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1 INTRODUCTION

In recent years, there has been a dynamic development

of Unmanned Aerial Vehicles (UAVs), which have

found wide application in areas such as environmental

monitoring, infrastructure inspection, search and

rescue operations, and precision agriculture. A key

component enabling the autonomous operation of

UAVs is the navigation system, which allows for the

determination of the vehicle’s current position and

orientation in space. In most contemporary UAV

systems, the Global Positioning System (GPS) is

utilized due to its availability, accuracy, and ease of

integration with other control system components [1].

However, in many operational scenarios—such as

missions conducted in dense forests, narrow urban

streets, tunnels, indoor environments, or under

conditions of electromagnetic interference (e.g., due to

intentional GPS jamming)—the availability of satellite

signals is limited or entirely absent [2]. In such cases,

the development of alternative localization methods

becomes essential to maintain the navigational

functionality of UAVs in GPS-denied environments.

Figure 1. GPS signal interference in the vicinity of the

Kaliningrad region (source: https://gpsjam.org)

Fusion of Optical Flow and Dead Reckoning Algorithms

for UAV Navigation Without GPS

J. Walczak, B. Szykuła, P. Targowski & T. Pałys

Military University of Technology, Warsaw, Poland

ABSTRACT: The article presents an innovative navigation system for unmanned aerial vehicles (UAVs) operating

in environments with limited or unavailable GPS signal. The developed solution integrates dead reckoning

navigation methods with advanced computer vision algorithms utilizing optical flow analysis, enabling precise

drone positioning. The research includes implementation of data fusion algorithms from inertial measurement

units (IMU) and analysis of image sequences from a downward-facing camera. Experimental results from tests

conducted in both simulated environments and on real flight platforms are presented. The study demonstrates

that the application of optical flow techniques significantly improves dead reckoning navigation accuracy in GPS-

denied conditions, reducing the accumulating position error. The proposed system offers a promising solution

for UAV operations in challenging navigation conditions, such as urban areas, indoor environments, or regions

with electromagnetic interference.

http://www.transnav.eu

the International Journal

on Marine Navigation

and Safety of Sea Transportation

Volume 19

Number 4

December 2025

DOI: 10.12716/1001.19.04.02

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One alternative approach involves the use of optical

flow, which enables the estimation of the UAV's

relative motion with respect to its surroundings based

on the analysis of image sequences captured by

onboard cameras [3]. Another approach is inertial

navigation based on dead reckoning, which estimates

the current position by integrating data from

accelerometers and gyroscopes without relying on

external signals [4]. Both approaches, however, have

inherent limitations: optical flow is susceptible to

errors in homogeneous or poorly textured

environments, while dead reckoning suffers from

cumulative position drift over time.

The aim of this study is to propose and evaluate a

fusion method combining optical flow and dead

reckoning navigation to improve the accuracy and

robustness of UAV navigation in GPS-denied

environments. Integrating these two approaches

allows for mutual compensation of their respective

weaknesses, resulting in a more stable and accurate

position estimation. The following sections present a

review of related work on GPS-independent

localization methods, a description of the implemented

algorithms, and the results of simulation-based and

field experiments.

2 SURVEY OF ALTERNATIVE UAV NAVIGATION

APPROACHES

In response to the growing need for reliable UAV

navigation in environments where access to GPS

signals is limited or entirely unavailable, several

alternative localization methods have been proposed

in the literature. Particular attention has been given to

systems based on the fusion of data from optical and

inertial sources, such as cameras and Inertial

Measurement Units (IMUs). This chapter presents

previous approaches that utilize optical flow and dead

reckoning independently, as well as studies that

integrate both techniques within GPS-independent

localization systems.

2.1 Optical Flow in UAV Navigation

Optical flow is a technique for estimating a vector field

that describes the motion of image points between

consecutive frames. It is commonly used in mobile

robotics to estimate both velocity and direction of

movement within an environment. Classical

algorithms such as the Horn–Schunck and Lucas–

Kanade methods enable accurate optical flow

estimation in well-textured scenes [5].

In the context of UAVs, Santos-Victor and Sandini

demonstrated that optical flow can be effectively

employed for docking manoeuvres and navigation

within enclosed spaces [6]. More recent studies, such as

those by Kendall and Cipolla, have applied deep

learning techniques to improve flow estimation

accuracy under challenging lighting conditions and in

environments with low texture [7].

Although optical flow provides valuable

information about relative motion, its accuracy is

highly dependent on image quality, and it may result

in significant errors in homogeneous or poorly lit

environments. Therefore, it is often combined with

other sources of information to enhance robustness and

reliability.

2.2 Inertial Navigation and the Dead Reckoning Method

Dead reckoning is a method for estimating the current

position based on the previous state and information about

the traversed path, typically obtained from inertial sensors

such as accelerometers and gyroscopes. These solutions are

characterized by high-frequency measurements and

independence from external sources of information [8].

However, the primary limitation of this method lies in the

accumulation of error over time, due to its recursive nature—

inferring the current state solely from the last known state.

Classical inertial navigation systems (INS) have

been thoroughly described by Titterton and Weston,

who emphasized the necessity of incorporating

auxiliary data sources to compensate for inertial drift

[9]. In the case of UAVs, dead reckoning remains

effective only for short durations without correction

from external positioning systems.

2.3 Fusion of Optical Flow and Dead Reckoning

One of the most promising approaches to GPS-denied

UAV localization involves the integration of visual and

inertial data, commonly referred to as Visual-Inertial

Odometry (VIO). Mourikis and Roumeliotis proposed

the Multi-State Constraint Kalman Filter (MSCKF),

which enables real-time trajectory estimation of UAVs

while accounting for measurement uncertainties [10].

