MEMS Inertial Sensor Application: Tilt Detection Using Accelerometer

01 Prerequisite knowledge

02 Principle (single axis as an example)

The first thing we need to know is that when the target axis (the X-axis in this case) is parallel to the Earth's surface, the sensor is in a 0g field. Rotating 90° clockwise or counterclockwise will produce a +1g or −1g field respectively. The following figure shows the layout of the sensor in different directions and the corresponding output g value:

Single axis tilt

When the X-axis is tilted, according to the trigonometric identity, the projection of the gravity vector on the X-axis will produce an output acceleration equal to the sine of the angle between the accelerometer's X-axis and the horizontal plane. The horizontal plane is usually the plane orthogonal to the gravity vector. When the gravity is the ideal value 1g, the output acceleration is:

Acceleration can be converted into tilt angle using the arcsine function.

Among them, the unit of tilt angle θ is radians.

Biaxial tilt

Now that an axis has been added to the system, the calculation method of the tilt angle needs to be re-examined. The simple method is to calculate the X-axis as usual, and then calculate the Y-axis in a similar way, but remember to use the cosine of the angle. (The Y-axis uses the cosine of the angle) When the gravity is the ideal value 1g, the output acceleration is:

Convert acceleration to angle using inverse cosine function

Among them, the unit of tilt angle θ is radians.

We can easily find the following relationship:

Compared with a single axis, using the ratio of two axes to determine the inclination angle makes it very difficult to determine the incremental sensitivity. Instead, it is more useful to determine the minimum resolution the accelerometer needs to achieve, assuming the required tilt resolution is known. Assuming that the incremental sensitivity of one axis increases as the incremental sensitivity of the other axis decreases, the net result will be an effective incremental sensitivity that is essentially constant in value. This means that if an accelerometer is selected to achieve the required tilt step size for a certain angle, the accelerometer will have sufficient resolution to handle all angles.

three-axis tilt

The angle between each axis of the accelerometer and the reference position is determined individually. The reference position is usually chosen so that the x- and y-axes of the device are in the direction of the horizontal plane (0 g field), and the z-axis is perpendicular to the horizontal plane (1g field).

Basic trigonometric identities can be used to calculate inclination angles

Since the ratio of the arctangent function and the acceleration is used, it has the advantages mentioned in the two-axis example, that is, the effective incremental sensitivity is constant and the angle within the unit range can be measured accurately at all points.