scholarly journals A Single-pass Noise Covariance Estimation Algorithm in Adaptive Kalman Filtering for Non-stationary Systems

2021 ◽  
Author(s):  
Hee-Seung Kim ◽  
Lingyi Zhang ◽  
Adam Bienkowski ◽  
Krishna Pattipati
Keyword(s):  
Computational Efficiency ◽  
Measurement Data ◽  
Practical Interest ◽  
Estimation Algorithm ◽  
Covariance Estimation ◽  
Stochastic Gradient Descent ◽  
Fading Memory ◽  
Single Pass ◽  
Streaming Algorithm ◽  
Noise Covariance

Estimation of unknown noise covariances in a Kalman filter is a problem of significant practical interest in a wide array of applications. This paper presents a single-pass stochastic gradient descent (SGD) algorithm for noise covariance estimation for use in adaptive Kalman filters applied to non-stationary systems where the noise covariances can occasionally jump up or down by an unknown magnitude. Unlike our previous batch method or our multi-pass decision-directed algorithm, the proposed streaming algorithm reads measurement data exactly once and has similar root mean square error (RMSE). The computational efficiency of the new algorithm stems from its one-pass nature, recursive fading memory estimation of the sample cross-correlations of the innovations, and the RMSprop accelerated SGD algorithm. The comparative evaluation of the proposed method on a number of test cases demonstrates its computational efficiency and accuracy.

scholarly journals A Single-pass Noise Covariance Estimation Algorithm in Adaptive Kalman Filtering for Non-stationary Systems

2021 ◽  
Author(s):  
Hee-Seung Kim ◽  
Lingyi Zhang ◽  
Adam Bienkowski ◽  
Krishna Pattipati
Keyword(s):  
Computational Efficiency ◽  
Measurement Data ◽  
Practical Interest ◽  
Estimation Algorithm ◽  
Covariance Estimation ◽  
Stochastic Gradient Descent ◽  
Fading Memory ◽  
Single Pass ◽  
Streaming Algorithm ◽  
Noise Covariance

Estimation of unknown noise covariances in a Kalman filter is a problem of significant practical interest in a wide array of applications. This paper presents a single-pass stochastic gradient descent (SGD) algorithm for noise covariance estimation for use in adaptive Kalman filters applied to non-stationary systems where the noise covariances can occasionally jump up or down by an unknown magnitude. Unlike our previous batch method or our multi-pass decision-directed algorithm, the proposed streaming algorithm reads measurement data exactly once and has similar root mean square error (RMSE). The computational efficiency of the new algorithm stems from its one-pass nature, recursive fading memory estimation of the sample cross-correlations of the innovations, and the RMSprop accelerated SGD algorithm. The comparative evaluation of the proposed method on a number of test cases demonstrates its computational efficiency and accuracy.

scholarly journals Noise Covariance Estimation in Adaptive Kalman Filtering via sequential Mini-batch Stochastic Gradient Descent Algorithms

2021 ◽  
Author(s):  
Hee-Seung Kim ◽  
Lingyi Zhang ◽  
Adam Bienkowski ◽  
Krishna Pattipati
Keyword(s):  
Computational Efficiency ◽  
Gradient Descent ◽  
Sufficient Conditions ◽  
Covariance Estimation ◽  
Stochastic Gradient ◽  
Necessary And Sufficient Conditions ◽  
Stochastic Gradient Descent ◽  
Fading Memory ◽  
Noise Covariance ◽  
Necessary And Sufficient

<p>Estimation of unknown noise covariances in a Kalman filter is a problem of significant practical interest in a wide array of applications. Although this problem has a long history, reliable algorithms for their estimation were scant, and necessary and sufficient conditions for identifiability of the covariances were in dispute until recently. Necessary and sufficient conditions for covariance estimation and a batch estimation algorithm. This paper presents stochastic gradient descent (SGD) algorithms for noise covariance estimation in adaptive Kalman filters that are an order of magnitude faster than the batch method for similar or better root mean square error (RMSE) and are applicable to non-stationary systems where the noise covariances can occasionally jump up or down by an unknown magnitude. The computational efficiency of the new algorithm stems from adaptive thresholds for convergence, recursive fading memory estimation of the sample cross-correlations of the innovations, and accelerated SGD algorithms. The comparative evaluation of the proposed method on a number of test cases demonstrates its computational efficiency and accuracy.</p>

scholarly journals Noise Covariance Estimation in Adaptive Kalman Filtering via sequential Mini-batch Stochastic Gradient Descent Algorithms

