Source-linked AI summary
Design and Implementation of a Kalman Filter-Infused Algorithm for Tilt Estimation
Yuehan Ma, Hongji Dai
TL;DR
Low-cost inertial sensors face noise and drift that undermine stable tilt estimates. The paper combines MPU6050 accelerometer and gyroscope measurements with a Kalman filter on an RP2040 platform; across five experiments, tracking was smoother and less affected by noise.
Problem
Low-cost IMUs provide tilt measurements affected by accelerometer noise and short-term fluctuations, while gyroscope integration introduces long-term drift.
Source: §1 · p. 1Method
The paper implements an RP2040-based tilt-estimation system that fuses MPU6050 accelerometer and gyroscope measurements using a Kalman filter.
Source: §1 · p. 2Results
Across five experiments, the algorithm produced smoother tracking and was less influenced by noise than the original signals.
Source: §6 · p. 10, §7 · p. 11Takeaways & Limitations
The system is presented as a practical, accessible approach for educational and low-cost embedded applications.
Source: §1 · p. 2In experiment 5, manual pushing may contribute signal errors, and the power supply’s unbalanced wheel weight contributed to a flawed sinusoid.
Source: §6 · p. 11
Abstract
from arXiv · showhide
Accurate tilt angle estimation is important in many engineering applications, such as robotics, motion tracking, and embedded control systems. However, measurements from low-cost inertial sensors are often degraded by noise and drift. This paper presents a single-axis tilt angle estimation system based on the MPU6050 inertial measurement unit, implemented on an RP2040 microcontroller platform, with sensor fusion achieved through a Kalman filter. The accelerometer provides a direct estimate of tilt angle from gravity but is sensitive to noise and short-term fluctuations. The gyroscope provides smooth angular rate measurements, but integration over time introduces drift. To overcome these limitations, a Kalman filter is used to combine measurements from both sensors, leveraging the long-term stability of the accelerometer and the short-term smoothness of the gyroscope. Both simulation and hardware experiments are performed. In simulation, sensor noise and drift are modeled to evaluate the filter performance under control conditions. In the hardware implementation, real-time MPU6050 data is acquired and processed by the RP2040 platform, and the estimated tilt angle is compared with accelerometer-only and gyroscope-only outputs. The results show that the proposed method effectively reduces noise measurements and suppresses long-term drift while preserving good dynamic response. Overall, the system provides more stable and accurate tilt estimation than either sensor alone, demonstrating a practical and accessible approach for Kalman filter based sensor fusion in embedded application.
1. Introduction
Low-cost IMUs make embedded tilt estimation accessible, but accelerometer noise and gyroscope drift limit either sensor alone. The paper presents an RP2040-based system that fuses their estimates through a real-time Kalman filter.
1. Introduction
- Accelerometer fluctuations and gyroscope integration drift make either sensor alone insufficiently stable for tilt estimation.The Kalman filter combines gyroscope prediction with accelerometer correction to balance short-term smoothness and long-term stability.Source: §1 · pp. 1–2
- The work implements a real-time Kalman-filter tilt estimator using an MPU6050 on a STEPico RP2040 platform for accessible, low-cost embedded applications.The stated contributions also include controlled noise, drift, and accuracy evaluation, plus a qualitative display-interaction evaluation.Source: §1 · p. 2
2.1 Hardware Architecture
- The MPU6050 supplies 3-axis accelerometer and gyroscope data to the STEPico RP2040 over I2C, sampled at 100 Hz.The sensor is mounted on a rigid platform, and the microcontroller outputs estimates over serial; a display can be used optionally.Source: §2.1 · p. 2
- The hardware workflow links data acquisition and angle estimation between the MPU6050 and RP2040 microcontroller.The system can also provide real-time visualization through an optional display.Source: Figure 1 · p. 2, §2.1 · p. 2
2.2 Software Architecture
- At each sampling step, accelerometer and gyroscope measurements are read and converted into separate gravity-based and integrated-rate angle estimates.The Kalman filter fuses these intermediate estimates into the final tilt output, which can be sent over serial for logging or used in real-time applications.Source: §2.2 · p. 3
2.3 Data Processing Pipeline
- The data-processing pipeline is described as having four main stages.The supplied description identifies sensor reading, intermediate angle estimation, and Kalman fusion as part of the processing flow.Source: §2.3 · p. 3, §2.2 · p. 3
1. Sensor Data Acquisition
Sensor acquisition retrieves and prepares accelerometer and gyroscope measurements for angle estimation.
