Kalman Filter

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Eric A Wan - One of the best experts on this subject based on the ideXlab platform.

  • the square root unscented Kalman Filter for state and parameter estimation
    International Conference on Acoustics Speech and Signal Processing, 2001
    Co-Authors: R Van Der Merwe, Eric A Wan
    Abstract:

    Over the last 20-30 years, the extended Kalman Filter (EKF) has become the algorithm of choice in numerous nonlinear estimation and machine learning applications. These include estimating the state of a nonlinear dynamic system as well estimating parameters for nonlinear system identification (eg, learning the weights of a neural network). The EKF applies the standard linear Kalman Filter methodology to a linearization of the true nonlinear system. This approach is sub-optimal, and can easily lead to divergence. Julier et al. (1997), proposed the unscented Kalman Filter (UKF) as a derivative-free alternative to the extended Kalman Filter in the framework of state estimation. This was extended to parameter estimation by Wan and Van der Merwe et al., (2000). The UKF consistently outperforms the EKF in terms of prediction and estimation error, at an equal computational complexity of (OL/sup 3/)/sup l/ for general state-space problems. When the EKF is applied to parameter estimation, the special form of the state-space equations allows for an O(L/sup 2/) implementation. This paper introduces the square-root unscented Kalman Filter (SR-UKF) which is also O(L/sup 3/) for general state estimation and O(L/sup 2/) for parameter estimation (note the original formulation of the UKF for parameter-estimation was O(L/sup 3/)). In addition, the square-root forms have the added benefit of numerical stability and guaranteed positive semi-definiteness of the state covariances.

  • the unscented Kalman Filter for nonlinear estimation
    Proceedings of the IEEE 2000 Adaptive Systems for Signal Processing Communications and Control Symposium (Cat. No.00EX373), 2000
    Co-Authors: Eric A Wan, R Van Der Merwe
    Abstract:

    This paper points out the flaws in using the extended Kalman Filter (EKE) and introduces an improvement, the unscented Kalman Filter (UKF), proposed by Julier and Uhlman (1997). A central and vital operation performed in the Kalman Filter is the propagation of a Gaussian random variable (GRV) through the system dynamics. In the EKF the state distribution is approximated by a GRV, which is then propagated analytically through the first-order linearization of the nonlinear system. This can introduce large errors in the true posterior mean and covariance of the transformed GRV, which may lead to sub-optimal performance and sometimes divergence of the Filter. The UKF addresses this problem by using a deterministic sampling approach. The state distribution is again approximated by a GRV, but is now represented using a minimal set of carefully chosen sample points. These sample points completely capture the true mean and covariance of the GRV, and when propagated through the true nonlinear system, captures the posterior mean and covariance accurately to the 3rd order (Taylor series expansion) for any nonlinearity. The EKF in contrast, only achieves first-order accuracy. Remarkably, the computational complexity of the UKF is the same order as that of the EKF. Julier and Uhlman demonstrated the substantial performance gains of the UKF in the context of state-estimation for nonlinear control. Machine learning problems were not considered. We extend the use of the UKF to a broader class of nonlinear estimation problems, including nonlinear system identification, training of neural networks, and dual estimation problems. In this paper, the algorithms are further developed and illustrated with a number of additional examples.

R Van Der Merwe - One of the best experts on this subject based on the ideXlab platform.

  • the square root unscented Kalman Filter for state and parameter estimation
    International Conference on Acoustics Speech and Signal Processing, 2001
    Co-Authors: R Van Der Merwe, Eric A Wan
    Abstract:

    Over the last 20-30 years, the extended Kalman Filter (EKF) has become the algorithm of choice in numerous nonlinear estimation and machine learning applications. These include estimating the state of a nonlinear dynamic system as well estimating parameters for nonlinear system identification (eg, learning the weights of a neural network). The EKF applies the standard linear Kalman Filter methodology to a linearization of the true nonlinear system. This approach is sub-optimal, and can easily lead to divergence. Julier et al. (1997), proposed the unscented Kalman Filter (UKF) as a derivative-free alternative to the extended Kalman Filter in the framework of state estimation. This was extended to parameter estimation by Wan and Van der Merwe et al., (2000). The UKF consistently outperforms the EKF in terms of prediction and estimation error, at an equal computational complexity of (OL/sup 3/)/sup l/ for general state-space problems. When the EKF is applied to parameter estimation, the special form of the state-space equations allows for an O(L/sup 2/) implementation. This paper introduces the square-root unscented Kalman Filter (SR-UKF) which is also O(L/sup 3/) for general state estimation and O(L/sup 2/) for parameter estimation (note the original formulation of the UKF for parameter-estimation was O(L/sup 3/)). In addition, the square-root forms have the added benefit of numerical stability and guaranteed positive semi-definiteness of the state covariances.

