Online Detection of State Estimator Performance Degradation via Efficient Numerical Observability Analysis

An efficient observability analysis method is proposed to enable online detection of performance degradation of an optimization-based sliding window visual-inertial state estimation framework.The proposed methodology leverages numerical techniques in nonlinear observability analysis to enable online evaluation of the system observability and indication of the state estimation performance.Specifically,an empirical observability Gramian based approach is introduced to efficiently measure the observability condition of the windowed nonlinear system,and a scalar index is proposed to quantify the average system observability.The proposed approach is specialized to a challenging optimizationbased sliding window monocular visual-inertial state estimation formulation and evaluated through simulation and experiments to assess the efficacy of the methodology.The analysis result shows that the proposed approach can correctly indicate degradation of the state estimation accuracy with real-time performance.

Improved Particle Filter for Non-Gaussian Forecasting-aided State Estimation

Gaussian assumptions of non-Gaussian noises hinder the improvement of state estimation accuracy.In this paper,an asymmetric generalized Gaussian distribution(AGGD),as a unified representation of various unimodal distributions,is applied to formulate the non-Gaussian forecasting-aided state estimation problem.To address the problem,an improved particle filter is proposed,which integrates a near-optimal AGGD proposal function and an AGGD sampling method into the typical particle filter.The AGGD proposal function can approximate the target distribution of state variables to greatly alleviate particle degeneracy and promote precise estimation,through considering both state transitions and latest measurements.For rapid particle generation from the AGGD proposal function,an efficient inverse cumulative distribution function(CDF)sampling method is employed based on the derived approximation of inverse CDF of AGGD.Numerical simulations are carried out on a modified balanced IEEE 123-bus test system.The results validate that the proposed method outperforms other popular state estimation methods in terms of accuracy and robustness,whether in Gaussian,non-Gaussian,or abnormal measurement errors.

Adaptive Gaussian sum squared-root cubature Kalman filter with split-merge scheme for state estimation

The paper deals with state estimation problem of nonlinear non-Gaussian discrete dynamic systems for improvement of accuracy and consistency. An efficient new algorithm called the adaptive Gaussian-sum square-root cubature Kalman filter（AGSSCKF） with a split-merge scheme is proposed. It is developed based on the squared-root extension of newly introduced cubature Kalman filter（SCKF） and is built within a Gaussian-sum framework. Based on the condition that the probability density functions of process noises and initial state are denoted by a Gaussian sum using optimization method, a bank of SCKF are used as the sub-filters to estimate state of system with the corresponding weights respectively, which is adaptively updated. The new algorithm consists of an adaptive splitting and merging procedure according to a proposed split-decision model based on the nonlinearity degree of measurement. The results of two simulation scenarios（one-dimensional state estimation and bearings-only tracking） show that the proposed filter demonstrates comparable performance to the particle filter with significantly reduced computational cost.