scholarly journals Gait Phase Estimation Based on User–Walker Interaction Force

2021 ◽  
Vol 11 (17) ◽  
pp. 7888
Author(s):  
Pengcheng Li ◽  
Yasuhiro Akiyama ◽  
Xianglong Wan ◽  
Kazunori Yamada ◽  
Mayu Yokoya ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Estimation Error ◽  
Estimation Method ◽  
Time Estimation ◽  
Force Sensor ◽  
Interaction Force ◽  
Gait Parameter ◽  
Multiple Model ◽  
Estimation Performance ◽  
Gait Phase

Smart walkers have been developed for assistance and rehabilitation of elderly people and patients with physical health conditions. A force sensor mounted under the handle is widely used in smart walkers to establish a human–machine interface. The interaction force can be used to control the walker and estimate gait parameters using methods such as the Kalman filter for real-time estimation. However, the estimation performance decreases when the peaks of the interaction force are not captured. To improve the stability and accuracy of gait parameter estimation, we propose an online estimation method to continuously estimate the gait phase and cadence. A multiple model switching mechanism is introduced to improve the estimation performance when gait is asymmetric, and an adaptive rule is proposed to improve the estimation robustness and accuracy. Simulations and experiments demonstrate the effectiveness and accuracy of the proposed gait parameter estimation method. Here, the average estimation error for the gait phase is 0.691 rad when the gait is symmetric and 0.722 rad when it is asymmetric.

Lower Bound on the Accuracy of Parameter Estimation Methods for Linear Sensorimotor Synchronization Models

2015 ◽  
Vol 3 (1-2) ◽  
pp. 32-51 ◽  
Author(s):  
Nori Jacoby ◽  
Peter E. Keller ◽  
Bruno H. Repp ◽  
Merav Ahissar ◽  
Naftali Tishby
Keyword(s):  
Parameter Estimation ◽  
Lower Bound ◽  
Computational Models ◽  
Linear Models ◽  
Estimation Error ◽  
Explanatory Power ◽  
Estimation Method ◽  
Sensorimotor Synchronization ◽  
Estimation Methods ◽  
Unbiased Estimation

The mechanisms that support sensorimotor synchronization — that is, the temporal coordination of movement with an external rhythm — are often investigated using linear computational models. The main method used for estimating the parameters of this type of model was established in the seminal work of Vorberg and Schulze (2002), and is based on fitting the model to the observed auto-covariance function of asynchronies between movements and pacing events. Vorberg and Schulze also identified the problem of parameter interdependence, namely, that different sets of parameters might yield almost identical fits, and therefore the estimation method cannot determine the parameters uniquely. This problem results in a large estimation error and bias, thereby limiting the explanatory power of existing linear models of sensorimotor synchronization. We present a mathematical analysis of the parameter interdependence problem. By applying the Cramér–Rao lower bound, a general lower bound limiting the accuracy of any parameter estimation procedure, we prove that the mathematical structure of the linear models used in the literature determines that this problem cannot be resolved by any unbiased estimation method without adopting further assumptions. We then show that adding a simple and empirically justified constraint on the parameter space — assuming a relationship between the variances of the noise terms in the model — resolves the problem. In a follow-up paper in this volume, we present a novel estimation technique that uses this constraint in conjunction with matrix algebra to reliably estimate the parameters of almost all linear models used in the literature.

scholarly journals Diffusion Logarithm-Correntropy Algorithm for Parameter Estimation in Non-Stationary Environments over Sensor Networks

Sensors ◽  
2018 ◽  
Vol 18 (10) ◽  
pp. 3381 ◽  
Author(s):  
Limei Hu ◽  
Feng Chen ◽  
Shukai Duan ◽  
Lidan Wang
Keyword(s):  
Parameter Estimation ◽  
Sensor Networks ◽  
Unknown Parameter ◽  
Estimation Error ◽  
Tracking Performance ◽  
Time Varying ◽  
Parameter Vector ◽  
Parameter Estimation Problem ◽  
Estimation Performance ◽  
Unknown Parameter Vector

This paper considers the parameter estimation problem under non-stationary environments in sensor networks. The unknown parameter vector is considered to be a time-varying sequence. To further promote estimation performance, this paper suggests a novel diffusion logarithm-correntropy algorithm for each node in the network. Such an algorithm can adopt both the logarithm operation and correntropy criterion to the estimation error. Moreover, if the error gets larger due to the non-stationary environments, the algorithm can respond immediately by taking relatively steeper steps. Thus, the proposed algorithm achieves smaller error in time. The tracking performance of the proposed logarithm-correntropy algorithm is analyzed. Finally, experiments verify the validity of the proposed algorithmic schemes, which are compared to other recent algorithms that have been proposed for parameter estimation.