2. Angle Computation
The system computes one tilt estimate from gravity and another by integrating gyroscope measurements over time.
3. Kalman Filter-Based Sensor Fusion
A Kalman filter combines the two sensor-derived angle estimates, using gyroscope prediction and accelerometer correction.
4. Output and Logging
Filtered angles are logged for quantitative analysis, with timing and calibration measures supporting embedded execution and materials available for reproducibility.
4. Output and Logging
- Filtered tilt angles are recorded in CSV for quantitative noise, drift, and accuracy analysis, then plotted using R.Source: §4 · p. 3
2.4 Implementation Details
- Sensor reading and Kalman filtering are completed within each sampling interval, with dynamically calculated dt and gyroscope bias calibration supporting integration accuracy and drift reduction.Source: §2.4 · p. 3
2.5 Reproducibility
- The hardware configuration and source code are publicly available to support reproducibility and further development.Source: §2.5 · p. 3
3. Methodology
The methodology combines a gravity-based accelerometer angle with integrated gyroscope measurements through recursive Kalman prediction and correction. This balances the sensors’ complementary behavior while accounting for noise, drift, and embedded implementation constraints.
3.1 Accelerometer-Based Angle Estimation
- The accelerometer estimates tilt relative to gravity from acceleration components, but noise and external disturbances cause short-term angle fluctuations.Source: §3.1 · p. 3
3.2 Gyroscope-Based Angle Estimation
- Gyroscope angular velocity is integrated over time to estimate angle, yielding smooth short-term response but accumulating bias- and noise-related drift.Source: §3.2 · pp. 3–4
3.3 Kalman Filter for Sensor Fusion
- The Kalman filter recursively updates a tilt-angle state through prediction and correction, combining the accelerometer and gyroscope measurements.Source: §3.3 · p. 4
3.3.1 Prediction Step
- The prediction step uses gyroscope measurements to estimate the current angle from the previous state, leveraging short-term gyroscope smoothness.Source: §3.3.1 · p. 4
3.3.2 Update Step
- The update step corrects the predicted angle with the accelerometer-based angle, using a Kalman gain that weights prediction against measurement.Source: §3.3.2 · p. 4
3.4 Filter Characteristics
- The combined estimate is described as stable and responsive; tuning balances noise reduction with responsiveness, alongside measures for embedded timing, calibration, numerical stability, and computational efficiency.Source: §3.4 · p. 4, §3.5 · p. 4
3.5 Implementation Considerations
- Implementation considerations include dynamically measured dt, gyroscope-bias compensation, a simplified real-time model, and execution within the fixed sampling interval.Source: §3.5 · p. 4
4. Experimental Setup
Five experiments use static and moving conditions to examine the MPU6050’s angle estimates over short and extended periods. The setups compare accelerometer, gyroscope, and Kalman-filter outputs across stationary noise, fixed inclines, rapid repositioning, and circular motion.
4. Experimental Setup
- The five experiments compare accelerometer, gyroscope, and Kalman-filter signals under static and kinetic conditions, over 10–30-second or 120-second periods.The collected data are analyzed to assess whether sensor fusion produces smoother tracking.Source: §4 · p. 4
4.1.2 Experiment description; 4.2.2 Experiment description
- Experiments 1 and 2 keep the sensor stationary to examine short-term measurement variation and long-term sensor characteristics.Experiment 1 records the sensor while it rests on a flat surface; Experiment 2 retains that setup for an extended-period investigation.Source: §4.1.2 · p. 5, §4.2.2 · p. 5
4.3 Experiment 3 Setup; 4.3.2 Experiment description
- Experiment 3 places the stationary sensor at predefined inclines to compare angle estimates with assumed ideal values and assess accuracy under fixed-angle conditions.A digital protractor angle finder sets the inclines; the experiment also considers noise and destabilization when the surface is not completely flat.Source: §4.3.2 · pp. 5–6, §4.3 · p. 5
4.4 Experiment 4 Setup; 4.4.2 Experiment description
- Experiment 4 uses fixed-angle supports to move the sensor rapidly among 0°, 30°, 45°, and 60° positions, then hold it stable for response observations.The setup targets sudden movements and noise introduced by inconsistencies during repositioning.Source: §4.4.2 · p. 6, §4.4 · p. 6
4.5 Experiment 5 Setup; 4.5.2 Experiment description
- Experiment 5 mounts the RP2040–MPU6050 system for circular motion to examine whether the three signals track smoothly, repeatably, and periodically.A portable battery powers the rolling setup, and a green LED indicates active data recording.Source: §4.5 · p. 6, §4.5.2 · p. 7, §4.5.1 · p. 7
5. Quantitative Results and Analysis
Across five experiments, the Kalman estimates were generally smoother and less variable than the individual sensor estimates. The results also show limits: error increased with set angle, and recovery took time after sudden jolts.
