AN4508 STMICROELECTRONICS | Alldatasheet
Document overview
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Technical content
Datasheet sections
- 1 Terminology
- 1.1 Accelerometer datasheet
- 1.2 Definitions
- 2 Calibrating the accelerometer
Parameters and calibration of a low-g 3-axis accelerometer Introduction This application note describes the parameters and calibration of a low-g 3-axis accelerometer. In general, the procedures described here may also be applied to 3-axis analog or digital accelerometers, depending on their respective specifications. Section 1 of this application note introduces the terminology and parameters related to the accelerometer, while Section 2 presents the accelerometer calibration techniques.
1 Terminology
1.1 Accelerometer datasheet
The first step is to examine the accelerometer specifications and understand the meaning of each parameter. Understanding the parameters Vdd - Power supply: This parameter defines the accelerometer operating DC power supply. Correct operation of the accelerometer using a power supply voltage outside of this range is not guaranteed. The parameters are provided by the accelerometer manufacturer under Vdd = +2.5 V at a room temperature of T = 25 °C. It is recommended to keep Vdd clean, with minimum ripple. One possible way to do this is to use an ultra-low-noise low-dropout regulator to power the accelerometer. Idd - Current consumption in normal mode: lower ODR corresponds to lower current consumption. ODR - Output data rate in normal mode: This parameter shows the possible output data rates in normal mode from which the user may select. BW - System bandwidth: This parameter defines the bandwidth of the system. When ODR = 100 Hz, BW is typically 50 Hz with a built-in low pass filter. The system recognizes any motion below 50 Hz. If the system has dynamic motion higher than
50 Hz, then the ODR needs to be increased to a higher setting in order to cover all
useful system signals. Ton - Turn-on time: This parameter defines the time required before the accelerometer is ready to output measured acceleration data after exiting power-down mode. Top - operating temperature range: This parameter defines the operating temperature range. When the device is operated inside the specified range, proper behavior of the sensor is guaranteed. FS - Full-scale measurement range: For tilt sensing applications, a ±2.0 g range is sufficient because the Earth’s gravity is ±1 g only. If the application requires measurement of higher g acceleration, the user can set the device to a higher full-scale range which results in lower sensitivity. So - Sensitivity: This parameter defines the value of 1 LSB with respect to mg in the digital representation. TCSo - Sensitivity change vs. temperature: This parameter defines how sensitivity changes with temperature. For example, at a ±2.0 g full-scale range, the sensitivity changes within ±0.01%/°C. Therefore, if the environmental temperature changes 40 °C, from 25 °C to 65 °C, then the sensitivity changes within the range of ±0.01% * 40 = ±0.4%, which means the sensitivity change over 40 °C is within 0.996 mg/LSB and 1.004 mg/LSB, which shows that the sensitivity is very stable versus temperature change. Thus, temperature compensation for sensitivity can be ignored. TyOff - Typical zero-g level offset accuracy: This parameter defines the zero-g accuracy at room temperature of 25 °C. For example, at a ±2.0 g full-scale range, the
±20 mg around the expected ideal value. zero-g level is affected by temperature variations. user can obtain from the accelerometer (once the desired BW is selected). 1 resolution = . The higher BW leads to lower resolution. measurement), the non-linearity effect is negligible and can be ignored. misalignment between the accelerometer sensing axes and the board axes.
1.2 Definitions
PDA or simply on a PCB board as shown in Figure 1. Figure 1. Accelerometer inside a handheld device Xb, Yb and Zb are the handheld device body axes with a forward-right-down configuration. same direction as the device body axes.
Table 1. Sign definition of sensor raw measurements
Calibrating the accelerometer AN4508
2 Calibrating the accelerometer
Section 1 describes the accelerometer parameters, the next step is to calibrate the accelerometer. Please note that all accelerometers from ST have been factory-calibrated. For most applications, such as screen portrait/landscape rotation and laptop lid open/close detection, accelerometer calibration is not necessary. This means that users can use the zero-g level and sensitivity parameters from the datasheet directly to convert raw measurements A x, Ay and Az to normalized measurements Ax1, Ay1 and Az1. For applications that require better than 1° tilt-measurement accuracy, such as automobile alert systems, tilt-compensated electronic compasses and level monitoring systems, accelerometer calibration is recommended. The relationship between the normalized A x1, Ay1 and Az1 and the accelerometer raw measurements Ax, Ay and Az can be expressed as, Equation 1 where [A_m] is the 3 x 3 misalignment matrix between the accelerometer sensing axes and the device body axes, A_SCi (i = x, y, z) is the sensitivity (or scale factor) and A_OSi is the zero-g level (or offset). The goal of accelerometer calibration is to determine 12 parameters from ACC10 to ACC33, so that with any given raw measurements at arbitrary positions, the normalized values Ax1, Ay1 and Az1 can be obtained, resulting in: Equation 2 Calibration can be performed at 6 stationary positions as shown in Table 1. Collect 5 to 10 seconds of accelerometer raw data with ODR = 100 Hz at each position with known Ax1, Ay1 and Az1. Then apply the least square method to obtain the 12 accelerometer calibration parameters. Refer to Appendix A for additional details.
AN4508 Least square method Appendix A Least square method Let's consider accelerometer calibration at the 6 stationary positions shown in Table 1. Equation 1 can be rewritten as: Equation 3 Or Equation 4 where: Matrix X is the 12 calibration parameters that need to be determined Matrix w is sensor raw data LSBs collected at 6 stationary positions Matrix Y is the known normalized Earth gravity vector For example, At Zb down position (P1 position), , and assume that at Z b down position, n1 sets of accelerometer raw data Ax, Ay and Az have been collected. Then, Equation 5 where: Matrix Y1 has the same row of [0 0 1]. Matrix w1 contains raw data in the format of LSBs. At Zb up position (P2 position), , and assume that at Z b up position, n2 sets of accelerometer raw data Ax, Ay and Az have been collected. Then, Equation 6 At Yb down position (P3 position), , and assume that at Y b down position, n3 sets of accelerometer raw data Ax, Ay and Az have been collected. Then, Equation 7
Least square method AN4508 At Yb up position (P4 position), , and assume that at Y b up position, n4 sets of accelerometer raw data Ax, Ay and Az have been collected. Then, Equation 8 At Xb down position (P5 position), , and assume that at Xb down position, n5 sets of accelerometer raw data Ax, Ay and Az have been collected. Then, Equation 9 At Xb up position (P6 position), , and assume that at X b up position, n6 sets of accelerometer raw data Ax, Ay and Az have been collected. Then, Equation 10 Combine Equation 5 to 10 and let n = n1 + n2 + n3 + n4 + n5 + n6, then Equation 4 becomes: Equation 11 where: Equation 12
AN4508 Least square method Therefore, the calibration parameter matrix X can be determined by the least square method as: Equation 13 where: Equation 14 means matrix transpose means matrix inverse
Revision history
Table 2. Document revision history 10-Jun-2014 1 Initial release.