557  Sensor Fusion Visualizer

Combining Multiple Sensors for Enhanced Accuracy

557.1 Overview

Sensor fusion is the process of combining data from multiple sensors to achieve more accurate and reliable measurements than any single sensor could provide. This interactive tool demonstrates various fusion algorithms and their effectiveness in different scenarios.

TipLearning Objectives

After using this tool, you will be able to:

  • Understand why sensor fusion is essential in IoT applications
  • Compare different fusion algorithms and their trade-offs
  • Visualize how noise, bias, and update rates affect fusion quality
  • Apply appropriate fusion techniques for specific use cases

557.2 Why Sensor Fusion?

Every sensor has inherent limitations:

Sensor Strengths Weaknesses
Accelerometer Accurate long-term orientation Noisy, affected by vibration
Gyroscope Smooth, responsive Drifts over time
Magnetometer Absolute heading reference Affected by magnetic interference
GPS Absolute position Low update rate, no indoor coverage
Odometry High update rate, relative motion Cumulative error

By combining sensors intelligently, we compensate for individual weaknesses while leveraging their strengths.

Imagine you’re trying to find your way in a dark room. Your eyes can’t see well, but you can feel with your hands and hear sounds. By combining all these senses, you get a much better picture of the room than using just one sense alone.

Sensor fusion works the same way! A drone uses multiple sensors - one that measures tilting (accelerometer), one that measures spinning (gyroscope), and one that points north like a compass (magnetometer). Each sensor has problems on its own, but together they give the drone a perfect sense of its orientation.

TipHow to Use This Tool
  1. Select Scenario: Choose Drone Orientation, Indoor Navigation, Vehicle Tracking, or Gesture Recognition to load appropriate sensor configurations
  2. Choose Fusion Algorithm: Select from Simple Averaging, Weighted Averaging, Complementary Filter, Kalman Filter, or Madgwick Filter
  3. Adjust Sensor Parameters: Use the sliders to modify noise, bias, and update rate for each sensor to see how they affect fusion quality
  4. Tune Algorithm Settings: Adjust algorithm-specific parameters like alpha (complementary), Q/R (Kalman), or beta (Madgwick)
  5. Run Simulation: Click “Start Simulation” and enable/disable “Simulated Motion” to see real-time sensor fusion in action

Tips: - Watch the time-series plot to compare raw sensor readings (faded lines) with the fused output (bold teal line) - The error display shows MAE/RMSE and compares fusion performance against individual sensors - The orientation display visualizes angular position with the arrow showing fused output and small circles showing individual sensor readings - Try disabling sensors mid-simulation to see how different algorithms handle sensor failure

557.3 Interactive Sensor Fusion Visualizer

557.4 Algorithm Comparison

557.5 Sensor Characteristics Reference

557.6 Conceptual Diagrams

%% fig-alt: "Flowchart showing the sensor fusion pipeline from multiple sensor inputs to fused output"
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flowchart LR
    subgraph Sensors["Sensor Inputs"]
        A1[Accelerometer]
        A2[Gyroscope]
        A3[Magnetometer]
        A4[GPS]
    end

    subgraph Processing["Preprocessing"]
        B1[Noise Filtering]
        B2[Bias Compensation]
        B3[Time Alignment]
    end

    A1 --> B1
    A2 --> B1
    A3 --> B2
    A4 --> B3

    B1 --> C[Fusion Algorithm]
    B2 --> C
    B3 --> C

    C --> D{Output Type}
    D --> E[Orientation]
    D --> F[Position]
    D --> G[Velocity]

    style Sensors fill:#ECF0F1
    style Processing fill:#ECF0F1
    style C fill:#16A085,color:#fff
    style E fill:#27AE60,color:#fff
    style F fill:#27AE60,color:#fff
    style G fill:#27AE60,color:#fff


%% fig-alt: "Decision tree for selecting the appropriate sensor fusion algorithm"
%%{init: {'theme': 'base', 'themeVariables': {'primaryColor': '#2C3E50', 'primaryTextColor': '#fff', 'primaryBorderColor': '#16A085', 'lineColor': '#E67E22', 'secondaryColor': '#ECF0F1', 'tertiaryColor': '#fff'}}}%%
flowchart TD
    A{How many<br/>sensors?} --> B[2 Sensors]
    A --> C[3+ Sensors]

