An autoregressive (AR) model based stochastic unknown input realization and filtering technique

This paper studies the state estimation problem of linear discrete-time systems with stochastic unknown inputs. The unknown input is a wide-sense stationary process while no other prior informaton needs to be known. We propose an autoregressive (AR) model based unknown input realization technique which allows us to recover the input statistics from the output data by solving an appropriate least squares problem, then fit an AR model to the recovered input statistics and construct an innovations model of the unknown inputs using the eigensystem realization algorithm (ERA). An augmented state system is constructed and the standard Kalman filter is applied for state estimation. A reduced order model (ROM) filter is also introduced to reduce the computational cost of the Kalman filter. Two numerical examples are given to illustrate the procedure.Comment: 14 page

The Effect of Education on Marital Status and Partner Characteristics: Evidence from the UK

This paper uses a particular school exit rule previously in effect in England and Wales that allowed students born within the first five months of the academic year to leave school one term earlier than those born later in the year. Focusing on women, we show that those who were required to stay on an extra term more frequently hold some academic qualification. Using having been required to stay on as an exogenous factor affecting academic attainment, we find that holding a (low level) academic qualification has no effect on a women's probability of being married, but increases the probability of her husband holding some academic qualification and being economically active.education, marriage, assortative mating

Stochastic Feedback Control of Systems with Unknown Nonlinear Dynamics

This paper studies the stochastic optimal control problem for systems with unknown dynamics. First, an open-loop deterministic trajectory optimization problem is solved without knowing the explicit form of the dynamical system. Next, a Linear Quadratic Gaussian (LQG) controller is designed for the nominal trajectory-dependent linearized system, such that under a small noise assumption, the actual states remain close to the optimal trajectory. The trajectory-dependent linearized system is identified using input-output experimental data consisting of the impulse responses of the nominal system. A computational example is given to illustrate the performance of the proposed approach.Comment: 7 pages, 7 figures, submitted to 56th IEEE Conference on Decision and Control (CDC), 201

Achieving Max-Min Throughput in LoRa Networks

With growing popularity, LoRa networks are pivotally enabling Long Range connectivity to low-cost and power-constrained user equipments (UEs). Due to its wide coverage area, a critical issue is to effectively allocate wireless resources to support potentially massive UEs in the cell while resolving the prominent near-far fairness problem for cell-edge UEs, which is challenging to address due to the lack of tractable analytical model for the LoRa network and its practical requirement for low-complexity and low-overhead design. To achieve massive connectivity with fairness, we investigate the problem of maximizing the minimum throughput of all UEs in the LoRa network, by jointly designing high-level policies of spreading factor (SF) allocation, power control, and duty cycle adjustment based only on average channel statistics and spatial UE distribution. By leveraging on the Poisson rain model along with tailored modifications to our considered LoRa network, we are able to account for channel fading, aggregate interference and accurate packet overlapping, and still obtain a tractable and yet accurate closed-form formula for the packet success probability and hence throughput. We further propose an iterative balancing (IB) method to allocate the SFs in the cell such that the overall max-min throughput can be achieved within the considered time period and cell area. Numerical results show that the proposed scheme with optimized design greatly alleviates the near-far fairness issue, and significantly improves the cell-edge throughput.Comment: 6 pages, 4 figures, published in Proc. International Conference on Computing, Networking and Communications (ICNC), 2020. This paper proposes stochastic-geometry based analytical framework for a single-cell LoRa network, with joint optimization to achieve max-min throughput for the users. Extended journal version for large-scale multi-cell LoRa network: arXiv:2008.0743