STM32-Based IMU Attitude Estimation

This project involves using an STM32 microcontroller and an MPU6050 sensor module to measure angular velocity and acceleration. The collected sensor data will be processed to determine the attitude angles (roll, pitch, and yaw) of the system. The project will include sensor calibration, data filtering (e.g., complementary or Kalman filter), and real-time angle computation for accurate motion tracking applications.

Introduction

In this project, we built a simple attitude estimation system using the STM32F103C8T6 microcontroller and the MPU6050 inertial measurement unit (IMU). The MPU6050 contains a 3-axis accelerometer and a 3-axis gyroscope, which together allow us to sense both linear acceleration and angular velocity in space.

Our goal was to estimate the orientation of the sensor in real time—specifically the roll, pitch, and yaw angles—by processing the raw physical signals output by the sensor. The core idea is based on how physical forces like gravity and rotational motion affect the internal elements of MEMS sensors, and how these effects can be digitized and interpreted.

To make the system work, we wrote low-level I²C communication routines to read data directly from the MPU6050 registers. The raw measurements were then converted into meaningful physical quantities, and passed into a complementary filter, which combines accelerometer and gyroscope data to produce smoother and more stable angle estimates.

The main steps of the project include:

• Reading raw acceleration and gyroscope data via I²C
• Calibrating the sensor to reduce offset and random noise
• Computing roll and pitch using a complementary filter
• Updating and displaying the estimated angles in real time on an OLED screen

Although this system is relatively simple, it closely reflects the principles used in real-world applications like drone stabilization, smartphone orientation sensing, and robot balancing. More importantly, it helps us explore how sensor physics—particularly the detection of inertial forces—can be harnessed in embedded systems to measure motion and orientation.

Team Members

LI DING

FAN XUTING

Project Overview

The core idea of this project is to estimate the orientation (attitude) of an object in space using inertial sensor data. We used the MPU6050 module, which integrates a 3-axis accelerometer and a 3-axis gyroscope, to measure two different physical quantities: linear acceleration and angular velocity. These are fundamental mechanical observables when analyzing motion.

The data from the sensor is acquired through I²C communication using the STM32F103C8T6 microcontroller. However, the raw measurements—especially from the gyroscope—tend to drift over time, and the accelerometer is sensitive to external vibrations. Therefore, we applied a complementary filter to combine the short-term precision of the gyroscope with the long-term stability of the accelerometer. This approach helps us reduce noise and improve the reliability of the estimated angles.

Our objective is to continuously compute the roll, pitch, and yaw angles of the sensor in real time. In practice, only roll and pitch can be estimated reliably without a magnetometer, since yaw depends on integrating rotational velocity around the vertical axis and is subject to drift.

Systems like this are commonly found in drones, balancing robots, camera gimbals, and even smartphones for orientation detection. In our project, we replicated the basic functionality of such systems on a smaller scale in order to understand how physical quantities—like gravity and rotation—can be sensed, processed, and interpreted through embedded electronics.

Setup

Equipment

The following components were used to build our attitude estimation system:

• **STM32F103C8T6 ("Blue Pill")** – A low-cost 32-bit microcontroller used here to handle I²C communication, filtering, and OLED output.
• **MPU6050** – A 6-axis IMU that combines a 3-axis accelerometer (for sensing gravity and linear motion) and a 3-axis gyroscope (for measuring angular velocity).
• **USB to TTL Serial Converter** – Used mainly during development to upload programs to the STM32 and read data from the serial port.
• **Breadboard and jumper wires** – For making temporary connections during prototyping.
• **3.3V Power Supply** – The MPU6050 operates at 3.3V, which is provided by the STM32 board itself.

The MPU6050 is connected to the STM32 using the I²C protocol. I²C is widely used in sensor interfacing due to its simplicity and ability to handle multiple devices over just two lines (SDA and SCL).

STM32F103C8T6 "Blue Pill" development board

Wiring / Circuit Overview

The sensor communicates with the STM32 via I²C, and the wiring is shown below:

MPU6050 Pin	STM32 Pin	Notes
VCC	3.3V	Sensor powered by STM32
GND	GND	Common ground reference
SDA	PB7	I²C data line
SCL	PB6	I²C clock line

Below are two views of the hardware setup: a breadboard diagram and an abstract schematic:

Breadboard wiring diagram

Schematic representation of connections

Software & Code

The firmware was written in C using STM32's standard peripheral libraries. The program runs in a loop, repeatedly collecting data from the MPU6050 and computing the corresponding attitude angles in real time.