scholarly journals Consensus-Based Distributed Target Tracking with False Data Injection Attacks over Radar Network

2021 ◽  
Vol 11 (10) ◽  
pp. 4564
Author(s):  
Yongtao Shui ◽  
Yu Wang ◽  
Yu Li ◽  
Yongzhi Shan ◽  
Naigang Cui ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
State Estimation ◽  
Target Tracking ◽  
Estimation Error ◽  
Estimation Method ◽  
Estimation Accuracy ◽  
Consensus Method ◽  
False Data Injection ◽  
Radar Network ◽  
Global Consistency

For target tracking in radar network, any anomaly in a part of the system can quickly spread over the network and lead to tracking failures. False data injection (FDI) attacks can damage the state estimation mechanism by modifying the radar measurements with unknown and time-varying attack variables, therefore making traditional filters inapplicable. To tackle this problem, we propose a novel consensus-based distributed state estimation (DSE) method for target tracking with FDI attacks, which is effective even when all radars are under FDI attacks. First, a real-time residual-based detector is introduced to the DSE framework, which can effectively detect FDI attacks by analyzing the statistical properties of the residual. Secondly, a simple yet effective attack parameter estimation method is proposed to provide attack parameter estimation based on a pseudo-measurement equation, which has the advantage of decoupled estimation of state and attack parameters compared with augmented state filters. Finally, for timely attack mitigation and global consistency achievement, a novel hybrid consensus method is proposed which can compensate for the estimation error caused by FDI attacks and provide estimation accuracy improvement. The simulation results show that the proposed solution is effective and superior to the traditional DSE method for target tracking in the presence of FDI attacks.

scholarly journals Auto-SOM: Recursive Parameter Estimation for Guidance of Self-Organizing Feature Maps

2001 ◽  
Vol 13 (3) ◽  
pp. 595-619 ◽  
Author(s):  
Karin Haese ◽  
Geoffrey J. Goodhill
Keyword(s):  
Parameter Estimation ◽  
Kalman Filter ◽  
Estimation Error ◽  
Estimation Method ◽  
Original Form ◽  
Self Organizing Map ◽  
Feature Maps ◽  
Parameter Estimation Method ◽  
Recursive Parameter Estimation ◽  
Self Organizing

An important technique for exploratory data analysis is to form a mapping from the high-dimensional data space to a low-dimensional representation space such that neighborhoods are preserved. A popular method for achieving this is Kohonen's self-organizing map (SOM) algorithm. However, in its original form, this requires the user to choose the values of several parameters heuristically to achieve good performance. Here we present the Auto-SOM, an algorithm that estimates the learning parameters during the training of SOMs automatically. The application of Auto-SOM provides the facility to avoid neighborhood violations up to a user-defined degree in either mapping direction. Auto-SOM consists of a Kalman filter implementation of the SOM coupled with a recursive parameter estimation method. The Kalman filter trains the neurons' weights with estimated learning coefficients so as to minimize the variance of the estimation error. The recursive parameter estimation method estimates the width of the neighborhood function by minimizing the prediction error variance of the Kalman filter. In addition, the “topographic function” is incorporated to measure neighborhood violations and prevent the map's converging to configurations with neighborhood violations. It is demonstrated that neighborhoods can be preserved in both mapping directions as desired for dimension-reducing applications. The development of neighborhood-preserving maps and their convergence behavior is demonstrated by three examples accounting for the basic applications of self-organizing feature maps.

scholarly journals Parameter estimation and empirical analysis of fractional O-U process based on three machine learning algorithms

2021 ◽  
Author(s):  
Yicun Li ◽  
Yuanyang Teng
Keyword(s):  
Machine Learning ◽  
Genetic Algorithm ◽  
Parameter Estimation ◽  
Newton Method ◽  
Estimation Error ◽  
Estimation Method ◽  
Machine Learning Algorithms ◽  
Stock Index ◽  
Stock Index Futures ◽  
Discrete Observations

Abstract Fractional O-U process is a very classical stochastic process which is used to describe the time series of financial volatility. Three parameters need to be estimated in this process, and the estimation method based on discrete observations can be realized by machine learning optimization algorithm. In this study, the parameter estimation method of fractional O-U process is briefly described, and three optimization algorithms, Newton method, quasi Newton method and genetic algorithm, are used to estimate the parameters. The comparison shows that genetic algorithm is relatively accurate and efficient. Finally, the minute data of stock index futures are estimated based on fractional O-U process. The results show that the estimation of theta and Hurst index is relatively accurate, and the estimation error of volatility is large.

