Nonlinear estimation problems, such as range-only and bearing-only target tracking, are often addressed using linearized estimators, e.g., the extended Kalman filter (EKF). These estimators generally suffer from linearization errors as well as the inability to track multimodal probability density functions (pdfs). In this paper, we propose a bank of batch maximum a posteriori (MAP) estimators a...

Forbidden ordinal patterns are ordinal patterns (or ‘rank blocks’) that cannot appear in the orbits generated by a map taking values on a linearly ordered space, in which case we say that the map has forbidden patterns. Once a map has a forbidden pattern of a given length L0, it has forbidden patterns of any length L ≥ L0 and their number grows superexponentially with L. Using recent results on...

Texture mapping on scanned objects, that is, the method to map current color images on a 3D geometric model measured by a range sensor, is a key technique of photometric modeling for virtual reality. Usually range and color images are obtained from different viewing positions, through two independent range and color sensors. Thus, in order to map those color images on the geometric model, it is...

Salah satu hal penting dalam analisis statistik adalah prosedur estimasi suatu fungsi padat peluang yang biasa disebut densitas. Ada dua metode pendekatan biasanya digunakan, yaitu parameter terkait dengan asumsi distribusi tertentu dan densitas secara non parametrik. Metode parametrik sering kita jumpai histogram.
 Beberapa kelemahan histogram menjadi acuan untuk dikembangkannya lain kern...

This paper addresses the problem of maximum a posteriori (MAP) sequence estimation in general state-space models. We consider two algorithms based on the sequential Monte Carlo (SMC) methodology (also known as particle filtering). We prove that they produce approximations of the MAP estimator and that they converge almost surely. We also derive a lower bound for the number of particles that are...

A hybrid Bayesian/ frequentist approach is presented for the Simultaneous Localization and Mapping Problem (SLAM). A frequentist approach is proposed for mapping with time varying robotic poses and is generalized to the case when the robotic pose is both time varying and uncertain. The SLAM problem is then solved in two steps: 1) the robot is localized with respect to a sparse set of landmarks ...

We find quantum signatures of chaos in various metrics of information gain in quantum tomography. We employ a quantum state estimator based on weak collective measurements of an ensemble of identically prepared systems. The tomographic measurement record consists of a sequence of expectation values of a Hermitian operator that evolves under repeated application of the Floquet map of the quantum...

The Kalman filter computes the maximum a posteriori (MAP) estimate of the states for linear state space models with Gaussian noise. We interpret the Kalman filter as the solution to a convex optimization problem, and show that we can generalize the MAP state estimator to any noise with log-concave density function and any combination of linear equality and convex inequality constraints on the s...

We extend Bayesian MAP and Minimum Description Length (MDL) learning by testing whether the data can be substantially more compressed by a mixture of the MDL/MAP distribution with another element of the model, and adjusting the learning rate if this is the case. While standard Bayes and MDL can fail to converge if the model is wrong, the resulting “safe” estimator continues to achieve good rate...