2021 ◽  
Author(s):  
Hee-Seung Kim ◽  
Lingyi Zhang ◽  
Adam Bienkowski ◽  
Krishna Pattipati
Keyword(s):  
Computational Efficiency ◽  
Gradient Descent ◽  
Sufficient Conditions ◽  
Covariance Estimation ◽  
Stochastic Gradient ◽  
Necessary And Sufficient Conditions ◽  
Stochastic Gradient Descent ◽  
Fading Memory ◽  
Noise Covariance ◽  
Necessary And Sufficient

<p>Estimation of unknown noise covariances in a Kalman filter is a problem of significant practical interest in a wide array of applications. Although this problem has a long history, reliable algorithms for their estimation were scant, and necessary and sufficient conditions for identifiability of the covariances were in dispute until recently. Necessary and sufficient conditions for covariance estimation and a batch estimation algorithm. This paper presents stochastic gradient descent (SGD) algorithms for noise covariance estimation in adaptive Kalman filters that are an order of magnitude faster than the batch method for similar or better root mean square error (RMSE) and are applicable to non-stationary systems where the noise covariances can occasionally jump up or down by an unknown magnitude. The computational efficiency of the new algorithm stems from adaptive thresholds for convergence, recursive fading memory estimation of the sample cross-correlations of the innovations, and accelerated SGD algorithms. The comparative evaluation of the proposed method on a number of test cases demonstrates its computational efficiency and accuracy.</p>

Robust autocovariance least-squares noise covariance estimation algorithm

Measurement ◽  
2021 ◽  
pp. 110331
Author(s):  
Wei Li ◽  
Xu Lin ◽  
Shaoda Li ◽  
Jiang Ye ◽  
Chaolong Yao ◽  
...  
Keyword(s):  
Least Squares ◽  
Estimation Algorithm ◽  
Covariance Estimation ◽  
Noise Covariance

scholarly journals Robust and Fast State Estimation for Poorly-Observable Low Voltage Distribution Networks Based on the Kalman Filter Algorithm

Energies ◽  
2019 ◽  
Vol 12 (23) ◽  
pp. 4457 ◽  
Author(s):  
Antončič ◽  
Papič ◽  
Blažič
Keyword(s):  
Kalman Filter ◽  
State Estimation ◽  
Low Voltage ◽  
Least Squares Method ◽  
Weighted Least Squares ◽  
Measurement Data ◽  
Estimation Algorithm ◽  
Distribution Networks ◽  
Voltage Distribution ◽  
State Estimator

This paper presents a novel approach for the state estimation of poorly-observable low voltage distribution networks, characterized by intermittent and erroneous measurements. The developed state estimation algorithm is based on the Extended Kalman filter, where we have modified the execution of the filtering process. Namely, we have fixed the Kalman gain and Jacobian matrices to constant matrices; their values change only after a larger disturbance in the network. This allows for a fast and robust estimation of the network state. The performance of the proposed state-estimation algorithm is validated by means of simulations of an actual low-voltage network with actual field measurement data. Two different cases are presented. The results of the developed state estimator are compared to a classical estimator based on the weighted least squares method. The comparison shows that the developed state estimator outperforms the classical one in terms of calculation speed and, in case of spurious measurements errors, also in terms of accuracy.

scholarly journals Amplitude estimation without phase estimation

2020 ◽  
Vol 19 (2) ◽  
Author(s):  
Yohichi Suzuki ◽  
Shumpei Uno ◽  
Rudy Raymond ◽  
Tomoki Tanaka ◽  
Tamiya Onodera ◽  
...  
Keyword(s):  
Measurement Data ◽  
Likelihood Estimation ◽  
Estimation Algorithm ◽  
Quantum Circuits ◽  
Phase Estimation ◽  
Amplitude Estimation ◽  
Quantum Amplitude ◽  
Phase Estimation Algorithm ◽  
Near Term ◽  
Quantum Speedup

AbstractThis paper focuses on the quantum amplitude estimation algorithm, which is a core subroutine in quantum computation for various applications. The conventional approach for amplitude estimation is to use the phase estimation algorithm, which consists of many controlled amplification operations followed by a quantum Fourier transform. However, the whole procedure is hard to implement with current and near-term quantum computers. In this paper, we propose a quantum amplitude estimation algorithm without the use of expensive controlled operations; the key idea is to utilize the maximum likelihood estimation based on the combined measurement data produced from quantum circuits with different numbers of amplitude amplification operations. Numerical simulations we conducted demonstrate that our algorithm asymptotically achieves nearly the optimal quantum speedup with a reasonable circuit length.

Sign in / Sign up

Export Citation Format

Share Document