A square root unscented Kalman filter for estimating DAC and loopfilter nonidealities in continuous-time sigma-delta modulators

Lorenz, Matthias; Brückner, Timon; Ritter, Rudolf; Anders, Jens; Ortmanns, Maurits

doi:10.1109/iscas.2014.6865346

Cited by 3 publications

(6 citation statements)

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“…2) Square-Root Filtering: Another approach to improve stability of the UKF is square-root filtering [25], [33]. Even when the estimations are normalized the problem of an ill-conditioned covariance matrix might still exist, especially if word-lengths are very short.…”

Section: Numerical Considerations 1) Normalization Of Estimation Vmentioning

confidence: 99%

“…Thus their variances are already very small after a short time while the variances of the other parameters are still large-again leading to a bad condition. In the square-root UKF [25], [33] the square-root of the covariance matrix is used instead of its original form because the condition of the square-root is inherently better. Hence, the calculation of the square-root is completely avoided.…”

Section: Numerical Considerations 1) Normalization Of Estimation Vmentioning

confidence: 99%

“…The authors formerly proposed an unscented Kalman filter (UKF) which can be used to estimate system parameters, such as non-idealities, in modulators [22]- [25]. It was shown in simulation that the method can be used with arbitrary modulator structures and quantizer resolutions and allows for the joint estimation of up to 26 states and parameters in a fast and reliable fashion.…”

Section: Introductionmentioning

confidence: 99%

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Estimation of Non-Idealities in Sigma-Delta Modulators for Test and Correction Using Unscented Kalman Filters

Lorenz

Ritter

Anders

et al. 2015

IEEE Trans. Circuits Syst. I

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In this paper, an enhanced unscented Kalman filter is used for the estimation of non-idealities in sigma-delta modulators. As sigma-delta modulator based analog-to-digital converters are known to be prone to performance degradation from many circuit non-idealities, testing and selection of the manufactured chips as well as post-correction procedures are required to ensure a reliable performance. In contrast to most state-of-the art techniques, the proposed estimator is capable of simultaneously tracking a large set of non-ideal parameters with high accuracy and in a very short offline time within the range of microseconds. Three possible implementations are proposed and it is shown how the technique is used to perform an in situ non-ideality estimation and subsequent calibration of a manufactured chip, bringing the modulator back into its designed performance range. It is further demonstrated that the estimator can reliably detect the non-idealities over a wide range when intentionally degrading the performance of the chip by manually sweeping its trimming parameters. The presented hardware measurement results prove that the proposed technique is practically applicable to the test and/or calibration of sigma-delta data converters.

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Section: Numerical Considerations 1) Normalization Of Estimation Vmentioning

confidence: 99%

Section: Numerical Considerations 1) Normalization Of Estimation Vmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Estimation of Non-Idealities in Sigma-Delta Modulators for Test and Correction Using Unscented Kalman Filters

Lorenz

Ritter

Anders

et al. 2015

IEEE Trans. Circuits Syst. I

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“…Assuming a parallel implementation, the total runtime would finally shrink to ∼0.13 s only. Even an accelerated version of the UKF based on [4] would at least require 1.20 s on an Intel Core i5-2500 3.3 GHz central processing unit. Fig.…”

Section: Fig 3 Overview Of Ukf Hybrid Estimation Techniquementioning

confidence: 99%

“…We recently demonstrated that an unscented Kalman filter (UKF) solves the parameter estimation task very well [4]. However, for an application where the estimator must be implemented on-chip, the approach is not applicable because the UKF requires many complex calculations to operate and the size of its digital realisation would make the technique impractical.…”

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confidence: 99%

Hybrid of unscented Kalman filter and genetic algorithm for state and parameter estimation in sigma–delta modulators

2015

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A mathematically simple hybrid of the unscented Kalman filter and the genetic algorithm (GA) is presented and applied to the non-ideality estimation in sigma-delta modulators. Parameter estimation is a complicated task, especially if a system must be observed continuously and its internal states have to be tracked in addition. A GA is a low-cost method to find an optimal parameter set but if the system is vastly changing, it cannot be applied. In contrast, the basic Kalman filter is an effective state estimator but cannot be used to estimate parameters of a system without complex mathematical extensions. A combination of both techniques can be beneficial to enable fast and especially lowcost on-chip estimation procedures.Introduction: In case the internal parameters of a dynamic system must be observed during runtime, its internal states must be continuously tracked in order to enable parameter estimation. This turns the estimation task into a nonlinear problem because the system parameters become time variant [1]. Such an estimation problem must be solved for many technical applications e.g. in automotive and aeronautics fields.We present an innovative solution to the identification task focused on a modern data conversion system, namely a sigma-delta (ΣΔ) analogue-to-digital data converter (ADC). Such an ADC is used for high-resolution and wide-bandwidth applications and is affected by nonidealities, originating from manufacturing tolerances and run-time effects [2]. As deviations from the ideal behaviour noticeably affect the performance and stability of the converter, it is often beneficial to recalibrate the components of the ADC during operation in order to restore its ideal characteristics [3]. Therefore, the non-ideal parameters in the ΣΔ ADC's filter must be estimated reliably, quickly and precisely.We recently demonstrated that an unscented Kalman filter (UKF) solves the parameter estimation task very well [4]. However, for an application where the estimator must be implemented on-chip, the approach is not applicable because the UKF requires many complex calculations to operate and the size of its digital realisation would make the technique impractical. We also presented a pure genetic algorithm (GA) solution [5] which reduced the complexity of the estimations a lot. However, the system states were not tracked continuously but only an initial value was estimated and a model was simulated from this point on. Hence, the robustness and accuracy were not as good as from the UKF due to missing relationships of the dynamics and parameters.We propose a hybrid of the GA and the UKF for state and parameter estimations. A GA is powerful to heuristically find a set of parameters with extremely low computational effort but it cannot work on a state estimation task. In the proposed hybrid, we can replace the most costly part of the UKF by a simple GA and it is shown that the solution operates quickly and accurately on a complex example.

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A spherical simplex unscented Kalman filter with smart sigma-point processing for estimations in CT ΣΔ modulators

Lorenz

Maurer

Manoli

et al. 2014

2014 IEEE 12th International New Circuits and Systems Conference (NEWCAS)

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A square root unscented Kalman filter for estimating DAC and loopfilter nonidealities in continuous-time sigma-delta modulators

Cited by 3 publications

References 7 publications

Estimation of Non-Idealities in Sigma-Delta Modulators for Test and Correction Using Unscented Kalman Filters

Estimation of Non-Idealities in Sigma-Delta Modulators for Test and Correction Using Unscented Kalman Filters

Hybrid of unscented Kalman filter and genetic algorithm for state and parameter estimation in sigma–delta modulators

A spherical simplex unscented Kalman filter with smart sigma-point processing for estimations in CT ΣΔ modulators

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A square root unscented Kalman filter for estimating DAC and loopfilter nonidealities in continuous-time sigma-delta modulators

Cited by 3 publications

References 7 publications

Estimation of Non-Idealities in Sigma-Delta Modulators for Test and Correction Using Unscented Kalman Filters

Estimation of Non-Idealities in Sigma-Delta Modulators for Test and Correction Using Unscented Kalman Filters

Hybrid of unscented Kalman filter and genetic algorithm for state and parameter estimation in sigma–delta modulators

A spherical simplex unscented Kalman filter with smart sigma-point processing for estimations in CT &#x03A3;&#x0394; modulators

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A spherical simplex unscented Kalman filter with smart sigma-point processing for estimations in CT ΣΔ modulators