    B --> D{Need optimal<br/>estimation?}
    D -->|Simple OK| E[Complementary Filter]
    D -->|Yes| F[Kalman Filter]

    C --> G{Orientation<br/>only?}
    G -->|Yes| H[Madgwick Filter]
    G -->|Position too| I[Extended Kalman]

    E --> J[Alpha: 0.96-0.99]
    F --> K[Tune Q and R]
    H --> L[Beta: 0.01-0.5]
    I --> M[Full state model]

    style A fill:#2C3E50,color:#fff
    style E fill:#16A085,color:#fff
    style F fill:#E67E22,color:#fff
    style H fill:#9B59B6,color:#fff
    style I fill:#E74C3C,color:#fff


%% fig-alt: "State diagram showing the Kalman filter predict-update cycle"
%%{init: {'theme': 'base', 'themeVariables': {'primaryColor': '#2C3E50', 'primaryTextColor': '#fff', 'primaryBorderColor': '#16A085', 'lineColor': '#E67E22', 'secondaryColor': '#ECF0F1', 'tertiaryColor': '#fff'}}}%%
stateDiagram-v2
    [*] --> Initialize: Set x0, P0

    Initialize --> Predict: Start cycle

    state Predict {
        [*] --> StatePredict: x = A*x + B*u
        StatePredict --> CovPredict: P = A*P*A' + Q
    }

    Predict --> Update: Measurement z

    state Update {
        [*] --> Kalman: K = P*H'/(H*P*H' + R)
        Kalman --> StateUpdate: x = x + K*(z - H*x)
        StateUpdate --> CovUpdate: P = (I - K*H)*P
    }

    Update --> Predict: Next time step
    Update --> Output: Fused estimate x

    note right of Predict
        Prediction Step
        Uses motion model
    end note

    note right of Update
        Correction Step
        Uses measurements
    end note


%% fig-alt: "Comparison diagram of sensor strengths and weaknesses for fusion"
%%{init: {'theme': 'base', 'themeVariables': {'primaryColor': '#2C3E50', 'primaryTextColor': '#fff', 'primaryBorderColor': '#16A085', 'lineColor': '#E67E22', 'secondaryColor': '#ECF0F1', 'tertiaryColor': '#fff'}}}%%
flowchart TB
    subgraph Accel["Accelerometer"]
        A1[+ Long-term stable]
        A2[+ Gravity reference]
        A3[- Noisy short-term]
        A4[- Motion artifacts]
    end

    subgraph Gyro["Gyroscope"]
        G1[+ Smooth output]
        G2[+ High bandwidth]
        G3[- Drift over time]
        G4[- Integration error]
    end

    subgraph Mag["Magnetometer"]
        M1[+ Absolute heading]
        M2[+ No drift]
        M3[- Magnetic interference]
        M4[- Slow response]
    end

    Accel --> |Complements| Gyro
    Gyro --> |Complements| Mag
    Mag --> |Complements| Accel

    style Accel fill:#16A085,color:#fff
    style Gyro fill:#E67E22,color:#fff
    style Mag fill:#9B59B6,color:#fff

557.7 Understanding Sensor Fusion Algorithms

557.7.1 Simple Averaging

The simplest fusion approach treats all sensors equally:

\[\hat{x} = \frac{1}{n} \sum_{i=1}^{n} x_i\]

When to use: Quick prototypes, homogeneous sensors of equal quality.

557.7.2 Weighted Averaging

Assigns weights based on sensor reliability (inverse variance):

\[\hat{x} = \frac{\sum_{i=1}^{n} w_i x_i}{\sum_{i=1}^{n} w_i}, \quad w_i = \frac{1}{\sigma_i^2}\]

When to use: Known sensor characteristics, heterogeneous sensors.

557.7.3 Complementary Filter

Combines high-frequency response from gyroscope with low-frequency stability from accelerometer:

\[\theta_k = \alpha(\theta_{k-1} + \omega \cdot \Delta t) + (1-\alpha) \cdot \theta_{accel}\]

Where \(\alpha\) is typically 0.96-0.99.

When to use: IMU orientation estimation, real-time systems with limited compute.

