A new smallest sigma set for the Unscented Transform and its applications on SLAM

IEEE Trans. Veh. Technol.

et al. 2016

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Abstract-The paper presents an application of unscented Kalman filters to an automotive electronic throttle device. The motivation of this study is on estimating the position of the throttle device when measurements of position are inaccessible, e.g., due to failures in the sensor of position. In this case, an external wattmeter is connected in the circuitry to measure the power consumed by the throttle, and this information feeds unscented Kalman filters to produce the estimation for the position. Experimental data support the findings of this paper.Note to Practitioners: Abstract-Almost all of the brand-new vehicles based on spark-ignition combustion engines have an electronic throttle valve to control the power produced by the engine. The electronic throttle has a unique sensor for measuring the position of the throttle valve, and this feature can represent a serious problem when the sensor of position fails. As an attempt to prevent the effects of a failure from such sensor, we present an algorithm (unscented Kalman filter) combined with the use of an additional sensor, a wattmeter. The wattmeter is detached from the throttle's structure but is arranged so as to measure the electric power consumed by the throttle. Measurements of the power consumption then feed the unscented Kalman filter-this filter then produces an estimation of the position of the throttle valve. Experimental data illustrate the practical benefits of our approach.

“…Other filter that produces promising results is referred to as Additive Rho Minimum (ARM) UKF [29], and it is obtained by modifying Step 1 and Step 2 according to the next procedure:…”

Section: And Return To the Beginning Of Stepmentioning

confidence: 99%

Unscented Kalman Filters for Estimating the Position of an Automotive Electronic Throttle Valve

Vargas

IEEE Trans. Veh. Technol.

et al. 2016

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“…First, it can be numerically unstable for great values of n due to the fact that the weights are composed by fractions of 2 n [9]. Second, neither the sample mean, µ , nor the sample CM, ⌃ , are equal to the mean and CM of the prior distribution when n is greater than one [12]. In fact, from Tab I [3]…”

Section: B Definitions For Ukf's 1) Variations On Ukf Definitionsmentioning

confidence: 99%

“…As can be seen by Table I, among the major general and additive UKF variants that use symmetric sets, the UKF's of [1], [7], and [35] use with N = 2n+1 points. Among the major general and additive UKF variants that use asymmetric sets, the UKF's of [9] use with N = n + 2 points and the UKF's of [8], [34], and [12] use with N = n + 1 sigma points, which is the minimum amount [8]. Finally, the UKF of [36] uses with N = 2n 2 + 1 points and the one of [37] …”

Section: +Xmentioning

confidence: 99%

“…For points i symmetrically distributed in a geometrical sense, we have the UKF's [1], [7], [35], [36]. For asymmetric sets, one can mention the reduced of [8]; the spherical simplex of [9]; the simplex of [34]; and the minimum of [12].…”

Section: +Xmentioning

confidence: 99%

“…The sets of the UKF's of [1], [7], [8], [12], [34], [35] and [36] match the first two moments of any X. If X is symmetric, then the sets in the UKF's of [1], [7], [35] and [36] match also all odd moments.…”

mentioning

confidence: 99%

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A Systematization of the Unscented Kalman Filter Theory

IEEE Trans. Automat. Contr.

Borges

et al. 2015

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209

162

Abstract-In this paper, we propose a systematization of the (discrete-time) Unscented Kalman Filter (UKF) theory. We gather all available UKF variants in the literature, present corrections to theoretical inconsistencies, and provide a tool for the construction of new UKF's in a consistent way. This systematization is done, mainly, by revisiting the concepts of Sigma-Representation, Unscented Transformation (UT), Scaled Unscented Transformation (SUT), UKF, and Square-Root Unscented Kalman Filter (SRUKF). Inconsistencies are related to 1) matching the order of the transformed covariance and cross-covariance matrices of both the UT and the SUT; 2) multiple UKF definitions; 3) issue with some reduced sets of sigma points described in the literature; 4) the conservativeness of the SUT; 5) the scaling effect of the SUT on both its transformed covariance and crosscovariance matrices; and 6) possibly ill-conditioned results in SRUKF's. With the proposed systematization, the symmetric sets of sigma points in the literature are formally justified, and we are able to provide new consistent variations for UKF's, such as the Scaled SRUKF's and the UKF's composed by the minimum number of sigma points. Furthermore, our proposed SRUKF has improved computational properties when compared to state-ofthe-art methods.

New minimum sigma set for unscented filtering

Intl J Robust & Nonlinear

Borges

2014

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In this work, a new minimum set of sigma points for unscented filtering is proposed along with its unscented Kalman filter in both square-root and nonsquare-root forms. Comparative with the other reduced sigma sets of the literature, the new sigma set is, in some cases, better defined or, in another case, a generalization. In numerical examples, the unscented transform of the new sigma set is compared with the unscented transforms of the other reduced sigma sets of the literature. In addition, the performance of the new unscented Kalman filter is studied in an aircraft target tracking scenario.