Covariance profiling for an adaptive Kalman filter to suppress sensor quantization effects (original) (raw)
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Measurement Noise Covariance-Adapting Kalman Filters for Varying Sensor Noise Situations
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Online Sensor Noise Covariance Identification Using a Modified Adaptive Filter
Volume 2: Mechatronics; Estimation and Identification; Uncertain Systems and Robustness; Path Planning and Motion Control; Tracking Control Systems; Multi-Agent and Networked Systems; Manufacturing; Intelligent Transportation and Vehicles; Sensors and Actuators; Diagnostics and Detection; Unmanne..., 2017
Modern control systems heavily relay on sensors for closed-loop feedback control. Degradation of sensor performance due to sensor aging affects the closed-loop system performance, reliability, and stability. Sensor aging characterized by the sensor measurement noise covariance. This paper proposes an algorithm used to identify the slow varying sensor noise covariance online based on system sensor measurements. The covariance-matching technique, along with the adaptive Kalman filter is utilized based on the information about the quality of weighted innovation sequence to estimate the slow time-varying sensor noise covariance. The sequential manner of the proposed algorithm leads to significant reduction of the computational load. The covariance-matching of the weighted innovation sequence improves the prediction accuracy and reduces the computational load, which makes it suitable for online applications. Simulation results show that the proposed algorithm is capable of estimating the...
Decorrelated unbiased converted measurement Kalman filter
IEEE Transactions on Aerospace and Electronic Systems, 2014
Converted measurement tracking is a technique that filters in the coordinate system where the underlying process of interest is linear and Gaussian, and requires the measurements to be nonlinearly transformed to fit. The goal of the transformation is to allow for tracking in the coordinate system that is most natural for describing system dynamics.
arXiv: Optimization and Control, 2015
Traditional statements of the celebrated Kalman filter algorithm focus on the estimation of state, but not the output. For any outputs, measured or auxiliary, it is usually assumed that the posterior state estimates and known inputs are enough to generate the minimum variance output estimate, given by yn|n = Cxn|n + Dun. Same equation is implemented in most popular control design toolboxes. It will be shown that when measurement and process noises are correlated, or when the process noise directly feeds into measurements, this equation is no longer optimal, and a correcting term is needed in above output estimation. This natural extension can allow designer to simplify noise modeling, reduce estimator order, improve robustness to unknown noise models as well as estimate unknown input, when expressed as an auxiliary output. This is directly applicable in motion control applications which exhibits such feed-through, such as estimating disturbance thrust affecting the accelerometer mea...
Process and Measurement Noise Estimation for Kalman Filtering
Conference Proceedings of the Society for Experimental Mechanics Series, 2011
The Kalman filter gain can be extracted from output signals but the covariance of the state error cannot be evaluated without knowledge of the covariance of the process and measurement noise Q and R. Among the methods that have been developed to estimate Q and R from measurements the two that have received most attention are based on linear relations between these matrices and: 1) the covariance function of the innovations from any stable filter or 2) the covariance function of the output measurements. This paper reviews the two approaches and offers some observations regarding how the initial estimate of the gain in the innovations approach may affect accuracy.
In this paper is study the role of Measurement noise covariance R and Process noise covariance Q. As both the parameter in the Kalman filter is a important parameter to decide the estimation closeness to the True value , Speed and Bandwidth [1]. First of the most important work in integration is to consider the realistic dynamic model covariance matrix Q and measurement noise covariance matrix R for work in the Kalman filter. The performance of the methods to estimate and calculate both of these matrices depends entirely on the minimization of dynamic and measurement update errors that lead the filter to converge[2]. This paper evaluates the performances of Kalman filter method with different adaptations in Q and in R. This paper perform the estimation for different value of Q and R and make a study that how Q and R affects the estimation and how much it differ to true value to the estimated value by plot in graph for different value of Q and R as well as we give a that give the brief idea of error in estimation and true value by the help of the MATLAB.
Stochastic Environmental Research and Risk Assessment (SERRA), 2003
Least squares (LS) techniques, like Kalman filtering, are widely used in environmental science and engineering. In this paper, a new general approach is introduced for the study of the generation, propagation and accumulation of the quantization error in any algorithm. This methodology employs a number of fundamental propositions demonstrating the way the four operations addition, multiplication, division and subtraction, influence quantization error generation and transmission. Using these, one can obtain knowledge of the exact number of erroneous digits with which all quantities of any algorithm are computed at each step of it. This methodology offers understanding of the actual cause of the generation and propagation of finite precision error in any computational scheme. Application of this approach to all Kalman type LS algorithms shows that not all their formulas are equivalent concerning the quantization error effects. More specifically, few generate the greater amount of quantization error. Finally, a stabilization procedure, applicable to all Kalman type algorithms, is introduced that renders all these algorithms very robust.
Quantization Effects and Stabilization of the Fast-Kalman Algorithm
EURASIP Journal on Advances in Signal Processing, 2001
The exact and actual cause of the failure of the fast-Kalman algorithm due to the generation and propagation of finite-precision or quantization error is presented. It is demonstrated that out of all the formulas that constitute this fast Recursive Least Squares (RLS) scheme only three generate an amount of finite-precision error that consistently propagates in the subsequent iterations and eventually makes the algorithm fail after a certain number of recursions. Moreover, it is shown that there is a very limited number of specific formulas that transmit the generated finite-precision error, while there is another class of formulas that lift or "relax" this error. In addition, a number of general propositions is presented that allow for the calculation of the exact number of erroneous digits with which the various quantities of the fast-Kalman scheme are computed, including the filter coefficients. On the basis of the previous analysis a method of stabilization of the fast-Kalman algorithm is developed and is presented here, a method that allows for the fast-Kalman algorithm to follow very difficult signals such as music, speech, environmental noise, and other nonstationary ones. Finally, a general methodology is pointed out, that allows for the development of new algorithms which, intrinsically, suffer far less of finite-precision problems.
Embedded Kalman Filter for Inertial Measurement Unit (IMU) on the ATMega8535
2012 International Symposium on Innovations in Intelligent Systems and Applications, 2012
The Kalman Filter is very useful in prediction and estimation. In this paper, the Kalman Filter is implemented for Inertial Measurement Unit (IMU) on the ATMega8535. The sensors used in this system are accelerometer MMA7260QT and gyroscope GS-12. The system chooses the arbitrary sampling time and then it is evaluated for possible using smaller value. As the Kalman Filter operation needs matrix calculation, the formula is converted into several ordinary equations. The parameter being investigated in this paper is measurement covariance matrix. This parameter influences the way the Kalman Filter responses to noise. Bigger value makes the Kalman Filter less sensitive to noise and the estimation is too smooth, thus it does not give real angle estimation. Using smaller value makes the Kalman Filter more sensitive to noise. This makes the estimated angle still suffers from noise and it is likely that the Kalman Filter is useless. This paper recommends 0.0001 to 0.001 for the measurement covariance noise parameter. This paper also recommended a pipeline configuration if the control algorithm needs more space in a sampling time.