TipTuning Alpha
  • Higher alpha (0.98+): Smoother output, but may drift over time
  • Lower alpha (0.90-0.95): More responsive to accelerometer, but noisier
  • Start with 0.98 and adjust based on your motion profile

557.7.4 Kalman Filter

The optimal state estimator for linear systems with Gaussian noise:

Predict: \[\hat{x}_{k|k-1} = A\hat{x}_{k-1} + Bu_k\] \[P_{k|k-1} = AP_{k-1}A^T + Q\]

Update: \[K_k = P_{k|k-1}H^T(HP_{k|k-1}H^T + R)^{-1}\] \[\hat{x}_k = \hat{x}_{k|k-1} + K_k(z_k - H\hat{x}_{k|k-1})\] \[P_k = (I - K_kH)P_{k|k-1}\]

When to use: Systems with known dynamics, need for prediction, GPS/INS fusion.

WarningKalman Filter Assumptions
  1. Linear system dynamics
  2. Gaussian (white) noise
  3. Known noise covariances (Q and R)

For nonlinear systems, use Extended Kalman Filter (EKF) or Unscented Kalman Filter (UKF).

557.7.5 Madgwick Filter

A computationally efficient orientation filter using gradient descent:

\[\hat{q}_k = \hat{q}_{k-1} + \dot{\hat{q}} \cdot \Delta t\]

Where the quaternion derivative includes both gyroscope integration and gradient descent correction toward the accelerometer/magnetometer reference.

When to use: 6-DOF or 9-DOF IMUs, embedded systems, AHRS applications.

557.8 Practical Scenarios Deep Dive

557.9 Performance Metrics Explained

Understanding fusion quality requires several metrics:

Metric Formula Description
MAE \(\frac{1}{n}\sum |y_i - \hat{y}_i|\) Mean Absolute Error - average deviation
RMSE \(\sqrt{\frac{1}{n}\sum(y_i - \hat{y}_i)^2}\) Root Mean Square Error - penalizes large errors
Variance \(\frac{1}{n}\sum(\hat{y}_i - \bar{\hat{y}})^2\) Output smoothness/consistency
Latency \(t_{output} - t_{event}\) Response delay
NoteGood Fusion Characteristics
  • MAE/RMSE lower than any individual sensor
  • Low variance (smooth output)
  • Minimal latency
  • Graceful degradation when sensors fail

557.10 Implementation Checklist

557.11 Advanced Topics

557.11.1 Handling Sensor Failures

Robust fusion systems must detect and handle sensor failures:

557.11.2 Time Synchronization

Sensors with different update rates require careful time alignment:

  1. Interpolation: Estimate sensor values at fusion timestamps
  2. Extrapolation: Predict values using motion model
  3. Buffering: Store readings and process when all sensors report
  4. Asynchronous fusion: Update state whenever any sensor reports
ImportantCritical for Multi-rate Systems

GPS updates at 1-10 Hz while IMUs run at 100-1000 Hz. Naive fusion that only runs at GPS rate wastes IMU data. Proper asynchronous fusion updates the state estimate with every IMU reading and corrects with GPS when available.

557.11.3 Adaptive Algorithms

Modern systems adjust fusion parameters based on conditions:

  • Innovation monitoring: Large prediction errors indicate model mismatch
  • Covariance matching: Adjust noise parameters based on residuals
  • Context awareness: Different parameters for stationary vs. moving
  • Machine learning: Learn optimal parameters from data

557.12 Summary

TipKey Takeaways
  1. No single sensor is perfect - Each has unique strengths and weaknesses
  2. Fusion improves accuracy - Well-designed fusion outperforms any individual sensor
  3. Algorithm choice matters - Match complexity to your constraints
  4. Tuning is essential - Default parameters rarely optimal
  5. Plan for failures - Robust systems degrade gracefully

557.13 Further Reading

557.14 Exercises

Using the drone orientation scenario: 1. Set accelerometer noise to 0.3 and gyroscope noise to 0.02 2. Find the optimal alpha value that minimizes MAE 3. Observe how the optimal alpha changes when you increase gyroscope drift (bias)

Using the vehicle tracking scenario: 1. Run each fusion algorithm for 30 seconds 2. Record the final MAE and RMSE values 3. Explain why Kalman filter performs better than simple averaging

  1. Start with the indoor navigation scenario using all sensors
  2. Disable the magnetometer mid-simulation
  3. Observe how different algorithms handle the loss
  4. Which algorithm degrades most gracefully?

This interactive tool demonstrates fundamental sensor fusion concepts. Real implementations require careful calibration, testing, and validation for safety-critical applications.