A robust Kalman–Bucy filtering problem

Ji, Shaolin; Kong, Chuiliu; Sun, Chuanfeng

doi:10.1016/j.automatica.2020.109252

Cited by 6 publications

(2 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Hjalmarsson, H. et al [ 12 ] suggested a simple and explicit method for estimating the model uncertainty, which is also applicable to severe under-modelling. A generalized Kalman-Bucy model under model uncertainty and a corresponding robust problem are studied in the literature [ 13 ]. Ji, S. et al found that this robust problem is equivalent to an estimate problem under a sublinear operator.…”

Section: Introductionmentioning

confidence: 99%

A Two-Stage Feature Point Detection and Marking Approach Based on the Labeled Multi-Bernoulli Filter

Yang

Liu

2022

Sensors

View full text Add to dashboard Cite

In recent years, various algorithms using random finite sets (RFS) to solve the issue of simultaneous localization and mapping (SLAM) have been proposed. Compared with the traditional method, the advantage of the RFS method is that it can avoid data association, landmark appearance and disappearance, missed detections, and false alarms in Bayesian recursion. There are many problems in the existing robot SLAM methods, such as low estimation accuracy, poor back-end optimization, etc. On the basis of previous studies, this paper presents a labeled random finite set (L-RFS) SLAM method. We describe a scene where the sensor moves along a given path and avoids obstacles based on the L-RFS framework. Then, we use the labeled multi-Bernoulli filter (LMB) to estimate the state of the sensor and feature points. At the same time, the B-spline curve is used to smooth the obstacle avoidance path of the sensor. The effectiveness of the algorithm is verified in the final simulation.

show abstract

Section: Introductionmentioning

confidence: 99%

A Two-Stage Feature Point Detection and Marking Approach Based on the Labeled Multi-Bernoulli Filter

Yang

Liu

2022

Sensors

View full text Add to dashboard Cite

show abstract

“…Allan and Cohen [1] studied this type of estimate problem under nonlinear expectations by a control approach. Recently, Ji, Kong and Sun [11] considered a different generalized Kalman-Bucy filtering model where the ambiguity parameters affect the evolution of signal process.…”

Section: Introductionmentioning

confidence: 99%

A filtering problem with uncertainty in observation

Kong

Sun

2020

Systems & Control Letters

Self Cite

View full text Add to dashboard Cite

This paper is concerned with a generalized Kalman-Bucy filtering model and corresponding robust problem under model uncertainty. We find that this robust problem is equivalent to considering an estimate problem under some sublinear operator. Therefore, we turn to obtaining the minimum mean square estimator under a sublinear operator. By Girsanov theorem and minimax theorem, we obtain the optimal estimatorx t of the signal process x t for given time t ∈ [0, T ]. P θ ∈P E P θ [·] can be regarded as a sublinear operator E(·) and the problem (1.4) can be reformulated as a estimate problem under sublinear operator: min ζ E( x t − ζ 2 ).

show abstract