  • the unscented Kalman Filter for nonlinear estimation
    Proceedings of the IEEE 2000 Adaptive Systems for Signal Processing Communications and Control Symposium (Cat. No.00EX373), 2000
    Co-Authors: Eric A Wan, R Van Der Merwe
    Abstract:

    This paper points out the flaws in using the extended Kalman Filter (EKE) and introduces an improvement, the unscented Kalman Filter (UKF), proposed by Julier and Uhlman (1997). A central and vital operation performed in the Kalman Filter is the propagation of a Gaussian random variable (GRV) through the system dynamics. In the EKF the state distribution is approximated by a GRV, which is then propagated analytically through the first-order linearization of the nonlinear system. This can introduce large errors in the true posterior mean and covariance of the transformed GRV, which may lead to sub-optimal performance and sometimes divergence of the Filter. The UKF addresses this problem by using a deterministic sampling approach. The state distribution is again approximated by a GRV, but is now represented using a minimal set of carefully chosen sample points. These sample points completely capture the true mean and covariance of the GRV, and when propagated through the true nonlinear system, captures the posterior mean and covariance accurately to the 3rd order (Taylor series expansion) for any nonlinearity. The EKF in contrast, only achieves first-order accuracy. Remarkably, the computational complexity of the UKF is the same order as that of the EKF. Julier and Uhlman demonstrated the substantial performance gains of the UKF in the context of state-estimation for nonlinear control. Machine learning problems were not considered. We extend the use of the UKF to a broader class of nonlinear estimation problems, including nonlinear system identification, training of neural networks, and dual estimation problems. In this paper, the algorithms are further developed and illustrated with a number of additional examples.

Denis Gingras - One of the best experts on this subject based on the ideXlab platform.

Mackenna Hill - One of the best experts on this subject based on the ideXlab platform.

  • Cortical Decoding of Individual Finger Group Motions Using ReFIT Kalman Filter
    Frontiers Media S.A., 2018
    Co-Authors: Alex K. Vaskov, Zachary T. Irwin, Samuel R. Nason, Autumn J. Bullard, Mackenna Hill, Naia North
    Abstract:

    Objective: To date, many brain-machine interface (BMI) studies have developed decoding algorithms for neuroprostheses that provide users with precise control of upper arm reaches with some limited grasping capabilities. However, comparatively few have focused on quantifying the performance of precise finger control. Here we expand upon this work by investigating online control of individual finger groups.Approach: We have developed a novel training manipulandum for non-human primate (NHP) studies to isolate the movements of two specific finger groups: index and middle-ring-pinkie (MRP) fingers. We use this device in combination with the ReFIT (Recalibrated Feedback Intention-Trained) Kalman Filter to decode the position of each finger group during a single degree of freedom task in two rhesus macaques with Utah arrays in motor cortex. The ReFIT Kalman Filter uses a two-stage training approach that improves online control of upper arm tasks with substantial reductions in orbiting time, thus making it a logical first choice for precise finger control.Results: Both animals were able to reliably acquire fingertip targets with both index and MRP fingers, which they did in blocks of finger group specific trials. Decoding from motor signals online, the ReFIT Kalman Filter reliably outperformed the standard Kalman Filter, measured by bit rate, across all tested finger groups and movements by 31.0 and 35.2%. These decoders were robust when the manipulandum was removed during online control. While index finger movements and middle-ring-pinkie finger movements could be differentiated from each other with 81.7% accuracy across both subjects, the linear Kalman Filter was not sufficient for decoding both finger groups together due to significant unwanted movement in the stationary finger, potentially due to co-contraction.Significance: To our knowledge, this is the first systematic and biomimetic separation of digits for continuous online decoding in a NHP as well as the first demonstration of the ReFIT Kalman Filter improving the performance of precise finger decoding. These results suggest that novel nonlinear approaches, apparently not necessary for center out reaches or gross hand motions, may be necessary to achieve independent and precise control of individual fingers

  • cortical decoding of individual finger group motions using refit Kalman Filter
    Frontiers in Neuroscience, 2018
    Co-Authors: Alex K. Vaskov, Zachary T. Irwin, Samuel R. Nason, Autumn J. Bullard, Mackenna Hill, Naia North, Parag G Patil, Cynthia A Chestek
    Abstract:

    Objective. To date, many brain-machine interface (BMI) studies have developed decoding algorithms for neuroprostheses that provide users with precise control of upper arm reaches with some limited grasping capabilities. However, comparatively few have focused on quantifying the performance of precise finger control. Here we expand upon this work by investigating online control of individual finger groups. Approach. We have developed a novel training manipulandum for non-human primate (NHP) studies to isolate the movements of two specific finger groups: index and middle-ring-pinkie (MRP) fingers. We use this device in combination with the ReFIT (Recalibrated Feedback Intention-Trained) Kalman Filter to decode the position of each finger group during a single degree of freedom task in two rhesus macaques with Utah arrays in motor cortex. The ReFIT Kalman Filter uses a two-stage training approach that improves online control of upper arm tasks with substantial reductions in orbiting time, thus making it a logical first choice for precise finger control. Results. Both animals were able to reliably acquire fingertip targets with both index and MRP fingers, which they did in blocks of finger group specific trials. Decoding from motor signals online, the ReFIT Kalman Filter reliably outperformed the standard Kalman Filter, measured by bit rate, across all tested finger groups and movements by 31.0% and 35.2%. These decoders were robust when the manipulandum was removed during online control. While index finger movements and middle-ring-pinkie finger movements could be differentiated from each other with 81.7\% accuracy across both subjects, the linear Kalman Filter was not sufficient for decoding both finger groups together due to significant unwanted movement in the stationary finger, potentially due to co-contraction. Significance. To our knowledge, this is the first systematic and biomimetic separation of digits for continuous online decoding in a NHP as well as the first demonstration of the ReFIT Kalman Filter improving the performance of precise finger decoding. These results suggest that novel nonlinear approaches, apparently not necessary for center out reaches or gross hand motions may be necessary to achieve many degree of freedom control of the fingers}{independent and precise control of individual fingers.