The main software tasks are as follows:

• Initialize I²C interface – Configure STM32 to communicate with the MPU6050 using the I²C protocol.
• Set up MPU6050 – Select the measurement range for both the accelerometer and gyroscope, and enable continuous data output.
• Read raw sensor values – Acquire unprocessed data from the accelerometer and gyroscope registers.
• Convert to physical units – Translate raw values into real-world quantities:

 * Acceleration in g (gravitational units)
 * Angular velocity in °/s

• Estimate angles – Apply a complementary filter to combine the short-term precision of the gyroscope and the long-term stability of the accelerometer. The filter uses the formula:

$\theta =\alpha \cdot ({\theta }_{\text{prev}}+\omega \cdot \mathrm{\Delta }t)+(1-\alpha )\cdot {\theta }_{\text{acc}}$

• Output the result – Display the roll and pitch angles on the OLED screen. Optionally, angles can also be printed to the serial terminal for monitoring.

The system updates approximately every 10 milliseconds (100 Hz), which is fast enough to track slow and moderate human motion smoothly.

Theory & Angle Estimation

To estimate the orientation (attitude) of an object using the MPU6050, we need to understand the physical meaning of the quantities it measures. The accelerometer responds to linear acceleration (including gravity), while the gyroscope senses angular velocity. By interpreting and combining these outputs, we can reconstruct the rotation of the sensor in space.

Sensor Principles

The MPU6050 is a MEMS-based 6-axis Inertial Measurement Unit (IMU). Internally, it contains:

• 3-axis accelerometer – measures linear acceleration along the X, Y, and Z axes, in units of g.
• 3-axis gyroscope – measures angular velocity around the X, Y, and Z axes, in °/s.

These two types of data correspond to physical forces acting on the sensor:

• The accelerometer reflects the direction and magnitude of gravity (when stationary) or combined forces (when moving).
• The gyroscope provides information about how fast the object is rotating around each axis.

By combining both types of data, we can estimate the orientation of the sensor relative to a fixed reference frame.

MPU6050 breakout board showing the chip and I²C interface

Attitude Angles: Roll, Pitch, Yaw

Attitude in 3D space is commonly expressed using three angles:

Angle	Axis	Description
Roll	X-axis	Tilting left and right
Pitch	Y-axis	Tilting forward and backward
Yaw	Z-axis	Rotating around the vertical axis

In our project, we focus on roll and pitch. Yaw is difficult to measure accurately without a magnetometer, because the accelerometer does not respond to rotation around the vertical axis, and gyroscope-based yaw accumulates drift over time.

Roll (X), Pitch (Y), and Yaw (Z) in 3D space

Using the Accelerometer

When the sensor is at rest or moving slowly, the accelerometer mainly senses the Earth's gravity. We can use the direction of this gravity vector to estimate the tilt angles with respect to the horizontal plane. Using basic trigonometry:

$\text{pitch}=\arctan \left(\frac{a_x}{\sqrt{a_y^2+a_z^2}}\right)$

$\text{roll}=\arctan \left(\frac{a_y}{\sqrt{a_x^2+a_z^2}}\right)$

These estimates are relatively stable when the sensor is static but become noisy during motion, since linear acceleration disturbs the gravity vector.

Using the Gyroscope

The gyroscope gives angular velocity ω (in °/s), which can be integrated over time to estimate changes in orientation:

$\theta ={\theta }_{\text{prev}}+\omega \cdot \mathrm{\Delta }t$

However, this method suffers from drift because small measurement errors accumulate over time.

Complementary Filter

To reduce drift while keeping responsiveness, we apply a complementary filter, which fuses gyroscope and accelerometer data. The gyroscope provides short-term accuracy, while the accelerometer corrects long-term drift.

$\theta =\alpha \cdot ({\theta }_{\text{prev}}+\omega \cdot \mathrm{\Delta }t)+(1-\alpha )\cdot {\theta }_{\text{acc}}$

Where:

• $\omega$ is the angular velocity from the gyroscope
• ${\theta }_{\text{acc}}$ is the angle derived from the accelerometer
• $\alpha$ is a constant between 0.95 and 0.98

This gives us smooth and relatively accurate estimates for roll and pitch in real time.

Results

After completing the sensor initialization, calibration, and complementary filter implementation, we tested our system by manually changing the orientation of the MPU6050 module and observing the real-time calculated attitude angles: pitch, roll, and yaw. These values were displayed on the OLED screen in real time.

Initial State

In the initial state, the sensor was placed flat and stationary on the table. The calculated angles were close to zero, fluctuating slightly within ±1° due to sensor noise and environmental vibration.

