We consider a scenario in which a process of interest, evolving within an environment occupied by several agents, is well-described probablistically via a Markov model. The agents each have local views and observe only some limited partial aspects of the world, but their overall task is to fuse their data to construct an integrated, global portrayal. The problem, however, is that their communications are unreliable: network links may fail, packets can be dropped, and generally the network might be partitioned for protracted periods. The fundamental problem then becomes one of consistency as agents in different parts of the network gain new information from their observations but can only share this with those with whom they are able to communicate. As the communication network changes, different views may be at odds; the challenge is to reconcile these differences. The issue is that correlations must be accounted for, lest some sensor data be double counted, inducing overconfidence or bias. As a means to address these problems, a new recursive consensus filter for distributed state estimation on hidden Markov models is presented. It is shown to be well-suited to multi-agent settings and associated applications since the algorithm is scalable, robust to network failure, capable of handling non-Gaussian transition and observation models, and is, therefore, quite general. Crucially, no global knowledge of the communication network is ever assumed. We have dubbed the algorithm a Hybrid method because two existing pieces are used in concert: the first, iterative conservative fusion is used to reach consensus over potentially correlated priors, while consensus over likelihoods, the second, is handled using weights based on a Metropolis Hastings Markov chain. To attain a detailed understanding of the theoretical upper limit for estimator performance modulo imperfect communication, we introduce an idealized distributed estimator. It is shown that under certain general conditions, the proposed Hybrid method converges exponentially to the ideal distributed estimator, despite the latter being purely conceptual and unrealizable in practice. An extensive evaluation of the Hybrid method, through a series of simulated experiments, shows that its performance surpasses competing algorithms.
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Ahmed, N. R., Julier, S. J., Schoenberg, J. R., & Campbell, M. E. (2017). Decentralized Bayesian fusion in networks with non-Gaussian uncertainties. In Multisensor data fusion: From algorithms and architectural design to applications (p. 383). CRC Press.
Ajgl, J., Šimandl, M. (2015). Design of a robust fusion of probability densities. In Proceedings of IEEE American control conference (ACC) (pp. 4204–4209).
Anderson, B. D. (2001). Forgetting properties for hidden Markov models. In Proceedings of US/Australia joint workshop on defense applications of signal processing (pp. 26–39). Amsterdam: Elsevier.
Bahr, A., Walter, M. R., & Leonard, J. J. (May 2009). Consistent cooperative localization. In Proceedings of IEEE international conference on robotics and automation (ICRA) (pp. 3415–3422). Japan: Kobe.
Bailey, T., Julier, S., & Agamennoni, G. (2012). On conservative fusion of information with unknown non-Gaussian dependence. In Proceedings of international conference on information fusion (FUSION) (pp. 1876–1883).
Battistelli, G., & Chisci, L. (2014). Kullback–Leibler average, consensus on probability densities, and distributed state estimation with guaranteed stability. Automatica, 50(3), 707–718.
Battistelli, G., & Chisci, L. (2016). Stability of consensus extended Kalman filter for distributed state estimation. Automatica, 68, 169–178.
Battistelli, G., Chisci, L., & Fantacci, C. (2014). Parallel consensus on likelihoods and priors for networked nonlinear filtering. IEEE Signal Processing Letters, 21(7), 787–791.
Boem, F., Ferrari, R. M., Parisini, T., & Polycarpou, M. M. (2013). Distributed fault diagnosis for continuous-time nonlinear systems: The input-output case. Annual Reviews in Control, 37(1), 163–169.
Boem, F., Sabattini, L., & Secchi, C. (2015). Decentralized state estimation for heterogeneous multi-agent systems. In Proceedings of IEEE conference on decision and control (CDC) (pp. 4121–4126).
Campbell, M. E., & Ahmed, N. R. (2016). Distributed data fusion: Neighbors, rumors, and the art of collective knowledge. IEEE Control Systems, 36(4), 83–109.
Casbeer, D., & Beard, R. (June 2009). Distributed information filtering using consensus filters. In Proceedings of IEEE American control conference (ACC) (pp. 1882–1887).
Cattivelli, F. S., & Sayed, A. H. (2010). Diffusion strategies for distributed Kalman filtering and smoothing. IEEE Transactions on Automatic Control, 55(9), 2069–2084.
Durrant-Whyte, H., Stevens, M., & Nettleton, E. (2001). Data fusion in decentralised sensing networks. In Proceedings of the 4th international conference on information fusion (pp. 302–307).
