Computation-Communication Trade-offs and Sensor Selection in Real-time Estimation for Processing Networks

Recent advances in electronics are enabling substantial processing to be performed at each node (robots, sensors) of a networked system. Local processing enables data compression and may mitigate measurement noise, but it is still slower compared to a central computer (it entails a larger computational delay). However, while nodes can process the data in parallel, the centralized computational is sequential in nature. On the other hand, if a node sends raw data to a central computer for processing, it incurs communication delay. This leads to a fundamental communication-computation trade-off, where each node has to decide on the optimal amount of preprocessing in order to maximize the network performance. We consider a network in charge of estimating the state of a dynamical system and provide three contributions. First, we provide a rigorous problem formulation for optimal real-time estimation in processing networks in the presence of delays. Second, we show that, in the case of a homogeneous network (where all sensors have the same computation) that monitors a continuous-time scalar linear system, the optimal amount of local preprocessing maximizing the network estimation performance can be computed analytically. Third, we consider the realistic case of a heterogeneous network monitoring a discrete-time multi-variate linear system and provide algorithms to decide on suitable preprocessing at each node, and to select a sensor subset when computational constraints make using all sensors suboptimal. Numerical simulations show that selecting the sensors is crucial. Moreover, we show that if the nodes apply the preprocessing policy suggested by our algorithms, they can largely improve the network estimation performance.Comment: 15 pages, 16 figures. Accepted journal versio

Impact of time-variant turbulence behavior on prediction for adaptive optics systems

For high contrast imaging systems, the time delay is one of the major limiting factors for the performance of the extreme adaptive optics (AO) sub-system and, in turn, the final contrast. The time delay is due to the finite time needed to measure the incoming disturbance and then apply the correction. By predicting the behavior of the atmospheric disturbance over the time delay we can in principle achieve a better AO performance. Atmospheric turbulence parameters which determine the wavefront phase fluctuations have time-varying behavior. We present a stochastic model for wind speed and model time-variant atmospheric turbulence effects using varying wind speed. We test a low-order, data-driven predictor, the linear minimum mean square error predictor, for a near-infrared AO system under varying conditions. Our results show varying wind can have a significant impact on the performance of wavefront prediction, preventing it from reaching optimal performance. The impact depends on the strength of the wind fluctuations with the greatest loss in expected performance being for high wind speeds.Comment: 10 pages, 8 figures; Accepted to JOSA A March 201

State-space approach to nonlinear predictive generalized minimum variance control

A Nonlinear Predictive Generalized Minimum Variance (NPGMV) control algorithm is introduced for the control of nonlinear discrete-time multivariable systems. The plant model is represented by the combination of a very general nonlinear operator and also a linear subsystem which can be open-loop unstable and is represented in state-space model form. The multi-step predictive control cost index to be minimised involves both weighted error and control signal costing terms. The solution for the control law is derived in the time-domain using a general operator representation of the process. The controller includes an internal model of the nonlinear process but because of the assumed structure of the system the state observer is only required to be linear. In the asymptotic case, where the plant is linear, the controller reduces to a state-space version of the well known GPC controller

Adaptive Differential Feedback in Time-Varying Multiuser MIMO Channels

In the context of a time-varying multiuser multiple-input-multiple-output (MIMO) system, we design recursive least squares based adaptive predictors and differential quantizers to minimize the sum mean squared error of the overall system. Using the fact that the scalar entries of the left singular matrix of a Gaussian MIMO channel becomes almost Gaussian distributed even for a small number of transmit antennas, we perform adaptive differential quantization of the relevant singular matrix entries. Compared to the algorithms in the existing differential feedback literature, our proposed quantizer provides three advantages: first, the controller parameters are flexible enough to adapt themselves to different vehicle speeds; second, the model is backward adaptive i.e., the base station and receiver can agree upon the predictor and variance estimator coefficients without explicit exchange of the parameters; third, it can accurately model the system even when the correlation between two successive channel samples becomes as low as 0.05. Our simulation results show that our proposed method can reduce the required feedback by several kilobits per second for vehicle speeds up to 20 km/h (channel tracker) and 10 km/h (singular vector tracker). The proposed system also outperforms a fixed quantizer, with same feedback overhead, in terms of bit error rate up to 30 km/h.Comment: IEEE 22nd International Conference on Personal, Indoor and Mobile Radio Communications (2011

Neural Networks with Non-Uniform Embedding and Explicit Validation Phase to Assess Granger Causality

A challenging problem when studying a dynamical system is to find the interdependencies among its individual components. Several algorithms have been proposed to detect directed dynamical influences between time series. Two of the most used approaches are a model-free one (transfer entropy) and a model-based one (Granger causality). Several pitfalls are related to the presence or absence of assumptions in modeling the relevant features of the data. We tried to overcome those pitfalls using a neural network approach in which a model is built without any a priori assumptions. In this sense this method can be seen as a bridge between model-free and model-based approaches. The experiments performed will show that the method presented in this work can detect the correct dynamical information flows occurring in a system of time series. Additionally we adopt a non-uniform embedding framework according to which only the past states that actually help the prediction are entered into the model, improving the prediction and avoiding the risk of overfitting. This method also leads to a further improvement with respect to traditional Granger causality approaches when redundant variables (i.e. variables sharing the same information about the future of the system) are involved. Neural networks are also able to recognize dynamics in data sets completely different from the ones used during the training phase

GMV control of nonlinear multivariable systems

A Generalized Minimum Variance control law is derived for the control of nonlinear, possibly time-varying multivariable systems. The solution for the control law is original and was obtained in the time-domain using a simple operator representation of the process. The quadratic cost index involves both error and control signal costing terms. The controller obtained is simple to implement and includes an internal model of the process. In one form might be considered a nonlinear version of the Smith Predictor. However, unlike the Smith Predictor a stabilizing control law can be obtained even for some open-loop unstable processe

Polynomial approach to nonlinear predictive generalized minimum variance control

A relatively simple approach to non-linear predictive generalised minimum variance (NPGMV) control is introduced for non-linear discrete-time multivariable systems. The system is represented by a combination of a stable non-linear subsystem where no structure is assumed and a linear subsystem that may be unstable and modelled in polynomial matrix form. The multi-step predictive control cost index to be minimised involves both weighted error and control signal costing terms. The NPGMV control law involves an assumption on the choice of cost-function weights to ensure the existence of a stable non-linear closed-loop operator. A valuable feature of the control law is that in the asymptotic case, where the plant is linear, the controller reduces to a polynomial matrix version of the well known generalised predictive control (GPC) controller. In the limiting case when the plant is non-linear and the cost-function is single step the controller becomes equal to the polynomial matrix version of the so-called non-linear generalised minimum variance controller. The controller can be implemented in a form related to a non-linear version of the Smith predictor but unlike this compensator a stabilising control law can be obtained for open-loop unstable processes