration, an importance sampling proposal distribution is formed using an ensemble of particles. A stratified sample is taken from this distribution and weighted under the posterior, a state-of-the-art ensemble transport resampling method is then used to create an evenly weighted sample ready for the next iteration. We demonstrate that this ensemble transport adaptive importance sampling (ETAIS) method outperforms MCMC methods with equivalent proposal distributions for low dimensional problems, and in fact shows better than linear improvements in convergence rates with respect to the number of ensemble members. We also introduce a new resampling strategy, multinomial transformation (MT), which while not as accurate as the ensemble transport resampler, is substantially less costly for large ensemble sizes, and can then be used in conjunction with ETAIS for complex problems. We also focus on how algorithmic parameters regarding the mixture proposal can be quickly tuned to optimise performance. In particular, we demonstrate this methodology's superior sampling for multimodal problems, such as those arising from inference for mixture models, and for problems with expensive likelihoods requiring the solution of a differential equation, for which speed-ups of orders of magnitude are demonstrated. Likelihood evaluations of the ensemble could be computed in a distributed manner, suggesting that this methodology is a good candidate for parallel Bayesian computations

Measuring primordial non-Gaussianity through weak lensing peak counts

We explore the possibility of detecting primordial non-Gaussianity of the local type using weak lensing peak counts. We measure the peak abundance in sets of simulated weak lensing maps corresponding to three models f_NL={0, +100, -100}. Using survey specifications similar to those of Euclid and without assuming any knowledge of the lens and source redshifts, we find the peak functions of the non-Gaussian models with f_NL=+-100 to differ by up to 15% from the Gaussian peak function at the high-mass end. For the assumed survey parameters, the probability of fitting an f_NL=0 peak function to the f_NL=+-100 peak functions is less than 0.1%. Assuming the other cosmological parameters known, f_NL can be measured with an error \Delta f_NL ~ 13. It is therefore possible that future weak lensing surveys like Euclid and LSST may detect primordial non-Gaussianity from the abundance of peak counts, and provide complementary information to that obtained from the cosmic microwave background.Comment: 4 pages, 1 figur