Feasibility of Low Latency, Single-Sample Delay Resampling: A New Kriging Based Method

Abstract

Wireless sensor systems often fail to provide measurements with uniform time spacing. Measurements can be delayed or even miss completely. Resampling to uniform intervals is necessary to satisfy the requirements of subsequent signal processing. Common resampling algorithms, based on symmetric finite impulse response (FIR) filters, entail a group delay of 10 s of samples, which is not acceptable regarding the typical interval of wireless sensors of seconds or minutes. The purpose of this paper is to verify the feasibility of single-delay resampling, i.e., the algorithm resamples the data without waiting for future samples. A new method to parametrize Kriging interpolation is presented and compared with two variants of Lagrange interpolation in detailed simulations for the resulting prediction error. Kriging provided the most accurate resampling in the group-delay scenario. The single-delay scenario required almost double the OSR to achieve the same signal-to-noise ratio (SNR). An OSR between 1.8 and 3.1 was necessary for single-delay resampling, depending on the required SNR and signal distortions in terms of jitter, missing samples, and noise. Kriging was the least noise-sensitive method. Especially for signals with missing samples, Kriging provided the best accuracy. The simulations showed that single-delay resampling is feasible, but at the expense of higher OSR and limited SNR.

A4.2 - Correction of Inconsistent Sensor Timing: Missing Samples and Clock Deviations

“…However, there is still a lack of good methods for higher frequencies with r>20%. Last results concerning improved methods will be presented at the conference, including Kriging [2], Akima [3], and a newly developed modified local regression method. A Digital Twin platform for sensor data processing was presented at the previous conference [4].…”

“…In addition to WSI and ZOH, we tested Local Polynomial Regression (LPR) [2], also known as Locally Estimated Scatterplot Smoothing (LOESS), and linear connection of neighboring measurement points (LIN).…”

Modified Local Regression for Signal Resampling

“…Alternate methods for non-uniform resampling entail high mathematical effort, e.g., Lagrange interpolation [3] requires the calculation of a high-order polynomial, and Kriging interpolation [4] is based on a matrix inversion of order equal to the window length. Akima interpolation [5] provides a simple solution.…”