Zachary T. Irwin - One of the best experts on this subject based on the ideXlab platform.

  • Cortical Decoding of Individual Finger Group Motions Using ReFIT Kalman Filter
    Frontiers Media S.A., 2018
    Co-Authors: Alex K. Vaskov, Zachary T. Irwin, Samuel R. Nason, Autumn J. Bullard, Mackenna Hill, Naia North
    Abstract:

    Objective: To date, many brain-machine interface (BMI) studies have developed decoding algorithms for neuroprostheses that provide users with precise control of upper arm reaches with some limited grasping capabilities. However, comparatively few have focused on quantifying the performance of precise finger control. Here we expand upon this work by investigating online control of individual finger groups.Approach: We have developed a novel training manipulandum for non-human primate (NHP) studies to isolate the movements of two specific finger groups: index and middle-ring-pinkie (MRP) fingers. We use this device in combination with the ReFIT (Recalibrated Feedback Intention-Trained) Kalman Filter to decode the position of each finger group during a single degree of freedom task in two rhesus macaques with Utah arrays in motor cortex. The ReFIT Kalman Filter uses a two-stage training approach that improves online control of upper arm tasks with substantial reductions in orbiting time, thus making it a logical first choice for precise finger control.Results: Both animals were able to reliably acquire fingertip targets with both index and MRP fingers, which they did in blocks of finger group specific trials. Decoding from motor signals online, the ReFIT Kalman Filter reliably outperformed the standard Kalman Filter, measured by bit rate, across all tested finger groups and movements by 31.0 and 35.2%. These decoders were robust when the manipulandum was removed during online control. While index finger movements and middle-ring-pinkie finger movements could be differentiated from each other with 81.7% accuracy across both subjects, the linear Kalman Filter was not sufficient for decoding both finger groups together due to significant unwanted movement in the stationary finger, potentially due to co-contraction.Significance: To our knowledge, this is the first systematic and biomimetic separation of digits for continuous online decoding in a NHP as well as the first demonstration of the ReFIT Kalman Filter improving the performance of precise finger decoding. These results suggest that novel nonlinear approaches, apparently not necessary for center out reaches or gross hand motions, may be necessary to achieve independent and precise control of individual fingers

  • cortical decoding of individual finger group motions using refit Kalman Filter
    Frontiers in Neuroscience, 2018
    Co-Authors: Alex K. Vaskov, Zachary T. Irwin, Samuel R. Nason, Autumn J. Bullard, Mackenna Hill, Naia North, Parag G Patil, Cynthia A Chestek
    Abstract:

    Objective. To date, many brain-machine interface (BMI) studies have developed decoding algorithms for neuroprostheses that provide users with precise control of upper arm reaches with some limited grasping capabilities. However, comparatively few have focused on quantifying the performance of precise finger control. Here we expand upon this work by investigating online control of individual finger groups. Approach. We have developed a novel training manipulandum for non-human primate (NHP) studies to isolate the movements of two specific finger groups: index and middle-ring-pinkie (MRP) fingers. We use this device in combination with the ReFIT (Recalibrated Feedback Intention-Trained) Kalman Filter to decode the position of each finger group during a single degree of freedom task in two rhesus macaques with Utah arrays in motor cortex. The ReFIT Kalman Filter uses a two-stage training approach that improves online control of upper arm tasks with substantial reductions in orbiting time, thus making it a logical first choice for precise finger control. Results. Both animals were able to reliably acquire fingertip targets with both index and MRP fingers, which they did in blocks of finger group specific trials. Decoding from motor signals online, the ReFIT Kalman Filter reliably outperformed the standard Kalman Filter, measured by bit rate, across all tested finger groups and movements by 31.0% and 35.2%. These decoders were robust when the manipulandum was removed during online control. While index finger movements and middle-ring-pinkie finger movements could be differentiated from each other with 81.7\% accuracy across both subjects, the linear Kalman Filter was not sufficient for decoding both finger groups together due to significant unwanted movement in the stationary finger, potentially due to co-contraction. Significance. To our knowledge, this is the first systematic and biomimetic separation of digits for continuous online decoding in a NHP as well as the first demonstration of the ReFIT Kalman Filter improving the performance of precise finger decoding. These results suggest that novel nonlinear approaches, apparently not necessary for center out reaches or gross hand motions may be necessary to achieve many degree of freedom control of the fingers}{independent and precise control of individual fingers.