Trigonometric Moments of a Generalized von Mises Distribution in 2-D Range-Only Tracking
A 2D range-only tracking scenario is non-trivial due to two main reasons. First, when the states to be estimated are in Cartesian coordinates, the uncertainty region is multi-modal. The second reason is that the probability density function of azimuth conditioned on range takes the form of a generalized von Mises distribution, which is hard to tackle. Even in the case of implementing a uni-modal Kalman filter, one needs expectations of trigonometric functions of conditional bearing density, which are not available in the current literature. We prove that the trigonometric moments (circular moments) of the azimuth density conditioned on range can be computed as an infinite series, which can be sufficiently approximated by relatively few terms in summation. The solution can also be generalized to any order of the moments. This important result can provide an accurate depiction of the conditional azimuth density in 2D range-only tracking geometries. We also present a simple optimization problem that results in deterministic samples of conditional azimuth density from the knowledge of its circular moments leading to an accurate filtering solution. The results are shown in a two-dimensional simulation, where the range-only sensor platform maneuvers to make the system observable. The results prove that the method is feasible in such applications.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Moment-Based Exact Uncertainty Propagation Through Nonlinear Stochastic Autonomous Systems
In this paper, we address the problem of uncertainty propagation through nonlinear stochastic dynamical systems. More precisely, given a discrete-time continuous-state probabilistic nonlinear dynamical system, we aim at …
Moment State Dynamical Systems for Nonlinear Chance-Constrained Motion Planning
Chance-constrained motion planning requires uncertainty in dynamics to be propagated into uncertainty in state. When nonlinear models are used, Gaussian assumptions on the state distribution do not necessarily apply sinc…
Motion PlanningComplex Isotropic α-Stable-Rician Model for Heterogeneous SAR Images
This article introduces a novel probability distribution model, namely Complex Isotropic {\alpha}-Stable-Rician (CI{\alpha}SR), for characterizing the data histogram of synthetic aperture radar (SAR) images. Having its f…
parameter estimationPositive Trigonometric Polynomials on the Stability of Spatially Interconnected Systems
This paper is devoted to the stability analysis of spatially interconnected systems (SISs) via the sum-of-squares (SOS) decomposition of positive trigonometric polynomials. For each spatial direction of SISs, three types…
Estimation Beyond Data Reweighting: Kernel Method of Moments
Moment restrictions and their conditional counterparts emerge in many areas of machine learning and statistics ranging from causal inference to reinforcement learning. Estimators for these tasks, generally called methods…
Causal Inference