Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches

By Dan Simon. 2006

3,332 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/231b5f02444562e43eec48eceea42c706c4fc997

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Citations in the corpus

State Estimation and Control of Electric Loads to Manage Real-Time Energy Imbalance (2013, methodology): “For Scenarios 1–3, we designed a standard Kalman filter [35] using the MATLAB function kalman on the identified system:”
Analytic moment-based Gaussian process filtering (2009, unknown): “For example, the Extended Kalman Filter (EKF) linearizes the transition and measurement functions by means of a Taylor series expansion and applies the Kalman ﬁlter to propagate full densities through them (Simon, 2006).”
Build Your Own Quadrotor: Open-Source Projects on Unmanned Aerial Vehicles (2012, methodology): “Here, we provide only an overview of the EKF-based attitude estimation of the Openpilot project, and the complete EKF algorithm can be found in [20].”
Cooperative Collision Avoidance at Intersections: Algorithms and Experiments (2013, background): “By nature of the fixed rate of measurements (discrete-time) and continuous-time inputs, the filter is said to be hybrid [25].”
The Three-Pass Regression Filter: A New Approach to Forecasting Using Many Predictors (2015, methodology): “In contrast, the PCR forecast is asymptotically efficient when there are as many predictive factors as the total number of factors driving xt (Stock and Watson (2002a)).”
Robust Kalman filtering based on Mahalanobis distance as outlier judging criterion (2014, methodology): “Although there were no assumptions of Gaussian-distributed process or measurement noises in the seminal paper (Kalman 1960), it can be proven that only when the above assumptions hold, KF is optimal, i.e., that it has minimal mean squared error, and is unbiased and consistent (Simon 2006, p 130).”
SMOOTH VARIABLE STRUCTURE FILTERING: THEORY AND APPLICATIONS (2011, methodology): “The KF assumes that the system model is known and linear, the system and measurement noises are white, and the states have initial conditions with known means and variances [28,34].”
Industrial Applications of the Kalman Filter: A Review (2013, background): “In such cases, designers prefer to use unscented Kalman filters (UKFs) for their superiority [10], [60]–[63].”
Methods for Estimating State and Measurement Noise Covariance Matrices: Aspects and Comparison (2009, unknown): “[Simon, 2006], was shown in [Wiberg and DeWolf, 1993] for continuous-time systems and in [Wiberg et al.”
A Constrained Formulation for Hybrid State Estimation (2011, methodology): “The classical method does not provide any extra information about higher order terms [14].”
An Overview to Visual Odometry and Visual SLAM: Applications to Mobile Robotics (2015, background): “Another difference between the two filters is that the estimation error in a UKF does not converge to zero, whereas the estimation error in a particle filter converges to zero as the number of particles approaches infinity (at the expense of computational complexity) [105].”
Fusion of Multirate Measurements for Nonlinear Dynamic State Estimation of the Power Systems (2019, methodology): “In order to apply the standard Kalman filtering equations [28], both the system dynamical equation and measurements should be obtained at the same sampling rate, which is not true here.”
State Estimation for Robotics (2017, methodology): “This approach was inspired by and builds on the works of Su and Lee (1991, 1992); Chirikjian and Kyatkin (2001); Smith et al. (2003); Wang and Chirikjian (2006, 2008); Chirikjian (2009); Wolfe et al. (2011); Long et al.”
INTERACTION Dataset: An INTERnational, Adversarial and Cooperative moTION Dataset in Interactive Driving Scenarios with Semantic Maps (2019, background): “smooth motions of the vehicles, a Rauch-Tung-Striebel (RTS) smoother [27] is also incorporated.”
Monte Carlo Simulation (2010, methodology): “Revision History: bc1d11, 31/01/2018, version 4 Page 2 of 5 1 Estimating ππ using Monte Carlo Method Consider a unit circle (a circle of radius 1 whose centre is at (0,0)) on a Cartesian plane, and a square whose corners are at (-1,1), (1,1), (1,-1), and (-1,-1) (shown below in Figure 1).”
Seizure prediction with spectral power of EEG using cost‐sensitive support vector machines (2011, methodology): “To eliminate these isolated FPs and FNs, we postprocess the SVM classification output using the Kalman filter (Simon, 2006; Chisci et al., 2010).”