Hlinka, O., Hlawatsch, F., & Djuric, P. M. (2013). Distributed particle filtering in agent networks: A survey, classification, and comparison. IEEE Signal Processing Magazine, 30(1), 61–81.
Hlinka, O., Sluciak, O., Hlawatsch, F., Djuric, P. M., & Rupp, M. (2012). Likelihood consensus and its application to distributed particle filtering. IEEE Transactions on Signal Processing, 60(8), 4334–4349.
Hu, J., Chen, D., & Du, J. (2014). State estimation for a class of discrete nonlinear systems with randomly occurring uncertainties and distributed sensor delays. International Journal of General Systems, 43(3–4), 387–401.
Hu, J., Xie, L., & Zhang, C. (2012). Diffusion Kalman filtering based on covariance intersection. IEEE Transactions on Signal Processing, 60(2), 891–902.
Li, W., & Jia, Y. (2012). Distributed consensus filtering for discrete-time nonlinear systems with non-gaussian noise. Signal Processing, 92(10), 2464–2470.
Liverani, C., Saussol, B., & Vaienti, S. (1999). A probabilistic approach to intermittency. Ergodic Theory and Dynamical Systems, 19(3), 671–685.
Lucchese, R., & Varagnolo, D. (2015) Networks cardinality estimation using order statistics. In Proceeedings of IEEE American control conference (ACC) (pp. 3810–3817).
Lucchese, R., Varagnolo, D., Delvenne, J.-C. & Hendrickx, J. M. (2015) Network cardinality estimation using max consensus: The case of Bernoulli trials. In Proceedings of the IEEE conference on decision and control (CDC) (pp. 895–901). IEEE Communications Society.
Mao, L., & Yang, D. W. (August 2014). Distributed information fusion particle filter. In Proceedings of international conference on intelligent human–machine systems and cybernetics (Vol. 1, pp. 194–197).
Niu, Y., & Sheng, L. (2017). Distributed consensus-based unscented Kalman filtering with missing measurements. In Proceedings of Chinese control conference (CCC) (pp. 8993–8998).
Olfati-Saber, R. (2005). Distributed Kalman filter with embedded consensus filters. In Proceedings of IEEE decision and control, and European control conference (CDC-ECC) (pp. 8179–8184).
Seneta, E. (2006). Non-negative matrices and Markov chains. New York: Springer.
Simonetto, A., Keviczky, T., & Babuška, R. (May 2010). Distributed nonlinear estimation for robot localization using weighted consensus. In IEEE international conference on robotics and automation, (pp. 3026–3031).
Tamjidi, A., Chakravorty, S., & Shell, D. (2016). Unifying consensus and covariance intersection for decentralized state estimation. In Proceedings of IEEE/RSJ international conference on intelligent robots and systems (IROS) (pp. 125–130).
Tamjidi, A., Oftadeh, R., Chakravorty, S., & Shell, D. (2017). Efficient distributed state estimation of hidden Markov models over unreliable networks. In Proceedings of IEEE international symposium on multi-robot and multi-agent systems (MRS) (pp. 112–119).
Terelius, H., Varagnolo, D., & Johansson, K. H. (2012) Distributed size estimation of dynamic anonymous networks. In Proceedings of the IEEE conference on decision and control (CDC). IEEE conference proceedings (pp. 5221–5227).
Wang, Y., & Li, X. (2012). Distributed estimation fusion with unavailable cross-correlation. IEEE Transactions on Aerospace and Electronic Systems, 48(1), 259–278.
Xiao, L., Boyd, S., & Lall, S. (2005). A scheme for robust distributed sensor fusion based on average consensus. In Proceedings of the 4th international symposium on information processing in sensor networks (p. 9).
Zhang, H., Moura, J., & Krogh, B. (2009). Dynamic field estimation using wireless sensor networks: Tradeoffs between estimation error and communication cost. IEEE Transactions on Signal Processing, 57(6), 2383–2395.
This work was supported by the National Science Foundation in part by IIS-1302393, IIS-1453652, and ECCS-1637889.
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This is one of the several papers published in Autonomous Robots comprising the Special Issue on Multi-Robot and Multi-Agent Systems.
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Tamjidi, A., Oftadeh, R., Chakravorty, S. et al. Efficient recursive distributed state estimation of hidden Markov models over unreliable networks. Auton Robot 44, 321–338 (2020). https://doi.org/10.1007/s10514-019-09854-3
- Distributed state estimation
- Multi-robot systems
- Unreliable networks
- Hidden Markov models