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Asymptotic Effectiveness of the Event-Based Sampling according to the Integral Criterion

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ABSTRACT

A rapid progress in intelligent sensing technology creates new interest in a development of analysis and design of non-conventional sampling schemes. The investigation of the event-based sampling according to the integral criterion is presented in this paper. The investigated sampling scheme is an extension of the pure linear send-on-delta/level-crossing algorithm utilized for reporting the state of objects monitored by intelligent sensors. The motivation of using the event-based integral sampling is outlined. The related works in adaptive sampling are summarized. The analytical closed-form formulas for the evaluation of the mean rate of event-based traffic, and the asymptotic integral sampling effectiveness, are derived. The simulation results verifying the analytical formulas are reported. The effectiveness of the integral sampling is compared with the related linear send-on-delta/level-crossing scheme. The calculation of the asymptotic effectiveness for common signals, which model the state evolution of dynamic systems in time, is exemplified.

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Comparison of the adaptive integral sampling (a), and the event-based integral one (b). The “local extremum trap” is illustrated in the adaptive sampling scheme (a). Note that the event-based scheme is immune to the such instability of the sampling error (b). Both sampling schemes are based on the constant integral-difference criterion with the same resolution. The sampled signal is the unit response of the second-order closed-loop system, the maximum sampling period in the adaptive sampling equals Tmax = 0.2[s] ; the zero-order hold is used.
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f5-sensors-07-00016: Comparison of the adaptive integral sampling (a), and the event-based integral one (b). The “local extremum trap” is illustrated in the adaptive sampling scheme (a). Note that the event-based scheme is immune to the such instability of the sampling error (b). Both sampling schemes are based on the constant integral-difference criterion with the same resolution. The sampled signal is the unit response of the second-order closed-loop system, the maximum sampling period in the adaptive sampling equals Tmax = 0.2[s] ; the zero-order hold is used.

Mentions: However, as follows from our experience, the adaptive sampling scheme has the significant disadvantage, which we call the “local extremum trap”. Namely, the estimated current sampling interval is theoretically infinite, although practically bounded to its maximum value Tmax, if the most recent sample is taken when the signal reached its local minimum or maximum (Fig. 5a). It is because the signal first time-derivative crosses zero at that moment and the predicted signal change is very low or even zero. As a result, the adaptive sampling is prone to the temporary instability of the signal tracking error (see Fig. 5a). On the other hand, the event-based integral sampling is in general not subject to similar problem since the (integral) sampling error is the same by the definition in every sampling interval (Fig. 5b).


Asymptotic Effectiveness of the Event-Based Sampling according to the Integral Criterion
Comparison of the adaptive integral sampling (a), and the event-based integral one (b). The “local extremum trap” is illustrated in the adaptive sampling scheme (a). Note that the event-based scheme is immune to the such instability of the sampling error (b). Both sampling schemes are based on the constant integral-difference criterion with the same resolution. The sampled signal is the unit response of the second-order closed-loop system, the maximum sampling period in the adaptive sampling equals Tmax = 0.2[s] ; the zero-order hold is used.
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Related In: Results  -  Collection

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f5-sensors-07-00016: Comparison of the adaptive integral sampling (a), and the event-based integral one (b). The “local extremum trap” is illustrated in the adaptive sampling scheme (a). Note that the event-based scheme is immune to the such instability of the sampling error (b). Both sampling schemes are based on the constant integral-difference criterion with the same resolution. The sampled signal is the unit response of the second-order closed-loop system, the maximum sampling period in the adaptive sampling equals Tmax = 0.2[s] ; the zero-order hold is used.
Mentions: However, as follows from our experience, the adaptive sampling scheme has the significant disadvantage, which we call the “local extremum trap”. Namely, the estimated current sampling interval is theoretically infinite, although practically bounded to its maximum value Tmax, if the most recent sample is taken when the signal reached its local minimum or maximum (Fig. 5a). It is because the signal first time-derivative crosses zero at that moment and the predicted signal change is very low or even zero. As a result, the adaptive sampling is prone to the temporary instability of the signal tracking error (see Fig. 5a). On the other hand, the event-based integral sampling is in general not subject to similar problem since the (integral) sampling error is the same by the definition in every sampling interval (Fig. 5b).

View Article: PubMed Central

ABSTRACT

A rapid progress in intelligent sensing technology creates new interest in a development of analysis and design of non-conventional sampling schemes. The investigation of the event-based sampling according to the integral criterion is presented in this paper. The investigated sampling scheme is an extension of the pure linear send-on-delta/level-crossing algorithm utilized for reporting the state of objects monitored by intelligent sensors. The motivation of using the event-based integral sampling is outlined. The related works in adaptive sampling are summarized. The analytical closed-form formulas for the evaluation of the mean rate of event-based traffic, and the asymptotic integral sampling effectiveness, are derived. The simulation results verifying the analytical formulas are reported. The effectiveness of the integral sampling is compared with the related linear send-on-delta/level-crossing scheme. The calculation of the asymptotic effectiveness for common signals, which model the state evolution of dynamic systems in time, is exemplified.

No MeSH data available.


Related in: MedlinePlus