Recursive B-spline approximation using the Kalman filter

Jauch, Jens; Bleimund, Felix; Rhode, Stephan; Gauterin, Frank

doi:10.1016/j.jestch.2016.09.015

Cited by 10 publications

(15 citation statements)

References 16 publications

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“…This combination was determined from trajectory optimization experiments. In data approximation experiments for RBA and NRBA performed in [5,19], the equivalent to R −1 a is ten and two times, respectively, larger and the equivalent to R −1 j is 1000 and 200 times, respectively, larger. This is because in these experiments the goal is to smooth jumps of an amplitude of ten in the data set.…”

Section: Trajectory Optimizationmentioning

confidence: 93%

“…In [19] we presented a method denoted recursive B-spline approximation (RBA) that iteratively adapts the coefficients of a B-spline function such that the function approximates data in the weighted least squares (WLS) sense. In [5] we proposed an analogous algorithm called nonlinear recursive B-spline approximation (NRBA) for nonlinear weighted least squares (NWLS) approximation problems.…”

Section: Contributionmentioning

confidence: 99%

“…Due to the choice of κ, the trajectory can be evaluated for t ≥ 0. For mathematical details concerning this function type and relevant formulas we refer to [5,19].…”

Section: Representation Of Velocity Trajectorymentioning

confidence: 99%

“…The goal of RBA and NRBA is to approximate data points [5,19]. However, the data points in (13) also present a constraint to v TJY .…”

Section: Trajectory Optimizationmentioning

confidence: 99%

“…In (17) the coefficient vector x is nonlinearly linked to the error (v Lim,TJY (s TJY ) − v TJY ) by (19). This makes (17) a NWLS problem that we can solve with NRBA.…”

Section: Trajectory Optimizationmentioning

confidence: 99%

See 4 more Smart Citations

Automated Longitudinal Control Based on Nonlinear Recursive B-Spline Approximation for Battery Electric Vehicles

Jauch

Bleimund

Frey

et al. 2019

WEVJ

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This works presents a driver assistance system for energy-efficient ALC of a BEV. The ALC calculates a temporal velocity trajectory from map data. The trajectory is represented by a cubic B-spline function and results from an optimization problem with respect to travel time, driving comfort and energy consumption. For the energetic optimization we propose an adaptive model of the required electrical traction power. The simple power train of a BEV allows the formulation of constraints as soft constraints. This leads to an unconstrained optimization problem that can be solved with iterative filter-based data approximation algorithms. The result is a direct trajectory optimization method of which the effort grows linearly with the trajectory length, as opposed to exponentially as with most other direct methods. We evaluate ALC in real test drives with a BEV. We also investigate the energy-saving potential in driving simulations with ALC compared to MLC. On the chosen reference route the ALC saves up to 3.4% energy compared to MLC at same average velocity, and achieves a 2.6% higher average velocity than MLC at the same energy consumption.

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Section: Trajectory Optimizationmentioning

confidence: 93%

Section: Contributionmentioning

confidence: 99%

“…Due to the choice of κ, the trajectory can be evaluated for t ≥ 0. For mathematical details concerning this function type and relevant formulas we refer to [5,19].…”

Section: Representation Of Velocity Trajectorymentioning

confidence: 99%

“…The goal of RBA and NRBA is to approximate data points [5,19]. However, the data points in (13) also present a constraint to v TJY .…”

Section: Trajectory Optimizationmentioning

confidence: 99%

“…In (17) the coefficient vector x is nonlinearly linked to the error (v Lim,TJY (s TJY ) − v TJY ) by (19). This makes (17) a NWLS problem that we can solve with NRBA.…”

Section: Trajectory Optimizationmentioning

confidence: 99%

See 3 more Smart Citations

Automated Longitudinal Control Based on Nonlinear Recursive B-Spline Approximation for Battery Electric Vehicles

Jauch

Bleimund

Frey

et al. 2019

WEVJ

Self Cite

View full text Add to dashboard Cite

show abstract

Design of Recursive Digital Filters with Penalized Spline Method

Kochegurova

Khozhaev

Ezangina

2018

Computational Collective Intelligence

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Real-time sea-level monitoring using Kalman filtering of GNSS-R data

2019

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Current GNSS-R (GNSS reflectometry) techniques for sea surface measurements require data collection over longer periods, limiting their usability for real-time applications. In this work, we present a new, alternative GNSS-R approach based on the unscented Kalman filter and the so-called inverse modeling approach. The new method makes use of a mathematical description that relates SNR (signal-to-noise ratio) variations to multipath effects and uses a B-spline formalism to obtain time series of reflector height. The presented algorithm can provide results in real time with a precision that is significantly better than spectral inversion methods and almost comparable to results from inverse modeling in post-processing mode. To verify the performance, the method has been tested at station GTGU at the Onsala Space Observatory, Sweden, and at the station SPBY in Spring Bay, Australia. The RMS (root mean square) error with respect to nearby tide gauge data was found to be 2.0 cm at GTGU and 4.8 cm at SPBY when evaluating the output corresponding to real-time analysis. The method can also be applied in post-processing, resulting in RMS errors of 1.5 cm and 3.3 cm for GTGU and SPBY, respectively. Finally, based on SNR data from GTGU, it is also shown that the Kalman filter approach is able to detect the presence of sea ice with a higher temporal resolution than the previous methods and traditional remote sensing techniques which monitor ice in coastal regions.

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Recursive B-spline approximation using the Kalman filter

Cited by 10 publications

References 16 publications

Automated Longitudinal Control Based on Nonlinear Recursive B-Spline Approximation for Battery Electric Vehicles

Automated Longitudinal Control Based on Nonlinear Recursive B-Spline Approximation for Battery Electric Vehicles

Design of Recursive Digital Filters with Penalized Spline Method

Real-time sea-level monitoring using Kalman filtering of GNSS-R data

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