Modal Kalman Filter

Mohammaddadi, Gh.; Pariz, Naser; Karimpour, Ali

doi:10.1002/asjc.1425

Cited by 9 publications

(11 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These approaches can be primarily classified into two categories, approximating either the nonlinear function or the nonlineartransformed PDFs. The former, with typical examples of extended KF (EKF), modal KF (Mohammaddadi et al, 2017), divided difference filter (Nørgaard et al, 2000;Wang et al, 2017), and Fourier-Hermite KF (Sarmavuori and Särkkä, 2012), seeks functions' approximation using polynomial expansions (e.g., Taylor series, Fourier-Hermite series, Stirling's interpolation, or Modal series). The latter, with representative examples of unscented KF (UKF) (Julier and Uhlmann, 2004), Gauss-Hermite filter and central difference filter (Ito and Xiong, 2000), cubature KF (CKF) (Arasaratnam and Haykin, 2009;Jia et al, 2013), sparse-grid quadrature filter (Arasaratnam and Haykin, 2008;Jia et al, 2012), stochastic integration filter (Duník et al, 2013), and iterated posterior linearization filter (IPLF) (García-Fernández et al, 2015b;Raitoharju et al, 2017), is based on a set of deterministically chosen weighted sigma points.…”

Section: Nonlinearitymentioning

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

View full text Add to dashboard Cite

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.

show abstract

Section: Nonlinearitymentioning

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

View full text Add to dashboard Cite

show abstract

“…where D is the set value by which to narrow the bounds, and v i0 and v iN are the maximum and minimum values of each row, respectively. After the ranges of each parameter have been updated, the parameter matrix is reconstructed according to equation (19), and the initial pheromone values of each point are reset according to equation (21). The search process is then repeated until the bias between v il and v iu finally achieves an established accuracy e, as illustrated by the overall process flowchart shown in Figure 4.…”

Section: Ant Colony Algorithm To Obtain Optimal Parametersmentioning

confidence: 99%

Use of ant colony optimization and the Kalman filter to deduce thigh dip angle via acceleration and angular velocity sensing

Zheng

Wang

et al. 2018

Measurement and Control

View full text Add to dashboard Cite

Background: Acceleration and angular velocity sensors are commonly used in the measurement of gait parameters. A representative application calculates the limb segment dip angle. The rotation angle is typically deduced by a conventional Kalman filter, which includes the use of two empirically derived parameters. We improved this conventional method by introducing colony algorithm to find the optimal parameter combination instead of empirically assignment. Method: To achieve optimal results, a servo motor with an inertial measurement unit was used to simulate human limb segment motion according to programmed rotation angles that was employed as the ground truth. To minimize the bias between the ground truth and the calculated result, the ant colony algorithm was employed to obtain the optimal Kalman filter parameter combination in two-dimensional space. Results: By the motor experiment, the sum of the angle squared error was only 1.9305 rad 2 , much better than the 6.7723 rad 2 error by the conventional method. The optimal parameter combination obtained was then used in a human experiment involving a basketball player. The frames from video of a whole gait cycle period were all showed with a corresponding deduced thigh dip angle curve diagram. Conclusion: The colony algorithm for parameters optimization results in less angle errors deduced by Kalman filter using the data from inertial measurement unit. The subject experiment verified the feasibility and performance of this method.

show abstract

“…They are usually carried out based on the closed‐form Markov–Bayes recursion [8], e.g. Kalman filter (KF), extended KF, model KF [9], unscented KF [10], and cubature KF [11]. When the state‐space model and measurement model are all linear and Gaussian, the KF is the optimum filter without bias.…”

Section: Introductionmentioning

confidence: 99%

Marginal tracking algorithm for hypersonic reentry gliding vehicle

Yu¹,

Tan²,

Qu³

et al. 2019

IET Radar, Sonar & Navigation

View full text Add to dashboard Cite

Modal Kalman Filter

Cited by 9 publications

References 16 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

Use of ant colony optimization and the Kalman filter to deduce thigh dip angle via acceleration and angular velocity sensing

Marginal tracking algorithm for hypersonic reentry gliding vehicle

Contact Info

Product

Resources

About