5.1.2 Experiment 1 Result Analysis
- 0.075° average standard deviation for the Kalman estimate, compared with 0.192° for the accelerometer and 0.136° for the gyroscope, across Experiment 1 trials.The Kalman standard deviation excludes adjustment-period outliers, defined using the 1.5-IQR rule.Source: Figure 10 · p. 7, Figure 11 · p. 7, Figure 12 · p. 7
5.2.2 Experiment 2 Result Analysis
- 0.063° average standard deviation for the Kalman estimate after initial adjustment in the two-minute tracking experiment, versus 0.172° for the accelerometer and 0.217° for the gyroscope.The gyroscope’s long-term drift was pronounced enough for its standard deviation to exceed the accelerometer’s.Source: §5.2.2 · p. 8, Figure 13 · p. 8, Figure 14 · p. 8
5.3.2 Experiment 3 Result Analysis
- Kalman estimates drifted farther from the actual value as the set angle increased, with the authors attributing this to per-angle overcalibration not accounted for when discarding outliers.The three trials were consistent; each angle’s data were averaged over 10 seconds, and initial-calibration outliers were discarded.Source: §5.3.2 · p. 9, Figure 16 · p. 9
6.4.2 Experiment 4 Result Analysis
- During abrupt angle changes, the Kalman estimate tracked more smoothly than the spiking accelerometer and gyroscope readings, but needed time to recover after each jolt.Once calibration finished, the signal steadied.Source: Figure 19 · p. 9, §6.4.2 · p. 10
5.5.2 Experiment 5 Result Analysis
- During rotation, the gyroscope failed to recognize circular motion, while the Kalman estimate smoothed the accelerometer’s noisy, sine-like trace.The noise source was uncertain, and intentional microadjustments could be omitted as measurement noise.Source: §5.5.2 · p. 10
6. Discussion
Across five experiments, the Kalman-filtered tracking was smoother and less affected by noise than the original signals. The study is limited to single-axis, planar estimation and reports additional experimental setup constraints.
Discussion
- Across five experiments, the fused tracking was smoother and substantially reduced noise compared with the original accelerometer and gyroscope signals.The authors describe the results as demonstrating the algorithm’s utility for object tracking.Source: §6 · p. 10
- The method estimates tilt on a single axis using a two-dimensional projection, so it does not assess full three-dimensional orientation or cross-axis coupling.The authors identify multi-axis sensor fusion, including quaternion-based or complementary filters, as possible future work.Source: §6 · pp. 10–11
- Small data-generation errors may arise because the MPU6050 sensor may not be perfectly parallel to the breadboard.Source: §6 · p. 11
- In Experiment 5, manual pushing could introduce signal errors; the authors suggest using a motor with a set RPM in future work.Source: §6 · p. 11
- The portable power supply’s unbalanced weight on the wheel contributed to a flawed sinusoid in the experiment.Source: §6 · p. 11
7. Conclusion
The study combines accelerometer and gyroscope signals with a Kalman filter to reduce measurement noise. Across five static and kinetic experiments, the algorithm produced smoother tracking, supporting its use in real-world motion tracking with imperfect measurements.
Conclusion
- The study addresses accelerometer short-term fluctuations and gyroscope cumulative error that causes long-term drift by combining their measurements with a Kalman filter.Source: §7 · p. 11
- Across five static and kinetic experiments, the algorithm produced smoother tracking and was less influenced by noise.Source: §7 · p. 11
- The authors relate the results to real-world motion tracking, where measurements are imperfect and multiple noisy data sources must be combined.Source: §7 · p. 11