In target tracking, the measurements collected by sensors can be biased in some real scenarios, e.g., due to systematic error. To accurately estimate the target trajectory, it is essential that the measurement bias be...In target tracking, the measurements collected by sensors can be biased in some real scenarios, e.g., due to systematic error. To accurately estimate the target trajectory, it is essential that the measurement bias be identified in the first place. We investigate the iterative bias estimation process based on the expectation-maximization（EM）algorithm, for cases where sufficiently large numbers of measurements are at hand. With the assistance of extended Kalman filtering and smoothing, we derive two EM estimation processes to estimate the measurement bias which is formulated as a random variable in one state-space model and a constant value in another. More importantly,we theoretically derive the global convergence result of the EM-based measurement bias estimation and reveal the link between the two proposed EM estimation processes in the respective state-space models. It is found that the bias estimate in the second state-space model is more accurate and of less complexity. Furthermore, the EM-based iterative estimation converges faster in the second state-space model than in the first one. As a byproduct, the target trajectory can be simultaneously estimated with the measurement bias, after processing a batch of measurements.These results are confirmed by our simulations.展开更多
In Einstein-aether theory,violating Lorentz invariance permits some super-luminal communications,and the universal horizon can trap excitations traveling at arbitrarily high velocities.To better understand the nature ...In Einstein-aether theory,violating Lorentz invariance permits some super-luminal communications,and the universal horizon can trap excitations traveling at arbitrarily high velocities.To better understand the nature of these universal horizons,we first modify the ray tracing method,and then use it to study their surface gravity in charged Einstein-aether black hole spacetime.Instead of the previous result by Cropp et al.,our results show that the surface gravity of the universal horizon is dependent on the specific dispersion relation,k_(uh)-2(z-1)k_(uh)/z,where z denotes the power of the leading term in the superluminal dispersion relation,characterizing different species of particles.And the associated Hawking temperatures also are different with z.These findings,which coincide with those derived by the tunneling method,provide some full understanding of black hole thermodynamics in Lorentz-violating theories.展开更多
基金supported by the National Natural Science Foundation of China(No.61601254)the KC Wong Magna Fund of Ningbo University,China
文摘In target tracking, the measurements collected by sensors can be biased in some real scenarios, e.g., due to systematic error. To accurately estimate the target trajectory, it is essential that the measurement bias be identified in the first place. We investigate the iterative bias estimation process based on the expectation-maximization（EM）algorithm, for cases where sufficiently large numbers of measurements are at hand. With the assistance of extended Kalman filtering and smoothing, we derive two EM estimation processes to estimate the measurement bias which is formulated as a random variable in one state-space model and a constant value in another. More importantly,we theoretically derive the global convergence result of the EM-based measurement bias estimation and reveal the link between the two proposed EM estimation processes in the respective state-space models. It is found that the bias estimate in the second state-space model is more accurate and of less complexity. Furthermore, the EM-based iterative estimation converges faster in the second state-space model than in the first one. As a byproduct, the target trajectory can be simultaneously estimated with the measurement bias, after processing a batch of measurements.These results are confirmed by our simulations.
基金supported by the National Natural Science Foundation of China(Grant No.11247013)Hunan Provincial Natural Science Foundation of China(Grant Nos.2015JJ2085,and QSQC1203)the Special Fund of the National Natural Science Foundation of China(Grant No.11447168)
文摘In Einstein-aether theory,violating Lorentz invariance permits some super-luminal communications,and the universal horizon can trap excitations traveling at arbitrarily high velocities.To better understand the nature of these universal horizons,we first modify the ray tracing method,and then use it to study their surface gravity in charged Einstein-aether black hole spacetime.Instead of the previous result by Cropp et al.,our results show that the surface gravity of the universal horizon is dependent on the specific dispersion relation,k_(uh)-2(z-1)k_(uh)/z,where z denotes the power of the leading term in the superluminal dispersion relation,characterizing different species of particles.And the associated Hawking temperatures also are different with z.These findings,which coincide with those derived by the tunneling method,provide some full understanding of black hole thermodynamics in Lorentz-violating theories.
