Performance analysis of two EM-based measurement bias estimation processes for tracking systems

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.

On extended state based Kalman filter for nonlinear time-varying uncertain systems with measurement bias

This paper addresses the state estimation for a class of nonlinear time-varying stochastic systems with both uncertain dynam-ics and unknown measurement bias.A novel extended state based Kalman filter(ESKF)algorithm is developed to estimate the original state,the uncertain dynamics and the measurement bias.It is shown that the estimation error of the proposed algorithm is bounded in the mean square sense.Also,the estimation of the measurement bias asymptotically converges to its true value,such that the infuence of measurement bias is eliminated.Furthermore,the asymptotic optimality of the estima-tion result is proved while the uncertain dynamics approaches to a constant vector.Finally,a simulation study for harmonic oscillator system model is provided to ilustrate the effectiveness of proposed method.

Intergenerational Transmission of Income Gap for Chinese Urban and Rural Households

An accurate understanding of the intergenerational transmission of income gap is the foundation for theoretical research and policy formulation to address this issue. This paper has employed the method of two sample instrumental variables to effectively integrate CHIP data and CFPS data and correct the temporal income bias, life-cycle bias and coresidence bias, which are common problems in existing studies, and investigated the tendencies of intergenerational transmission of income gap for China's urban and rural households between 2002 and 2012. Results of empirical study indicate that the intergenerational transmission of income gap for China's urban and rural households has been on the decline yet the level of intergenerational transmission is greater for urban residents than for rural residents. This level of intergenerational transmission of income gap in China is at a medium international level lower than that of countries like the United States, Brazil and Japan and higher than that of Sweden and Chinese Taiwan. Further analysis of the intergenerational mobility of various income groups suggests the following: the intergenerational solidification of the bottom and top income groups of urban residents has significantly improved, which is the source for the reduction of intergenerational transmission of income gap. Rural residents of bottom income group are vulnerable to falling into the trap of intergenerational transmission of low income. In order to mitigate the intergenerational transmission of income gap, efforts must be made to improve educational allowance policy and increase the opportunities for children from poor and underprivileged families to receive education and to eliminate the divide of labor markets to create equal job opportunities for each and every worker.

Effects of Power Inversion Spatial Only Adaptive Array on GNSS Receiver Measurements

The Spatial Only Processing Power Inversion(SOP-PI) algorithm is frequently used in Global Navigation Satellite System(GNSS) adaptive array receivers for interference mitigation because of its simplicity of implementation. This study investigates the effects of SOP-PI on receiver measurements for high-precision applications. Mathematical deductions show that if an array with a centro-symmetrical geometry is used, ideally,SOP-PI is naturally bias-free; however, this no longer stands when non-ideal factors, including array perturbations and finite-sample effect, are added. Simulations are performed herein to investigate how exactly the array perturbations affect the carrier phase biases, while diagonal loading and forward-backward averaging are proposed to counter the finite-sample effect. In conclusion, whether SOP-PI with a centro-symmetrical array geometry will satisfy the high precision demands mainly depends on the array perturbation degree of the element amplitude and the phase center.