Generalized Iterated Kalman Filter and its Performance Evaluation

Hu, Xiaoqing; Bao, Ming; Zhang, Xiaoping; Guan, Lei; Hu, Yu-Hen

doi:10.1109/tsp.2015.2423266

Cited by 47 publications

(24 citation statements)

References 32 publications

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“…IEKF performs well when the true posterior is close to being Gaussian; however, convergence of the GN algorithm is not guaranteed. Furthermore, a generalized iterated KF (Hu et al, 2015) for nonlinear stochastic discrete-time estimation with state-dependent observation noise adopts the Newton-Raphson iterative optimization steps, yielding an approximate MAP estimate of the states. With a high relevance, IPLF (García-Fernández et al, 2015b;Raitoharju et al, 2017) uses statistical linear regression instead of the first-order TSE for a better linearization, and iterates a posterior estimate updating.…”

Section: Very Informative Observationmentioning

confidence: 99%

Approximate Gaussian conjugacy: parametric recursive filtering under nonlinearity, multimodality, uncertainty, and constraint, and beyond

Liu

et al. 2017

Frontiers Inf Technol Electronic Eng

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Since the landmark work of R. E. Kalman in the 1960s, considerable efforts have been devoted to time series state space models for a large variety of dynamic estimation problems. In particular, parametric filters that seek analytical estimates based on a closed-form Markov-Bayes recursion, e.g., recursion from a Gaussian or Gaussian mixture (GM) prior to a Gaussian/GM posterior (termed 'Gaussian conjugacy' in this paper), form the backbone for a general time series filter design. Due to challenges arising from nonlinearity, multimodality (including target maneuver), intractable uncertainties (such as unknown inputs and/or non-Gaussian noises) and constraints (including circular quantities), etc., new theories, algorithms, and technologies have been developed continuously to maintain such a conjugacy, or to approximate it as close as possible. They had contributed in large part to the prospective developments of time series parametric filters in the last six decades. In this paper, we review the state of the art in distinctive categories and highlight some insights that may otherwise be easily overlooked. In particular, specific attention is paid to nonlinear systems with an informative observation, multimodal systems including Gaussian mixture posterior and maneuvers, and intractable unknown inputs and constraints, to fill some gaps in existing reviews and surveys. In addition, we provide some new thoughts on alternatives to the first-order Markov transition model and on filter evaluation with regard to computing complexity.

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Section: Very Informative Observationmentioning

confidence: 99%

Approximate Gaussian conjugacy: parametric recursive filtering under nonlinearity, multimodality, uncertainty, and constraint, and beyond

Liu

et al. 2017

Frontiers Inf Technol Electronic Eng

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“…Note that the prior filtering equations are used in the case that the measurement noise is uncorrelated with the state. For a nonlinear stochastic system with state‐dependent multiplicative measurement noise, a generalized iterated Kalman filter (GIKF) is presented in .…”

Section: System Model and Filter Equationmentioning

confidence: 99%

“…The solution to the linear/Gaussian filtering problem is the Kalman filter (KF), which can be implemented recursively in two steps: prediction and update. The most well-known MAP estimator is the iterated extended Kalman filter (IEKF) [16][17][18], which is based on the Gauss-Newton optimization method. In the Gaussian case, the prediction step is relatively simple [4,5].…”

Section: Introductionmentioning

confidence: 99%

“…Several maximum a posteriori (MAP) estimators have been developed to compute the updated state accurately. The most well‐known MAP estimator is the iterated extended Kalman filter (IEKF) , which is based on the Gauss‐Newton optimization method. The Levenberg–Marquardt optimization method is used instead of the Gauss‐Newton method in .…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Adaptive Iterated Extended KALMAN Filter for Relative Spacecraft Attitude and Position Estimation

Xiong¹,

Wei²

2017

Asian Journal of Control

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This paper presents a novel adaptive iterated extended Kalman filter (AIEKF) for relative position and attitude estimation, taking into account the influence of model uncertainty. Considering a nonlinear stochastic discrete-time system with unknown disturbance, the AIEKF algorithm adopts the Gauss-Newton iterative optimization steps to implement a maximum a posteriori (MAP) estimation, and the switch-mode combination technique is used to achieve the adaptive capability. The mean-square estimation error (MSE) of the state estimate is derived. It is proved that the AIEKF can yield a smaller MSE than that of the traditional extended Kalman filter (EKF) or iterated extended Kalman filter (IEKF). The performance advantage of the AIEKF is illustrated via Monte Carlo simulations on a typical relative position and attitude estimation application. Through comparisons in different scenarios, the presented algorithm is shown to improve adaptability and ensure estimation accuracy.

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“…Hu [12] has proposed the GIKF based on Newton-Raphson method. It should be noted that the natural gradient method is completely different from the Newton-Raphson method.…”

Section: Comparison With Gikfmentioning

confidence: 99%

Bayesian Nonlinear Filtering via Information Geometric Optimization

Cheng

et al. 2017

Entropy

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Abstract:In this paper, Bayesian nonlinear filtering is considered from the viewpoint of information geometry and a novel filtering method is proposed based on information geometric optimization. Under the Bayesian filtering framework, we derive a relationship between the nonlinear characteristics of filtering and the metric tensor of the corresponding statistical manifold. Bayesian joint distributions are used to construct the statistical manifold. In this case, nonlinear filtering can be converted to an optimization problem on the statistical manifold and the adaptive natural gradient descent method is used to seek the optimal estimate. The proposed method provides a general filtering formulation and the Kalman filter, the Extended Kalman filter (EKF) and the Iterated Extended Kalman filter (IEKF) can be seen as special cases of this formulation. The performance of the proposed method is evaluated on a passive target tracking problem and the results demonstrate the superiority of the proposed method compared to various Kalman filter methods.

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Generalized Iterated Kalman Filter and its Performance Evaluation

Cited by 47 publications

References 32 publications

Approximate Gaussian conjugacy: parametric recursive filtering under nonlinearity, multimodality, uncertainty, and constraint, and beyond

Approximate Gaussian conjugacy: parametric recursive filtering under nonlinearity, multimodality, uncertainty, and constraint, and beyond

Adaptive Iterated Extended KALMAN Filter for Relative Spacecraft Attitude and Position Estimation

Bayesian Nonlinear Filtering via Information Geometric Optimization

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