A Low-Cost Calibration Method for Low-Cost MEMS Accelerometers Based on 3D Printing
Abstract
:1. Introduction
2. Related Work
3. Accelerometer Error Model
4. Calibration Method
- (1)
- Preliminary Evaluation: In this step, a sanity check is done in the accelerometer, to verify that the sensor performs according to the manufacturer’s specifications. The verification is necessary because the performance of MEMS sensors tends to degrade over time, due to its dependence on the hermetic seal of sensor’s packaging [32]. To perform it, the sensor’s output is observed for a short period of time with the device static; the orientation is not significant. Then, it is verified that the output is within the manufacturer’s specifications.Some sensors have a self-test mode, if the accelerometer under calibration has one, it can be used instead. The self-test mode just has to be enabled and the output observed.If the accelerometer output is not within the expected values, the sensor is not usable and should not be considered for further evaluations.
- (2)
- Multi-Position Test: The gravity vector is used as reference information to calibrate the sensor in this step. When an accelerometer is static, the only force influencing its proof-mass is gravity; because it is a known value, it can be used to calibrate against it. This step involves to place the sensor static in multiple specific orientations, observe its output and compare it with the gravity value. A polyhedron with 18 faces is used for the precise positioning of the sensor. The solid can be generated with a 3D printer, thus the calibration is accessible and low-cost. In Figure 1, the proposed polyhedron is shown. Figure 1a presents its concept and Figure 1b the printed polyhedron that we used for the calibration described in this article. For the making of the polyhedron, we started with a sphere; then, we performed cuts at every 45 degrees with a depth of 10% of its diameter. The sensor under calibration is attached to one of internal faces. Multiple sensors can be calibrated simultaneously, and the polyhedron can have as many as 14 sensors attached to its inner walls, making the calibration of all of them at the same time possible.Verification of the 3D printed polyhedron.An important factor of the polyhedron structure is that the opposite faces are parallel to each other. This can be verified by measuring the distance between opposite faces with a Vernier Caliper. Two faces are parallel if the distance between them is the same in every point. Additionally, we recommend printing the solid in two equal-sized parts that assemble horizontally, one above the other, as illustrated in Figure 1b. In this manner, the polyhedron flat faces 1A and 5E will be printed over the printer bed, which is a level surface; thus, possible unevenness in the printed faces are minimized.The faces of the polyhedron should be marked with different labels, thus they act as a guide to trace the positions that have already been used. An example of the solid labeling is shown in Figure 1a, where numbers are used in one rotating direction and letters in the other. When performing the calibration, the polyhedron should be put on a rubber mat to minimize any vibration present in the room where the procedure is conducted.After attaching the accelerometer inside the polyhedron, the solid is rotated to place the sensor in different orientations. With the proposed polyhedron, those orientations will cause the sensor to experience an acceleration of 0 g, ±0.707 g, and ±1 g. The sensor has to be static on each position for a short period of time; we recommend one minute so the polyhedron can be easily operated, and any noise caused by its manipulation is averaged out of the recorded data [33]. The rotation can start with the 1A face pointing up, followed by rotating in the direction of the labels with numbers, from the smaller number to the largest. After a full rotation, the same process has to be done on the faces marked with letters. When both full rotations have been performed, the accelerations when the sensor was subject to 0 g, −0.707 g, −1 g, 0.707 g, and 1 g have been measured. Figure 2 illustrates the rotating sequence with the polyhedron and the effect that the positions cause in the accelerometer axes.The measurements have to be recorded. The data will have certain artifacts caused by the polyhedron manipulation during the rotations. The procedure in Algorithm 1 can be used to remove the accelerations induced by the manipulation and identify the samples of interest. Thereafter, the clean data can be used to find the null bias and scale factor.The null bias can be approximated with [30,34]:The scale factor can be similarly found:
Algorithm 1:Find the measurements when the sensor was static in the orientations of interest. |
|
- (3)
- Stability Test: In this step, the accelerometer is placed static at a constant temperature for an extended period of time, at least four hours [35]. The acceleration measurements are recorded during this time, and used to determine the velocity random walk and bias instability of each of the sensor’s axis. The Allan Variance [20,21] is applied to estimate them. It is a method to measure frequency stability in oscillators in the time domain, and it can be used to find intrinsic noise in a system as a function of its sampling period. The use of the Allan Variance was firstly proposed in [35], and, because of its simplicity, it has become a popular method for determining the different noise terms that exist in inertial sensor data. Its advantages are the ease of computation and the simplicity in the determination of the source of error; the latter can be achieved through observing slopes variations on the Allan Plot. The results of this step are five basic noise terms appropriate for inertial sensors, they are: quantization noise, velocity random walk, bias instability, acceleration random walk, and rate ramp [11,22]. They are exemplified in Figure 3 [36].The Allan Variance, , can be computed in a data sequence, , of length N and fixed sample period of , as a function of an averaging time, . Through dividing in subsets of consecutive output values, , averaged over , using the following [22]:The confidence in the estimation of the Allan Variance is directly proportional to the number of independent subsets that can be formed from the sampled data. From the Allan Variance, we can get the Allan Deviation through its squared root. After computing a range of different sampling times and plotting it in a Log-Log graph, the different noise components can be identified by observing the gradient changes of the slope [11], as seen in Figure 3. Our main interests are velocity random walk and bias instability.Velocity random walk is a high-frequency noise term that appears when the slope has a gradient of −0.5 and the reading is done at . This is also considered the white noise component of the sensor’s output. Bias instability is located where the gradient is 0. This term, as the name implies, translates into the bias consistency in the measurements changes over a long period of time [4]. The reason why we focus on these two noise terms is because they are a high order integration error [11], and they must be compensated when the sensor is used in applications that require high accuracy, for example, on Inertial Navigation Systems.
5. Calibration of a MEMS Accelerometer
5.1. Preliminary Evaluation
5.2. Multi-Position Test
5.3. Stability Test
5.4. Results
- Misalignments in the vertical faces of the polyhedron caused by minor defects in the printing.
- Misalignments with the two halves of the polyhedron. This is a shortcoming of the current computer-aided design (CAD). Adding snap-on aligning pins to the polyhedron is on the future improvement list.
- Finally, movements of the sensor related to the printed object while it is being rotated. This is also a future mechanical improvement to the CAD, in order to achieve a firm sensor positioning with the printed object.
6. Discussion
7. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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x | y | z | |
---|---|---|---|
1.0175 | 0.9394 | 1.0389 | |
−0.9788 | −1.0043 | −0.9343 |
x | y | z | |
---|---|---|---|
0.0193 | −0.0324 | 0.0523 | |
−0.0018 | −0.0281 | −0.0134 |
x | y | z | |
---|---|---|---|
VRW () | |||
BI () |
Measurements | RMSE |
---|---|
Uncalibrated | 0.0442 |
Calibrated with the proposed method | 0.0051 |
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García, J.A.; Lara, E.; Aguilar, L. A Low-Cost Calibration Method for Low-Cost MEMS Accelerometers Based on 3D Printing. Sensors 2020, 20, 6454. https://doi.org/10.3390/s20226454
García JA, Lara E, Aguilar L. A Low-Cost Calibration Method for Low-Cost MEMS Accelerometers Based on 3D Printing. Sensors. 2020; 20(22):6454. https://doi.org/10.3390/s20226454
Chicago/Turabian StyleGarcía, Jesús A., Evangelina Lara, and Leocundo Aguilar. 2020. "A Low-Cost Calibration Method for Low-Cost MEMS Accelerometers Based on 3D Printing" Sensors 20, no. 22: 6454. https://doi.org/10.3390/s20226454
APA StyleGarcía, J. A., Lara, E., & Aguilar, L. (2020). A Low-Cost Calibration Method for Low-Cost MEMS Accelerometers Based on 3D Printing. Sensors, 20(22), 6454. https://doi.org/10.3390/s20226454