A constant guidance law-based collision avoidance for unmanned aerial vehicles

2018 ◽  
Vol 233 (4) ◽  
pp. 1204-1216 ◽  
Author(s):  
Wendong Gai ◽  
Ning Zhang ◽  
Jing Zhang ◽  
Yuxia Li
Keyword(s):  
Collision Avoidance ◽  
Attitude Control ◽  
Estimation Error ◽  
Sufficient Conditions ◽  
Estimation Method ◽  
Time Estimation ◽  
System Stability ◽  
Guidance Law ◽  
Tracking Differentiator ◽  
Dynamic Inverse

A method of automatic collision avoidance based on constant guidance law is proposed to solve the problem that the collision avoidance time is difficult to be estimated accurately during the collision avoidance process. The guidance command of the collision avoidance method is constant, and the lower bound of the constant guidance command satisfying the safe collision avoidance requirement is given by geometric method. Then, a collision avoidance time estimation method based on particle swarm optimization is proposed. In addition, the attitude control loop adopts the nonlinear proportional-integral-derivative based on tracking-differentiator, and the sufficient conditions for the system stability are given using the T-passive method. The simulation results show that the collision avoidance time estimation error is small and the maneuvering range of collision avoidance is smaller than the collision avoidance method based on proportional guidance and nonlinear dynamic inverse guidance. This method can achieve collision avoidance under the influence of wind disturbance and safety distance abrupt change.

Parameter Estimation Using a Combined Variable Structure and Kalman Filtering Approach

2008 ◽  
Vol 130 (5) ◽  
Author(s):  
Saeid Habibi
Keyword(s):  
Neural Network ◽  
Parameter Estimation ◽  
Estimation Error ◽  
Estimation Method ◽  
Variable Structure ◽  
Network Adaptation ◽  
Estimation Process ◽  
Multiple Indicators ◽  
Modeling Uncertainties

A method that is often used for parameter estimation is the extended Kalman filter (EKF). EKF is a model-based strategy that implicitly considers the effect of modeling uncertainties. This implicit consideration often leads to the tuning of the filter by trial and error. When formulated for parameter estimation, the “tuned” EKF becomes sensitive to uncertainties in its internal model. The EKF’s robustness can be improved by combining it with the recently proposed variable structure filter (VSF) concept. In a combined form, the modeling uncertainties no longer affect stability, but impact the performance and the quality of the estimation process. Furthermore, the VSF concept provides a secondary set of indicators of performance that is in addition to the estimation error and that pertains to the range of parametric uncertainties. As such, the robustness of the combined method and its multiple indicators of performance allow the use of intelligent adaptation for improving the performance of the estimation process. For real-time applications, online neural network adaptation may be used to improve the performance by progressively reducing specific modeling uncertainties in the system. In this paper, a new parameter estimation method that uses concepts associated with the EKF, the VSF, and neural network adaptation is introduced. The performance of this method is considered and discussed for applications that involve parameter estimation such as fault detection.

Temporal Prediction Errors Affect Short-Term Memory Scanning Response Time

2016 ◽  
Vol 63 (6) ◽  
pp. 333-342
Author(s):  
Roberto Limongi ◽  
Angélica M. Silva
Keyword(s):  
Response Time ◽  
Short Term Memory ◽  
Estimation Error ◽  
Predictive Coding ◽  
Time Estimation ◽  
Prediction Errors ◽  
Memory Scanning ◽  
Short Term ◽  
Term Memory ◽  
Temporal Prediction

Abstract. The Sternberg short-term memory scanning task has been used to unveil cognitive operations involved in time perception. Participants produce time intervals during the task, and the researcher explores how task performance affects interval production – where time estimation error is the dependent variable of interest. The perspective of predictive behavior regards time estimation error as a temporal prediction error (PE), an independent variable that controls cognition, behavior, and learning. Based on this perspective, we investigated whether temporal PEs affect short-term memory scanning. Participants performed temporal predictions while they maintained information in memory. Model inference revealed that PEs affected memory scanning response time independently of the memory-set size effect. We discuss the results within the context of formal and mechanistic models of short-term memory scanning and predictive coding, a Bayes-based theory of brain function. We state the hypothesis that our finding could be associated with weak frontostriatal connections and weak striatal activity.

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