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.

Iterative Smooth Variable Structure Filter for Parameter Estimation

2011 ◽  
Vol 2011 ◽  
pp. 1-18 ◽  
Author(s):  
Mohammad Al-Shabi ◽  
Saeid Habibi
Keyword(s):  
Parameter Estimation ◽  
Sliding Mode ◽  
Estimation Method ◽  
Variable Structure ◽  
Model Parameters ◽  
Modeling Uncertainties ◽  
Control Concept ◽  
Chattering Effect ◽  
Combined Strategy ◽  
Smooth Variable Structure Filter

The smooth variable structure filter (SVSF) is a recently proposed predictor-corrector filter for state and parameter estimation. The SVSF is based on the sliding mode control concept. It defines a hyperplane in terms of the state trajectory and then applies a discontinuous corrective action that forces the estimate to go back and forth across that hyperplane. The SVSF is robust and stable to modeling uncertainties making it suitable for fault detection application. The discontinuous action of the SVSF results in a chattering effect that can be used to correct modeling errors and uncertainties in conjunction with adaptive strategies. In this paper, the SVSF is complemented with a novel parameter estimation technique referred to as the iterative bi-section/shooting method (IBSS). This combined strategy is used for estimating model parameters and states for systems in which only the model structure is known. This combination improves the performance of the SVSF in terms of rate of convergence, robustness, and stability. The benefits of the proposed estimation method are demonstrated by its application to an electrohydrostatic actuator.

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 VIAE-Net: An End-to-End Altitude Estimation through Monocular Vision and Inertial Feature Fusion Neural Networks for UAV Autonomous Landing

Sensors ◽  
2021 ◽  
Vol 21 (18) ◽  
pp. 6302
Author(s):  
Xupei Zhang ◽  
Zhanzhuang He ◽  
Zhong Ma ◽  
Peng Jun ◽  
Kun Yang
Keyword(s):  
Neural Network ◽  
Network Architecture ◽  
Feature Fusion ◽  
Estimation Error ◽  
Estimation Method ◽  
Signal Interference ◽  
Estimation Accuracy ◽  
Measurement Unit ◽  
End To End ◽  
Altitude Estimation

Altitude estimation is one of the fundamental tasks of unmanned aerial vehicle (UAV) automatic navigation, where it aims to accurately and robustly estimate the relative altitude between the UAV and specific areas. However, most methods rely on auxiliary signal reception or expensive equipment, which are not always available, or applicable owing to signal interference, cost or power-consuming limitations in real application scenarios. In addition, fixed-wing UAVs have more complex kinematic models than vertical take-off and landing UAVs. Therefore, an altitude estimation method which can be robustly applied in a GPS denied environment for fixed-wing UAVs must be considered. In this paper, we present a method for high-precision altitude estimation that combines the vision information from a monocular camera and poses information from the inertial measurement unit (IMU) through a novel end-to-end deep neural network architecture. Our method has numerous advantages over existing approaches. First, we utilize the visual-inertial information and physics-based reasoning to build an ideal altitude model that provides general applicability and data efficiency for neural network learning. A further advantage is that we have designed a novel feature fusion module to simplify the tedious manual calibration and synchronization of the camera and IMU, which are required for the standard visual or visual-inertial methods to obtain the data association for altitude estimation modeling. Finally, the proposed method was evaluated, and validated using real flight data obtained during a fixed-wing UAV landing phase. The results show the average estimation error of our method is less than 3% of the actual altitude, which vastly improves the altitude estimation accuracy compared to other visual and visual-inertial based methods.

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 A Sparse-Based Off-Grid DOA Estimation Method for Coprime Arrays

Sensors ◽  
2018 ◽  
Vol 18 (9) ◽  
pp. 3025 ◽  
Author(s):  
Weijian Si ◽  
Fuhong Zeng ◽  
Changbo Hou ◽  
Zhanli Peng
Keyword(s):  
Covariance Matrix ◽  
Estimation Error ◽  
Estimation Method ◽  
Doa Estimation ◽  
Sample Covariance Matrix ◽  
Estimation Methods ◽  
Matrix Estimation ◽  
Estimation Process ◽  
Sample Covariance ◽  
Coprime Arrays

Recently, many sparse-based direction-of-arrival (DOA) estimation methods for coprime arrays have become popular for their excellent detection performance. However, these methods often suffer from grid mismatch problem due to the discretization of the potential angle space, which will cause DOA estimation performance degradation when the target is off-grid. To this end, we proposed a sparse-based off-grid DOA estimation method for coprime arrays in this paper, which includes two parts: coarse estimation process and fine estimation process. In the coarse estimation process, the grid points closest to the true DOAs, named coarse DOAs, are derived by solving an optimization problem, which is constructed according to the statistical property of the vectorized covariance matrix estimation error. Meanwhile, we eliminate the unknown noise variance effectively through a linear transformation. Due to finite snapshots effect, some undesirable correlation terms between signal and noise vectors exist in the sample covariance matrix. In the fine estimation process, we therefore remove the undesirable correlation terms from the sample covariance matrix first, and then utilize a two-step iterative method to update the grid biases. Combining the coarse DOAs with the grid biases, the final DOAs can be obtained. In the end, simulation results verify the effectiveness of the proposed method.

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 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.

Aircraft parameter estimation using a new filtering technique based upon a neural network and Gauss-Newton method

2009 ◽  
Vol 113 (1142) ◽  
pp. 243-252 ◽  
Author(s):  
N. K. Peyada ◽  
A. K. Ghosh
Keyword(s):  
Neural Network ◽  
Parameter Estimation ◽  
Dynamic Model ◽  
Newton Method ◽  
Initial Conditions ◽  
Estimation Method ◽  
Wind Tunnel Test ◽  
Neural Model ◽  
Estimation Methods ◽  
Flight Data

Abstract A new parameter estimation method based upon neural network is proposed. The method proposed here uses feed forward neural networks to establish a neural model that could be used to predict subsequent time histories given the suitable measured initial conditions. The proposed neural model would not represent a generic flight dynamic model. The neural model in this case develops point to point fitting of the input and the output data. Thus, it could at best be referred to as flight dynamic model in restricted sense. Gauss-Newton method is then used to obtain optimal values of the aerodynamic parameters by minimising a suitable defined error cost function. The method has been validated using longitudinal and lateral-directional flight data of various test aircraft. The results thus obtained were compared with those obtained through wind tunnel test, or those obtained using Maximum likelihood and/or Filter error methods. Unlike, most of the parameter estimation methods, the proposed method does not require a prior description of the model. It also bypasses the requirement of solving equations of motion. This feature of the proposed method may have special significance in handling flight data of an unstable aircraft.

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.

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