Topic
Invariant extended Kalman filter
About: Invariant extended Kalman filter is a research topic. Over the lifetime, 7079 publications have been published within this topic receiving 187702 citations.
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TL;DR: A novel formulation of the Kalman filter for Tobit Type 1 censored measurements is introduced, called the TobitKalman filter, which is identical to the standard Kalman Filter in the no-censoring case.
Abstract: Tobit model censored data arise in multiple engineering applications through saturating sensors, limit-of-detection effects, and image frame effects. In this brief, we introduce a novel formulation of the Kalman filter for Tobit Type 1 censored measurements. Our proposed formulation, called the Tobit Kalman filter, is identical to the standard Kalman filter in the no-censoring case. At or near the censored region, the Tobit Kalman filter utilizes a local approximation of the probability of censoring in order to provide a fully recursive estimate of the state and state error covariance. The additional computational burden of the method compared with the standard Kalman filter is limited to the calculation of $m$ normal probability density functions and $m$ normal cumulative density functions per update, where $m$ is the number of measurements.
82 citations
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TL;DR: In this paper, an adaptive speed and flux estimation method based on the multiple-model extended Kalman filter (EKF) with Markov chain for sensorless induction motor (IM) drives is proposed.
Abstract: To improve the performance of sensorless induction motor (IM) drives, an adaptive speed and flux estimation method based on the multiple-model extended Kalman filter (EKF) with Markov chain for IMs is proposed in this paper. In this algorithm, the multiple model EKF for speed and flux estimation is established, and the transition of the models obeys the Markov chain and the estimation value is obtained by mixing the outputs of different models in different weightings, and the calculation of the weighting is researched. Simultaneously, the transition probability can be continuously self-tuned by the residual sequence, the prior information is modified by the posterior information, and the more accurate transition among the models is obtained. Therefore, the proposed method improves the model adaptability to the actual systems and the environmental variations, and reduces the speed estimation error. The correctness and the effectiveness of the proposed method are verified by the simulation and experimental results.
82 citations
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TL;DR: In this paper, a closed form solution to the stationary discrete-time linear filtering problem is obtained explicitly in terms of the system state-space matrices in the limiting singular case where the measurement noise tends to zero.
Abstract: A closed form solution to the stationary discrete-time linear filtering problem is obtained explicitly in terms of the system state-space matrices in the limiting singular case where the measurement noise tends to zero Simple expressions, in closed form, are obtained for the Kalman gain matrix both for uniform and nonuniform rank systems and the explicit eigenstructure of the Kalman filter closed loop matrix is derived The minimum error covariance matrices of the a priori and a posteriori filtered estimates are obtained using this special eigenstructure, and a remarkably different behavior of the solution in the minimum- and nonminimum-phase cases is found
82 citations
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TL;DR: In this paper, the equivalence between Pontryagin optimization and the Kalman filter was analyzed for a simple assimilating model and a procedure for diagnosing the effect of model error based on the observational cost function was developed.
Abstract: Modern atmospheric data assimilation theory is dominated by the four-dimensional variational (4DVAR) and Kalman filter/smoother approaches. Both generate analysis weights (explicitly or implicitly) which are dynamically determined by the assimilation model. A Kalman smoother is basically a generalization of the Kalman filter which can process future observations. In control theory, a generalization of 4DVAR called Pontryagin optimization can account for an imperfect assimilating model. Pontryagin optimization and the fixed-interval Kalman smoother are equivalent when both methods use the same statistical information. We use the equivalence between Pontryagin optimization and the Kalman smoother to examine the effect of the perfect model assumption on the error statistics and analysis weights of the 4DVAR algorithm. This is done by developing the Kalman smoother equations for a very simple assimilating model. A procedure for diagnosing the effect of model error, based on the observational cost function, is also developed. DOI: 10.1034/j.1600-0870.1996.t01-1-00003.x
82 citations
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TL;DR: The results demonstrate that the mean time consumption and the root mean square error of pitch/roll estimation under magnetic disturbances are reduced by 45.9% and 33.8%, respectively, when compared with a standard filter.
Abstract: In order to reduce the computational complexity, and improve the pitch/roll estimation accuracy of the low-cost attitude heading reference system (AHRS) under conditions of magnetic-distortion, a novel linear Kalman filter, suitable for nonlinear attitude estimation, is proposed in this paper. The new algorithm is the combination of two-step geometrically-intuitive correction (TGIC) and the Kalman filter. In the proposed algorithm, the sequential two-step geometrically-intuitive correction scheme is used to make the current estimation of pitch/roll immune to magnetic distortion. Meanwhile, the TGIC produces a computed quaternion input for the Kalman filter, which avoids the linearization error of measurement equations and reduces the computational complexity. Several experiments have been carried out to validate the performance of the filter design. The results demonstrate that the mean time consumption and the root mean square error (RMSE) of pitch/roll estimation under magnetic disturbances are reduced by 45.9% and 33.8%, respectively, when compared with a standard filter. In addition, the proposed filter is applicable for attitude estimation under various dynamic conditions.
82 citations