# Data driven fast measurements

#### Introduction

Measurement techniques have fundamental speed and accuracy limitations. The speed and precision of a measurement device used in monitoring and control tasks determines the quality of the available data, which in turn limits the accuracy of models derived from the data. In this project, we develop a method that overcomes the hardware constraints. The method performs calculations in real-time to speed up, by digital signal processing, measurement tasks.

Problem formulation

The metrology problem of speeding up a measurement device is modeled as an input estimation problem for a dynamical system with step input. The input step level is the unknown (to-be-measured) quantity, the output is the known (measured) quantity, and the input-output relation represents the unknown measurement process dynamics see Figure 1

Fig 1: Representation of the driven fast measurement approach

#### Data-Driven Fast Measurement method (DDFM)

A dynamic compensator performs on-line identification and model based design. The proposed method called DDFM is a model-free approach that bypasses the parameter identification and compensator design and finds directly the quantity of interest, see figure 2

Figure 2: Concept diagram of the proposed DDFM method [1]

#### Practical implementation

The DDFM algorithm is implemented on a digital signal processor (NXT Lego brick), see Figure 3. As a test bed we use temperature measurement, but this method can be applied to multivariable dynamical systems and is capable of performing sensor fusion

Figure 3: NXT Lego digital signal processor and its temperature sensor

In Figure 4 the estimation error  is shown as a function of time, for a particular experiment. Here  is the steady state value and  is the current prediction of . In this experiment, the following methods are compared:

1. direct (raw) measurement of the sensor,
2. estimate of the measured quantity, obtained by the DDFM method,
3. estimate of the measured quantity, obtained by the Kalman filter.

Figure 4: Estimation error comparison [2].

Note that the Kalman filter is designed using a model of the measurement process. This model is obtained using all the collected data. On the other hand, the instantaneous value of the DDFM prediction is calculated online using the (previously) measured values.

#### References:

[1] I. Markovsky, “Comparison of adaptive and model-free methods for dynamic measurement,” IEEE Signal Proc. Letters, 22:1094-1097, 2015.

[2] I. Markovsky, “An application of system identification in metrology,” Control Eng. Prac., 43:85-93, 2015