Generalized linear minimum mean-square error estimation with application to space-object tracking

Liu, Yu; Li, X. Rong; Chen, Huimin

doi:10.1109/acssc.2013.6810685

Cited by 5 publications

(6 citation statements)

References 18 publications

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“…The state of the art (Liu et al, 2013;Lan and Li, 2015) has demonstrated that proper 'uncorrelated conversion' of the nonlinear measurement can mine more information from the measurement information for better filtering accuracy, compared to the original measurement. This leads to an updating protocol which is based on linear combination of the original measurement and its uncorrelated conversions.…”

Section: Converted Measurement Filteringmentioning

confidence: 99%

“…More implementations for iterated/repeated observation (or its conversion) updating have been realized on different Gaussian filters (Zhan and Wan, 2007;Zanetti, 2012;Steinbring and Hanebeck, 2014;Huang et al, 2016b). These have a close connection to the concepts of progressive correction (Oudjane and Musso, 2000) and progressive Bayes (Hanebeck et al, 2003), both of which strive to apply Bayes updating in a progressive manner and aforementioned uncorrelated augmentation (Liu et al, 2013;Lan and Li, 2015;. In fact, the idea of emphasizing the observation when it is very informative has also inspired the development of random-sampling based filters such as annealed/unscented PFs (van der Merwe et al, 2000;Godsill and Clapp, 2001), particle flow filter (Daum and Huang, 2010), and feedback PF (Yang et al, 2016), and some (re)sampling approaches (Li et al, 2015a;.…”

Section: Very Informative Observationmentioning

confidence: 99%

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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: Converted Measurement Filteringmentioning

confidence: 99%

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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“…As shown in [24], the GLMMSE outperforms the LMMSE estimators. Thus, in S1 the UCF and the OUCF are compared with the LMMSE estimator of [30] and the GLMMSE estimator of [24].…”

Section: Simulation Resultsmentioning

confidence: 86%

“…As shown in [24], the GLMMSE outperforms the LMMSE estimators. Thus, in S1 the UCF and the OUCF are compared with the LMMSE estimator of [30] and the GLMMSE estimator of [24]. Because the LMMSE and the GLMMSE both use the transformed measurement z k = [r k cos(θ k ), r k sin(θ k )] T , the UCF and the OUCF also use this transformed measurement for a fair comparison.…”

Section: Simulation Resultsmentioning

confidence: 86%

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Nonlinear Estimation by LMMSE-Based Estimation With Optimized Uncorrelated Augmentation

Lan

2015

IEEE Trans. Signal Process.

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For nonlinear estimation, the linear minimum mean square error (LMMSE) estimator using the measurement augmented by its nonlinear conversion can achieve better performance than using the original measurement. The main reason is that the original measurement cannot be fully utilized by the LMMSE estimator in a linear way. To effectively extract additional measurement information which can be further utilized by a linear estimator, a nonlinear approach named uncorrelated conversion (UC) is proposed. The uncorrelated conversions of the measurement are uncorrelated with the measurement itself. Two specific approaches to generating UCs are proposed based on a Gaussian assumption and a reference distribution, respectively. Then a UC based filter (UCF) is proposed based on LMMSE estimation using the measurement augmented by its uncorrelated conversions. To minimize the mean square error of the overall estimate, an optimized UCF (OUCF) with an analytical form is proposed by optimizing the reference distribution based UCs. In the UCF, measurement augmentation can be continued using the proposed nonlinear UC approach, and all augmenting terms are uncorrelated under certain conditions. Thus, the performance of the UCF and the OUCF may be continually improved.Simulation results demonstrate the effectiveness of the proposed estimator compared with some popular nonlinear estimators. I. INTRODUCTIONNonlinear filters aim at estimating a quantity of a nonlinear problem from noisy measurements. Design, derivation, and application of nonlinear filters have received extensive attention over the past several decades, because nonlinear estimation has widespread applications in many fields, e.g., navigation, target tracking, and guidance systems. As an extension of the Kalman filter [17] for linear-Gaussian problems, the well-known extended Kalman filter (EKF) for nonlinear estimation is widely applied to many practical problems of a low nonlinearity. If the problem is highly nonlinear, however, EKF may diverge [13] [16].To solve this problem, some extensions of EKF have been proposed (e.g., the second-order EKF [4] [13] and iterated Kalman filter [8] [13]). These filters can be classified as function approximation methods [21]. Another class of nonlinear estimators based on approximations of the posterior state density [23] using the sequential Monte Carlo (SMC) method has also been proposed and applied (e.g., the particle filters [7] [9] [27] [18]). In this paper, we consider only the estimators which directly obtain the estimated quantity without obtaining its posterior distribution, since they are simpler and are adequate for many practical applications. Using deterministic sampling, the unscented transformation (UT) was proposed to calculate the first and second moments of a nonlinear function of a random variable [15] [16]. In UT, deterministic sigma points are generated and put through the nonlinear function. Then the moments are calculated using the obtained points [29] [25] [28]. Using UT to compute the moments in the linear m...

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Extended Kalman filter for extended object tracking

Yang

Baum

2017

2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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In this paper, we propose a novel method for estimating an elliptic shape approximation of a moving extended object that gives rise to multiple scattered measurements per frame. For this purpose, we parameterize the elliptic shape with its orientation and the lengths of the semi-axes. We relate an individual measurement with the ellipse parameters by means of a multiplicative noise model and derive a second-order extended Kalman filter for a closed-form recursive measurement update. The benefits of the new method are discussed by means of Monte Carlo simulations for both static and dynamic scenarios.

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Generalized linear minimum mean-square error estimation with application to space-object tracking

Cited by 5 publications

References 18 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

Nonlinear Estimation by LMMSE-Based Estimation With Optimized Uncorrelated Augmentation

Extended Kalman filter for extended object tracking

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