Probability of Error Analysis for Hidden Markov Model Filtering With Random Packet Loss

This paper studies the probability of error for maximum a posteriori (MAP) estimation of hidden Markov models, where measurements can be either lost or received according to another Markov process. Analytical expressions for the error probabilities are derived for the noiseless and noisy cases. Some relationships between the error probability and the parameters of the loss process are demonstated via both analysis and numerical results. In the high signal-to-noise ratio (SNR) regime, approximate expressions which can be more easily computed than the exact analytical form for the noisy case are presented

Optimal Energy Allocation for Kalman Filtering over Packet Dropping Links with Imperfect Acknowledgments and Energy Harvesting Constraints

This paper presents a design methodology for optimal transmission energy allocation at a sensor equipped with energy harvesting technology for remote state estimation of linear stochastic dynamical systems. In this framework, the sensor measurements as noisy versions of the system states are sent to the receiver over a packet dropping communication channel. The packet dropout probabilities of the channel depend on both the sensor's transmission energies and time varying wireless fading channel gains. The sensor has access to an energy harvesting source which is an everlasting but unreliable energy source compared to conventional batteries with fixed energy storages. The receiver performs optimal state estimation with random packet dropouts to minimize the estimation error covariances based on received measurements. The receiver also sends packet receipt acknowledgments to the sensor via an erroneous feedback communication channel which is itself packet dropping. The objective is to design optimal transmission energy allocation at the energy harvesting sensor to minimize either a finite-time horizon sum or a long term average (infinite-time horizon) of the trace of the expected estimation error covariance of the receiver's Kalman filter. These problems are formulated as Markov decision processes with imperfect state information. The optimal transmission energy allocation policies are obtained by the use of dynamic programming techniques. Using the concept of submodularity, the structure of the optimal transmission energy policies are studied. Suboptimal solutions are also discussed which are far less computationally intensive than optimal solutions. Numerical simulation results are presented illustrating the performance of the energy allocation algorithms.Comment: Submitted to IEEE Transactions on Automatic Control. arXiv admin note: text overlap with arXiv:1402.663

Optimal LQG Control Across a Packet-Dropping Link

We examine optimal Linear Quadratic Gaussian control for a system in which communication between the sensor (output of the plant) and the controller occurs across a packet-dropping link. We extend the familiar LQG separation principle to this problem that allows us to solve this problem using a standard LQR state-feedback design, along with an optimal algorithm for propagating and using the information across the unreliable link. We present one such optimal algorithm, which consists of a Kalman Filter at the sensor side of the link, and a switched linear filter at the controller side. Our design does not assume any statistical model of the packet drop events, and is thus optimal for an arbitrary packet drop pattern. Further, the solution is appealing from a practical point of view because it can be implemented as a small modification of an existing LQG control design

On the Performance of Short Block Codes over Finite-State Channels in the Rare-Transition Regime

As the mobile application landscape expands, wireless networks are tasked with supporting different connection profiles, including real-time traffic and delay-sensitive communications. Among many ensuing engineering challenges is the need to better understand the fundamental limits of forward error correction in non-asymptotic regimes. This article characterizes the performance of random block codes over finite-state channels and evaluates their queueing performance under maximum-likelihood decoding. In particular, classical results from information theory are revisited in the context of channels with rare transitions, and bounds on the probabilities of decoding failure are derived for random codes. This creates an analysis framework where channel dependencies within and across codewords are preserved. Such results are subsequently integrated into a queueing problem formulation. For instance, it is shown that, for random coding on the Gilbert-Elliott channel, the performance analysis based on upper bounds on error probability provides very good estimates of system performance and optimum code parameters. Overall, this study offers new insights about the impact of channel correlation on the performance of delay-aware, point-to-point communication links. It also provides novel guidelines on how to select code rates and block lengths for real-time traffic over wireless communication infrastructures

On Kalman smoothing with random packet loss

The abstract is included in the text

Quality-Aware Broadcasting Strategies for Position Estimation in VANETs

The dissemination of vehicle position data all over the network is a fundamental task in Vehicular Ad Hoc Network (VANET) operations, as applications often need to know the position of other vehicles over a large area. In such cases, inter-vehicular communications should be exploited to satisfy application requirements, although congestion control mechanisms are required to minimize the packet collision probability. In this work, we face the issue of achieving accurate vehicle position estimation and prediction in a VANET scenario. State of the art solutions to the problem try to broadcast the positioning information periodically, so that vehicles can ensure that the information their neighbors have about them is never older than the inter-transmission period. However, the rate of decay of the information is not deterministic in complex urban scenarios: the movements and maneuvers of vehicles can often be erratic and unpredictable, making old positioning information inaccurate or downright misleading. To address this problem, we propose to use the Quality of Information (QoI) as the decision factor for broadcasting. We implement a threshold-based strategy to distribute position information whenever the positioning error passes a reference value, thereby shifting the objective of the network to limiting the actual positioning error and guaranteeing quality across the VANET. The threshold-based strategy can reduce the network load by avoiding the transmission of redundant messages, as well as improving the overall positioning accuracy by more than 20% in realistic urban scenarios.Comment: 8 pages, 7 figures, 2 tables, accepted for presentation at European Wireless 201