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Custom Kalman filtering in Inertial Navigation Systems (INS) involves tailoring the filter's state vector, measurement models, and noise matrices (

cap Q

and

cap R

) to optimize sensor fusion for specific dynamics. It typically uses an Extended Kalman Filter (EKF) to combine high-rate IMU data with external sensors (GPS/GNSS) to estimate and correct INS drift, attitude errors, and sensor biases.

Key Components of Custom INS Kalman Filtering

State Vector Definition: A common 15-state vector includes position (

$delta cap L comma delta lambda comma delta h$

), velocity (

$delta cap V sub e comma delta cap V sub n comma delta cap V sub u$

), attitude (

$phi sub e comma phi sub n comma phi sub u$

), gyroscope biases (

$epsilon sub x comma epsilon sub y comma epsilon sub z$

), and accelerometer biases (

$nabla sub x comma nabla sub y comma nabla sub z$

).
Filter Type: The Extended Kalman Filter (EKF) is standard for handling nonlinearities in vehicle motion and attitude.
Integration Approach:
- Loosely Coupled: Uses GPS position/velocity to update the INS.
- Tightly Coupled: Uses raw GPS pseudorange/pseudo-range-rate measurements for improved accuracy.
Adaptive Tuning: Techniques like Innovation-based Adaptive Estimation (IAE) or Multiple-Model-based Adaptive Estimation (MMAE) adjust noise matrices (

$cap Q$

and

$cap R$

) dynamically to handle varying environmental conditions, such as GPS outages.

Implementation Steps

Prediction (INS Mechanization): Propagate state estimates and covariance using high-rate (e.g., 100Hz+) IMU data.
Observation (Measurement Update): When external data (e.g., GPS, magnetometer, velocity log) is available, compute the "innovation" (difference between observed and predicted measurements).
Correction: The Kalman gain dictates how much the correction is applied to the state vector. The computed errors are used to correct the inertial navigation algorithm (closed-loop).
Tuning: Adjust

$cap Q$

(process noise) and

$cap R$

(measurement noise) to balance trust between inertial data and external sensors.

Customization for Specific Applications

Low-Cost IMUs: Require higher bias stability estimation in the state vector.
UAV/Robotics: May include magnetometers, barometers, and cameras in the observation model.
High-Dynamics: Requires faster, higher-fidelity models and adaptive

$cap Q$

matrix updating.

Tools like the MATLAB


                                                   insEKF

(Extended Kalman Filter) allow for defining custom sensors, motion models, and measurement parameters to build these tailored filters.

Adaptive Kalman Filtering for INS/GPS - ADS
Abstract. After reviewing the two main approaches of adaptive Kalman filtering, namely, innovation-based adaptive estimation (IAE)

Harvard University
Adaptive Kalman Filtering Methods for Low-Cost GPS/INS ...

Carnegie Mellon University
An Improved Innovation Adaptive Kalman Filter for Integrated INS/ ...
Sep 7, 2022 — 3. Methodology of Proposed Improved Innovation Adaptive Kalman Filter * 3.1. Constructing a Chi-Squared Test Using the Innovation ...

MDPI

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Videos

GPS-INS kalman filter

YouTube Zead Ibraheem

Dec 3, 2022

15:23

The Kalman filter optimizes the innovation gains derived from GPS position error to align the INS model with GPS measurements.

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.

5+6. Intro to inertial navigation: Kalman Filter and GNSS-INS ...

YouTube Dr. Marcelo Santos

Nov 17, 2019

10:39

Learn how the Kalman filter integrates GNSS and INS data for a more accurate navigation solution, correcting INS drift with GNSS updates.

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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

Missing: ~~custom~~ ‎| Show results with: custom

Adaptive Kalman Filtering Methods for Low-Cost GPS/INS ...

Carnegie Mellon University

https://kilthub.cmu.edu › articles › files

Carnegie Mellon University

https://kilthub.cmu.edu › articles › files

PDF

by A Werries Cited by 34 — Kalman filters (KF) are a standard approach for GPS/INS integration , but require careful tuning in order to achieve quality results. This creates a motivation ...

Missing: ~~custom~~ ‎| Show results with: custom

2.8 Kalman Filter

VectorNav Technologies

https://www.vectornav.com › resources › math-kalman

VectorNav Technologies

https://www.vectornav.com › resources › math-kalman

The Kalman filter provides an optimal estimate of how a system is going to change given noisy measurements and imperfect knowledge about the system. Read more

How does Kalman filtering work in inertial navigation ...

Aviation Stack Exchange

https://aviation.stackexchange.com › questions › how-d...

Aviation Stack Exchange

https://aviation.stackexchange.com › questions › how-d...

Mar 9, 2017 — Basically, the Kalman filter extrapolates an expected value and compares that to the next measurement . The output is a combination of the two. Read more

3 answers · Top answer: First of all you should know that a Kalman filter is a state estimation technique. More ...

alirezaahmadi/KalmanFilter-Vehicle-GNSS-INS

GitHub

https://github.com › alirezaahmadi › KalmanFilter-Vehicl...

GitHub

https://github.com › alirezaahmadi › KalmanFilter-Vehicl...

KalmanFilter-Vehicle-GNSS- INS project is about the determination of the trajectory of a moving platform by using a Kalman filter . Read more

Custom Kalman Filter for UAV Attitude Estimation

Reddit · r/AerospaceEngineering

6 comments · 10 months ago

Reddit · r/AerospaceEngineering

6 comments · 10 months ago

Here's a medium article I wrote talking about the custom, quaternion-based Extended Kalman Filter I implemented for attitude estimation. Read more

Design and analysis of an inertial calibration Kalman filter

Iowa State University Digital Repository

https://dr.lib.iastate.edu › entities › publication

Iowa State University Digital Repository

https://dr.lib.iastate.edu › entities › publication

by CW Johnson 1996 Cited by 1 — This thesis addresses the application of Kalman filtering to the in-flight calibration of an Inertial Navigation System ( INS ) using decentralized cascaded ...

Missing: ~~custom~~ ‎| Show results with: custom

Extended Kalman Filter Navigation Overview and Tuning

ArduPilot

https://ardupilot.org › dev › docs › extended-kalman-fil...

ArduPilot

https://ardupilot.org › dev › docs › extended-kalman-fil...

This article describes the Extended Kalman Filter (EKF) algorithm used to estimate vehicle position, velocity and angular orientation. Read more

Direct Kalman Filtering of GPS/INS for Aerospace ...

University of Calgary

https://www.ucalgary.ca › engo_webdocs › PDF

University of Calgary

https://www.ucalgary.ca › engo_webdocs › PDF

PDF

by J Wendel Cited by 29 — Usually, an indirect Kalman filter formulation is applied to estimate the errors of an INS strapdown algorithm (SDA), which are used to correct the SDA.

6 pages

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