OVERVIEW

Errors in measurements are inevitable. In order to achieve high fidelity measurements from any sensor, there is a need to map from raw sensor readings to the correct values before the decision process is invoked. Figures 1 and 2 graphically demonstrate the two components of error in sensor measurements.

• Systematic Error (Bias): The bias is the time-invariant amplitude offset of the correct value*. The bias is due to device and/or human imperfections, and/or the natural process of deterioration.
• Random Noise: Random noise is time dependent and can be contributed by many factors such as environmental conditions and hardware noise. The behavior of random noise can be studied and modeled over time once the systematic bias has been addressed.

*Correct value: defined by golden standards or by the overall consistency of a collection of sensors monitoring the same environment.

Error compensation is particularly crucial in large-scale sensor networks since manual calibration is expensive and sometimes infeasible. In addition, until now calibration has always been conducted by considering a set of measurements in a single time frame and restricted to linear systems with the assumption of equal-quality sensors and a single modality.

We interpret calibration as the process of identifying and compensating the time-invariant systematic bias component of the error in sensor measurements. The basis for our calibration procedure is to distinguish the time-invariant systematic bias and the time-dependent random noise. Depending on the availability of resources and conditions, variations of calibration techniques can be applied.

APPROACHes

We have developed calibration techniques that operate in both off-line and on-line modes.

• Off-line calibration: Use a set of statistical modeling techniques to construct error models and correct the time-invariant systematic bias by selecting the calibration value based on different objectives (Fig 3 under systems/experiments).
• On-line calibration: Intrinsically localized and explores two different objectives: i) minimum number of sensors communicate in order to calibratie (only two sensors are sufficient); ii) minimum amount of communication power is used.

The two approaches are complementary and could be used together. Off-line calibration is conceptually simple and computationally optimal; where on-line calibration is dynamic, generic and does not require the existence of any authoritative sensing standard. Note that the results obtained by on-line calibration can serve as the reference for the off-line calibration. Finally, the resubstitution-based percentile method is applied to evaluate the techniques and obtain the interval of confidence.

SYSTEMS / EXPERIMENTS

We have developed simulation software for both off-line and on-line scenario for a point-light model (Figure 3). The experimental results are analyzed and studied when we varied a number of parameters such as the accuracy tolerance, network connectivity, noise level and the degree bound of polynomial fitting function. Comprehensive simulation results do show that incorporating multiple intervals instead of fitting all data points in one polynomial results in lower fitting error for both off-line and on-line calibration.

Figure 3. Performance of the 1st variant of the localized on-line technique.

ACCOMPLISHMENTS

Refereed Publication In submission:

• “Model-based Calibration”, Jessica Feng, Gang Qu, and Miodrag Potkonjak, in submission.

FUTURE DIRECTIONS

• More comprehensive study of the performance of on-line calibration under different parameters
• More extensive calibration validation techniques
• Centralized/localized ILP-based data aggregation
• Identify the suitable conditions for invoking on-line calibration

PEOPLE

FACULTY

Prof. Miodrag Potkonjak

GRADUATE STUDENTS

Jessica Feng
Gang Qu