Fourier-Hermite Kalman Filter

Sarmavuori, Juha; Särkkä, Simo

doi:10.1109/tac.2011.2174667

Cited by 48 publications

(34 citation statements)

References 20 publications

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“…Alternately, the Fourier-Hermite Kalman filter [247] avoids the numerical integration present in the family of cubature filters by replacing each integral with a Fourier-Hermite series. The Fourier-Hermite Kalman filter is not suitable for applications like filtering using refraction corrupted measurements, which is considered in the companion tutorial [71], because it requires the ability to take derivatives of the measurement function.…”

Section: A Estimation Using Nonlinear Measurementsmentioning

confidence: 99%

Basic tracking using nonlinear 3D monostatic and bistatic measurements

Crouse¹

2014

IEEE Aerosp. Electron. Syst. Mag.

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Monostatic and bistatic position and Doppler measurements used in radar and sonar systems are nonlinear transformations of a Cartesian state. These nonlinearities pose a challenge for many target tracking algorithms, causing the so-called contact lens problem, which describes the nonlinear appearance of the measurement probability density function in Cartesian coordinates. This tutorial considers methods for measurement filtering (tracking without considering data association) using a single-Gaussian approximation when monostatic and bistatic position and Doppler measurements are available. The connection between the cubature Kalman filter and numerous other filtering algorithms is shown, and the accuracy and consistency of different algorithms are compared through simulation. An effort is made to express the geometric relationships associated with multistatic tracking in a simple vectorial manner. This tutorial focuses on basic tracking, and the companion tutorials "Tracking Using 3D Monostatic and Bistatic Measurements in Refractive Environments" and "Basic Tracking Using Nonlinear Continuous-Time Dynamic Models" extend the results to more sophisticated physical models.

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Section: A Estimation Using Nonlinear Measurementsmentioning

confidence: 99%

Basic tracking using nonlinear 3D monostatic and bistatic measurements

Crouse¹

2014

IEEE Aerosp. Electron. Syst. Mag.

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“…Therefore several remedies have been proposed such as the cubature Kalman filter [6], which is the special case of the UKF [7]. As explained, since the UKF retains such high estimation accuracy along with a relatively low computational burden compared with the sampling based filter such as the particle filter, UKF is currently the representative realization for the GF approach and is also the state-of-the-art filtering method for the nonlinear Gaussian observation problems.…”

Section: ) Unscented Kalman Filter (Ukf)mentioning

confidence: 99%

“…The first approach assumes that the state and observation both follow Gaussian distributions even though the state is nonlinearly transformed. The resulting filter is called the Gaussian assumed density filter (ADF) or simply as the Gaussian filter (GF)[1] [2]. Since the algorithm involves expectation calculations that are not realizable for general nonlinear functions, several approximation techniques have been proposed to obtain their reasonable estimates.…”

Section: Introduction: Nonlinear Gaussian Observation Model Filteringmentioning

confidence: 99%

“…So, the problem is to pursue the linearization technique that minimizes the linearization error. This approach is called the series expansion based filter (SEF) [2][3] [4] and our proposing approach belongs to this category. Before describing our proposed method, we explain two state-of-the-art filtering methods for both the GF and SEF categories in the following section.…”

Section: Introduction: Nonlinear Gaussian Observation Model Filteringmentioning

confidence: 99%

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Iterative unscented statistically linearized filter for nonlinear Gaussian observation models

Murata¹,

Nagano²,

Kashino³

2014

53rd IEEE Conference on Decision and Control

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State filtering for nonlinear Gaussian observation models still remains as one of the challenging problems in the estimation and control research field. It is mainly due to the non-existence of the realizable optimal filter and for addressing to this problem, the following two approaches are often taken. The first approach is based on the Gaussian assumed density filter (Gaussian filter) and the most wellknown realization is the Unscented Kalman filter. The second approach is based on the series expansion based filter and the most widely-used algorithm is the extended Kalman filter or iterative extended Kalman filter. Note that both approaches are the approximation to the optimal filter and thus a room is still left for the further exploration into the effective filters in terms of both filtering accuracy and speed. In this paper, we focus on the unscented statistical linearization (USL) which is a realization method of the statistical linearization whose linearization accuracy is theoretically better than that of the truncated Taylor series. The filter employing the USL is called the unscented statistically linearized filter (USLF). We newly propose the iterative type algorithm to tackle the filtering problem of the nonlinear Gaussian observation models and numerically show the superior state filtering performance over the aforementioned state-of-the-art filtering approaches.

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“…At present, two methods, including the approximation of the nonlinear function and the approximation of the Gaussian pdf, are mainly taken. In the former method, the nonlinear function is approximated by the polynomial and results in an extended Kalman filter (EKF) [5,6], divided difference Kalman filter (DDKF) [7], and polynomial Kalman filter (PKF) [8,9], where the first-order Taylor expansion, the multidimensional Stirling interpolation, and polynomials including Chebyshev and Fourier-Hermit are adopted to approximate the nonlinear function, respectively, in EKF, DDKF, and PKF. However, the aforementioned methods tend to be restricted when the system has strong nonlinearity with high dimensionality.…”

Section: Introductionmentioning

confidence: 99%

A Novel Fifth-Degree Cubature Kalman Filter for Real-Time Orbit Determination by Radar

Li¹,

Yang²,

Ding³

et al. 2017

Mathematical Problems in Engineering

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A novel fifth-degree cubature Kalman filter is proposed to improve the accuracy of real-time orbit determination by ground-based radar. A fully symmetric cubature rule, approaching the Gaussian weighted integral of a nonlinear function in general form, is introduced, and the specific points and weights are calculated by matching the monomials of degree not greater than five with the exact values. On the basis of the above rule, a novel fifth-degree cubature Kalman filter, which can achieve a higher accuracy than UKF and CKF, is derived under the Bayesian filtering framework. Then, to describe the nonlinear system more accurately, the orbital dynamics equation with J2 perturbation is used as the state equation, and the nonlinear relationship between the radar measurement elements and orbital states is built as the measurement equation. The simulation results show that, compared with the traditional third-degree algorithm, the proposed fifth-degree algorithm has a higher accuracy of orbit determination.

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Fourier-Hermite Kalman Filter

Cited by 48 publications

References 20 publications

Basic tracking using nonlinear 3D monostatic and bistatic measurements

Basic tracking using nonlinear 3D monostatic and bistatic measurements

Iterative unscented statistically linearized filter for nonlinear Gaussian observation models

A Novel Fifth-Degree Cubature Kalman Filter for Real-Time Orbit Determination by Radar

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