摘要：An attitude and heading reference system (AHRS) is a nonlinear state estimator unit for computing orientation in 3D space. This paper designs an AH RS using three approaches: an in variant observer, an invaria nt exte nded Kalman filter (IEKF), and a conventional extended Kalman filter (EKF). The three designs are validated in experiment versus a ground truth, dem on strati ng the practical interest of the invariant observer methodology and the advantage of the IEKF over the EKF under model uncertainty.

摘要：We propose a thoroughly optimal signal design strategy to achieve the Pareto boundary （boundary of the achievable rate region） with improper Gaussian signaling （IGS） on the Z-interference channel （Z-IC） under the assumption that the interference is treated as additive Gaussian noise. Specifically, we show that the Pareto boundary has two different schemes determined by the two paths manifesting the characteristic of improperly transmitted signals. In each scheme, we derive several concise closed-form expressions to calculate each user＇s optimally transmitted power, covariance, and pseudo-covariance of improperly transmitted signals. The effectiveness of the proposed optimal signal design strategy is supported by simulations, and the results clearly show the superiority of IGS. The proposed optimal signal design strategy also provides a simple way to achieve the required rate region, with which we also derive a closed-form solution to quickly find the circularity coefficient that maximizes the sum rate. Finally, we provide an in-depth discussion of the structure of the Pareto boundary, characterized by the channel coefficient, the degree of impropriety measured by the covariance, and the pseudo-covaxiance of signals transmitted by two users.

摘要：Almost estimators are designed for the white observation noise. In the estimation problems, rather than the white observation noise, there might be actual cases where the observation noise is modeled by the colored noise process. This paper examines to design a new estimation technique of recursive least-squares (RLS) Wiener fixed-point smoother and filter for colored observation noise in linear discrete-time wide-sense stationary stochastic systems. The observation y(k) is given as the sum of the signal z(k)=Hx(k) and the colored observation noise vc(k). The RLS Wiener estimators explicitly require the following information: 1) the system matrix for the state vector x(k);2) the observation matrix H;3) the variance of the state vector x(k);4) the system matrix for the colored observation noise vc(k);5) the variance of the colored observation noise;6) the input noise variance in the state equation for the colored observation noise.