Abstract
In this chapter, we consider Kalman filtering over a packet-delaying network. Given the probability distribution of the delay, we can completely characterize the filter performance via a probabilistic approach. We assume the estimator maintains a buffer of length Dso that at each time k, the estimator is able to retrieve all available data packets up to time \(k - D + 1\). Both the cases of sensor with and without necessary computation capability for filter updates are considered. When the sensor has no computation capability, for a given D, we give lower and upper bounds on the probability for which the estimation error covariance is within a prescribed bound. When the sensor has computation capability, we show that the previously derived lower and upper bounds are equal to each other. An approach for determining the minimum buffer length for a required performance in probability is given and an evaluation on the number of expected filter updates is provided.
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Notes
- 1.
Since (A,C) is assumed to be observable and \((A,\sqrt{Q})\)controllable, from standard Kalman filtering analysis, P ∗exists.
- 2.
Note that we use the superscript kin \(\hat{{f}}_{k-i}^{k}\)to emphasize that it depends on the current time, k. For example, if \({d}_{k-i} = i + 1\), i.e., \({\gamma }_{k-i} = 0\)and \({\gamma }_{k-i}^{k+1} = 1\), then \(\hat{{f}}_{k-i}^{k} = h\)and \(\hat{{f}}_{k-i}^{k+1} =\tilde{ g} \circ h\).
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Shi, L., Xie, L., Murray, R.M. (2011). State Estimation Over an Unreliable Network. In: Mazumder, S. (eds) Wireless Networking Based Control. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7393-1_2
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