Initial state: pitch ≈ 0°, roll ≈ 0°, yaw ≈ 0° (flat and stable).

Pitch Variation

We manually tilted the sensor forward and backward around the Y-axis to generate positive and negative pitch angles.

Pitch ≈ +45°

Pitch ≈ -45°

The pitch angle responded clearly and symmetrically to changes in tilt. The results remained stable when holding the angle.

Roll Variation

Next, we tilted the sensor side-to-side around the X-axis to test roll estimation.

Roll ≈ +45°

Roll ≈ -45°

The roll angle also showed accurate and consistent results. There was some fluctuation due to hand-held movement, but the trend was clear and repeatable.

Yaw Rotation

Since our yaw angle is calculated by integrating the Z-axis angular velocity, it is expected to drift over time. However, for short-term motion, it could still reflect relative rotation. We rotated the device on a flat surface and observed the change.

Yaw ≈ 0°

Yaw ≈ 90°

The yaw angle changed appropriately during rotation. However, due to the lack of a magnetometer, long-term drift is still present and was not corrected in our system.

Summary

The table below summarizes the approximate angles observed during different manual movements. The "Reference" column represents rough estimates of the sensor orientation based on intuition and relative movement, not exact measured angles.

Test Condition	Estimated Tilt	Measured Angle (OLED)	Observation
Flat (Initial)	≈ 0°	0° ± 1°	Stable near zero
Pitch Forward	~ +45°	+46°	Correct trend
Pitch Backward	~ -45°	-46°	Correct trend
Roll Right	~ +45°	+46°	Correct trend
Roll Left	~ -45°	-48°	Correct trend
Yaw No Rotation	~ 0°	0°	As expected
Yaw Rotated Clockwise	~ +90°	+91°	Matches rotation

Note: The reference angles were estimated by eye during manual movement. No precise angle measurement tools were used.

Pitch and roll estimation was stable and consistent throughout the tests. The angle values responded smoothly to manual tilting and aligned well with expected trends within an approximate ±45° range.

Yaw angle changes were visible and directionally accurate during short-term rotation, but drifted over time due to the lack of a magnetometer for correction.

All three angles were displayed clearly on the OLED screen and updated in real time at approximately 100 Hz.

Overall, the complementary filter worked effectively for basic attitude estimation using only the MPU6050 sensor, especially for roll and pitch. The system demonstrates reliable performance for short-term orientation tracking without external reference.

7. Discussion

Accuracy and Stability of Roll and Pitch

The complementary filter performed well in estimating roll and pitch angles. These two values remained stable when the sensor was held still, and they responded consistently to manual tilting. The accelerometer provides reliable long-term reference based on gravity, while the gyroscope helps improve short-term responsiveness. Minor fluctuations were observed due to hand tremors and environmental vibrations, but they were within acceptable range for basic applications.

Yaw Angle Limitations

Unlike pitch and roll, yaw cannot be derived from the accelerometer alone. In this project, yaw was computed by integrating gyroscope data around the Z-axis. This approach worked for short-term motion but exhibited noticeable drift over time, as expected. Without a magnetometer to provide an external reference (e.g., Earth's magnetic field), yaw estimation lacks long-term accuracy. This is a known limitation of using MPU6050 without additional sensors.

Display and Refresh Rate

Displaying angles on the OLED screen in real time (~100 Hz) allowed for intuitive observation of system performance. However, the OLED display has limited resolution and update speed compared to serial terminals or PC-based plots. Some rapid changes may not be fully captured visually.

Potential Improvements

To further improve the system:

• A **magnetometer** (e.g., HMC5883L) can be added to correct yaw drift.
• **Kalman filter** or **Madgwick filter** could replace the complementary filter for higher accuracy.
• **Initial calibration** routines can be added to correct zero-bias errors in accelerometer and gyroscope.
• Angle output could also be sent to PC or mobile app via serial/Bluetooth for better visualization.

Applications and Extensions

This basic attitude estimation system could be extended for use in:

• Drone orientation feedback
• Self-balancing robots
• Gesture-based control systems
• VR/AR head tracking

The understanding gained from building this project from scratch—both in hardware wiring and software logic—provides a strong foundation for further exploration in embedded sensing systems.

References

• [1] **MPU6050 Register Map and Datasheet**, InvenSense.

   https://invensense.tdk.com/products/motion-tracking/6-axis/mpu-6050/

• [2] **STM32F103C8T6 Datasheet**, STMicroelectronics.

   https://www.st.com/en/microcontrollers-microprocessors/stm32f103c8.html