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Kalman filtering is

a fundamental, recursive algorithm used to process noisy data from Inertial Measurement Units (IMUs)—accelerometers, gyroscopes, and magnetometers—to provide accurate, real-time estimations of orientation, velocity, and position . It works by fusing noisy sensor measurements with a physical model of the system, optimizing the state estimation while handling sensor biases and noise.

Why Kalman Filters are Used for Inertial Sensors

Sensor Noise & Drift: Low-cost MEMS sensors are notoriously noisy and subject to drift; integrating acceleration to find position leads to error growing with the cube of time.
Sensor Fusion: Kalman filters allow combining sensors with complementary strengths (e.g., gyroscopes for fast, short-term motion; accelerometers/magnetometers for long-term orientation reference).
Bias Estimation: Kalman filters can augment the state vector to estimate time-varying sensor biases, such as gyroscope drift, significantly improving accuracy.

Key Aspects of Kalman Filtering in Inertial Data

Algorithm Steps: The filter operates in a loop of two main steps:
1. Prediction: Using the previous best estimation and gyroscope data, it predicts the next state.
2. Correction (Update): Using accelerometer or magnetometer data, it corrects the prediction, calculating the "Kalman Gain" to balance trust between the model and the new measurements.
Types of Filters:
- Linear Kalman Filter (KF): Suitable for linear systems.
- Extended Kalman Filter (EKF): The most common approach for IMUs, as orientation kinematics are non-linear.
- Unscented Kalman Filter (UKF): Handles stronger non-linearities better than EKF.
Common Implementations:
- AHRS (Attitude and Heading Reference Systems): Uses EKF to estimate orientation (pitch, roll, yaw).
- INS/GNSS Integration: Uses Kalman filters to combine INS data with GPS, crucial for navigation when GPS is interrupted.
- ZUPT (Zero Velocity Update): In pedestrian navigation, Kalman filters detect when a foot is on the ground to correct for drift.

Main Challenges and Considerations

Computational Cost: EKF/UKF involves matrix operations that increase with the number of states (e.g., 15+ states for navigation).
Tuning Q and R Matrices: The performance depends on setting the process noise covariance (

$cap Q$

) and measurement noise covariance (

$cap R$

).
Observability: For the filter to work, the system must be "observable"—there must be enough data (e.g., non-collinear magnetic field and gravity) to estimate the states.

IMU Signal Processing with Kalman Filter - Sparx Engineering
Feb 13, 2024 — IMU Signal Processing with Kalman Filter. ... Sensors play a pivotal role in gathering critical data from the world around us. One...

Sparx Engineering
kalman filters - Getting position data from 9-axis IMU

Signal Processing Stack Exchange
Direct Kalman Filtering of GPS/INS for Aerospace Applications
This model was augmented by six additional states to allow the estimation of time-constant or slowly varying angular rate sensor a...

University of Calgary

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IMU Signal Processing with Kalman Filter

Sparx Engineering

https://sparxeng.com › Blog

Sparx Engineering

https://sparxeng.com › Blog

Feb 13, 2024 — The main idea of Kalman Filter is to combine the data that comes from the model with the measurements that comes from the sensor . Read more

Scholarly articles for kalman filtering in inertial sensor data processing
… measurement using inertial sensors , ultrasonic sensors … - ‎ Zhao - Cited by 265 … Kalman filter for human motion tracking with an inertial … - ‎ Ligorio - Cited by 250 … processing from GPS and IMU using Kalman filtering … - ‎ Bistrovs - Cited by 18

Videos

Kalman Filter for Beginners, Part 3- Attitude Estimation, Gyro ...

YouTube Dr. Shane Ross

May 31, 2023

40:20

Learn how to estimate velocity from position using a Kalman filter . Compare it with finite differences.

(Sponsored) Extended Kalman Filter Software Implementation ...

YouTube Phil’s Lab

Aug 22, 2022

28:57

Learn to implement an Extended Kalman Filter in real-time on an embedded system using STM32 and C.

Real time Kalman filter on an ESP32 and sensor fusion.

YouTube T.J Moir

May 8, 2021

23:40

This video demonstrates a real-time Kalman filter demo on ESP32 using Arduino, fusing accelerometer and gyroscope data to estimate pitch and roll angles.

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Filtering of IMU data using Kalman filter

Sac State Scholars

https://scholars.csus.edu › view › pdfCoverPage

Sac State Scholars

https://scholars.csus.edu › view › pdfCoverPage

PDF

A Kalman filter is simply an optimal recursive data processing algorithm. It processes all available measurements, regardless of their precision, to estimate ... Read more

Mathematical Model of an IMU Kalman Filter ...

GitHub

https://nitinjsanket.github.io › tutorials › attitudeest

GitHub

https://nitinjsanket.github.io › tutorials › attitudeest

The magic of a Kalman filter is that it dynamically weights the estimates from both the process model and sensor measurements . Note that the state could ... Read more

kalman filters - Getting position data from 9-axis IMU

Signal Processing Stack Exchange

https://dsp.stackexchange.com › questions › getting-pos...

Signal Processing Stack Exchange

https://dsp.stackexchange.com › questions › getting-pos...

Dec 10, 2022 — I want to track the movement of a person in a 2D plane using a 9-axis IMU . The size of the plane in which the movement is not bigger than 6 by 6 meter. Read more

Kalman filter based integration of multiple sensor data for the ...

Technische Universität Wien | TU Wien

https://repositum.tuwien.at › bitstream › Li Qing - ...

Technische Universität Wien | TU Wien

https://repositum.tuwien.at › bitstream › Li Qing - ...

PDF

by Q Li 2023 — Over the past years, a loosely coupled Kalman filter algorithm based on the fusion of GNSS, IMU and odometer data was developed by the doctoral candidate. This ...

173 pages

A Novel Approach for Kalman Filter Tuning for Direct ... - PMC

National Institutes of Health (NIH) | (.gov)

https://pmc.ncbi.nlm.nih.gov › articles › PMC11598776

National Institutes of Health (NIH) | (.gov)

https://pmc.ncbi.nlm.nih.gov › articles › PMC11598776

by AJA Tavares Jr 2024 Cited by 16 — This work presents an innovative approach for tuning the Kalman filter in INS/GNSS integration , combining states from the inertial navigation system (INS) and ... Read more

comp.dsp | Kalman Filter Post processing of IMU data

DSPRelated.com

https://www.dsprelated.com › showthread › comp.dsp

Jul 21, 2008 — Hello All I'm quite a newbie to the Kalman Filter . I'm using a 3 axis accelerometer and gyroscope data to calculate angle, and from this 3D ... Read more

The Kalman Filter: An algorithm for making sense of fused ...

Medium · Sharath Srinivasan

1.7K+ likes · 7 years ago

Medium · Sharath Srinivasan

1.7K+ likes · 7 years ago

The Kalman filter is relatively quick and easy to implement and provides an optimal estimate of the condition for normally distributed noisy sensor values ... Read more

Missing: ~~inertial~~ ‎| Show results with: inertial

Kalman Filter - Solutions for Challenging Environments

Nordic Inertial

https://www.nordicinertial.com › Kalman+Filter+-+Solu...

Nordic Inertial

https://www.nordicinertial.com › Kalman+Filter+-+Solu...

The Kalman filter is a mathematical method that can estimate various quantities based on noisy measurement data . Here, noisy refers to measurement error. Read more