Weiss et al. developed a lightweight VIO system for

micro-UAVs, capable of real-time operation with

minimal computational overhead—an important

consideration for onboard applications [11]. Similarly,

Badino et al. demonstrated that combining optical flow

with IMU data enhances the robustness of the system

against sudden lighting changes and temporary loss of

visual features [12].

More recent approaches leverage deep neural

networks to estimate position based on sequences of

images and inertial data. The work by Zhan et al.

introduces DeepVO—a recurrent network that learns

temporal dependencies between visual and inertial

observations [13]. Although such methods achieve

high accuracy, their implementation requires

substantial computational resources and access to

extensive training datasets.

A review of the literature indicates that the fusion

of optical flow and inertial data represents a promising

solution to the challenge of UAV navigation in GPS-

denied environments. Key challenges include drift

mitigation, robustness to visual disturbances, and real-

time operation on platforms with limited resources. In

the following sections, the proposed system

architecture is presented, along with the results of its

validation in both simulated and real-world

environments.

3 METHOD FOR ESTIMATING UAV POSITION

3.1 Estimating UAV Velocity Using Optical Flow

To estimate the velocity of the UAV relative to the

ground, optical flow analysis was applied to images

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captured by a downward-facing onboard camera. The

method is based on the Farnebäck algorithm [14],

which allows for efficient computation of pixel

displacement vectors between two consecutive image

frames.

The approach proposed by Farnebäck [14] estimates

dense optical flow by approximating image intensity

using a quadratic function within local

neighbourhoods. It is assumed that the displacement of

points in the image between two frames results

primarily from the movement of the camera relative to

the environment. The optical flowv=(vx, vy) is estimated

as a displacement vector for each pixel between frames

It i It+1. The resulting flow field is decomposed into

horizontal and vertical components u(x, y) and v(x, y),

and the average flow magnitude is then computed as:

( ) ( )

v u x y v x y



(1)

where N is the number of pixels in the image.

To convert pixel displacement into real-world units

(meters), known camera parameters are used: focal

length f in millimetres, flight altitude h and the image

diagonal length dpx. If the camera's field of view

corresponds to that of a pinhole camera with focal

length f, the physical length of the image diagonal on

the ground dm is given by:

d 2 tan





=





(2)

where



is the camera’s field of view in radians. The

final scaling factor from pixels to meters allows the

computation of real-world velocity as:

real

FPS

vsf=

(3)

where fFPS is the frame rate of the video stream (frames

per second).

3.2 Integration of Velocity and Orientation in Position

Estimation

The integration process is based on continuously

updating the UAV’s position P(t) using its previous

state and the currently estimated velocity and flight

direction:

( ) ( ) ( )

Pt Δt ΔP t V t t+ = +

(4)

where V(t) is the velocity estimated from optical flow

using the Farnebäck method, t is the time interval

between successive measurements, and P(t) represents

the UAV’s position in the geographic coordinate

system (latitude, longitude, altitude).

The displacement d over time t is computed based

on the current speed V(t) and the heading angle



(t),

which can be obtained from onboard IMU and

magnetometer sensors:

( )

Vt Δdt=

(5)

Figure 2. Diagram of data flow used for determining UAV

motion parameters (own work).

The new geographic position is calculated using

spherical formulas that solve the direct geodesic

problem, given a distance and a bearing:

( ) ( ) ( )

2 1 1

arcsin sin cos cos sin cos

   



   



   

   



(6)

( ) ( ) ( ) ( )

2 1 1 1 2

λ arctan2 sin sin cos ,cos sin sin 

    



   

= + −



   

   



(7)

where



and



denote geographic latitude and

longitude, respectively, d is the ground distance

travelled by the UAV, and R is the Earth’s radius.

The main advantage of the proposed approach lies

in its resilience to temporary GNSS signal loss. The

system maintains continuity in position estimation by

relying on motion information from independent

sources, such as a downward-facing camera and

inertial sensors. As a result, it enables navigation in

environments with limited satellite visibility, such as

urban canyons, tunnels, or indoor spaces.

Additionally, velocity estimation based on optical flow

contributes to smoother trajectory estimation,

eliminating the abrupt positional jumps typically

associated with weak or degraded GPS signals.

4 EXPERIMENTAL ENVIRONMENT

The experiments were conducted in a simulated

environment, where sensor data (camera images and

IMU measurements) were previously recorded during

real-world UAV flights and subsequently processed

locally on a computer. The objective was to evaluate

the trajectory estimation system under GNSS-denied

conditions.

The block diagram in Figure 3 illustrates the overall

processing pipeline. The system takes as input video

frames and corresponding samples from the Inertial

Measurement Unit (IMU), which include altitude and

orientation data. These inputs are then passed to the

optical flow processing module, which estimates the

horizontal ground-relative velocity (groundspeed).

The resulting velocities are subsequently used by the

dead reckoning module to determine the UAV’s

position in geographic coordinates, based on current

speed and orientation.

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Figure 3. Diagram illustrating the operation of the software

prototype developed for experimental purposes (own work).

For the experimental validation, the industrial UAV

platform Yuneec H520 was used. This hexacopter is

equipped with a high-resolution camera (E90, 4K) and

was chosen for its stable flight performance, precise

trajectory control, and full access to sensor logs,

including:

− downward-facing video recordings from the

onboard camera,

− IMU data: accelerations, angular velocities, and

magnetometer readings,

− barometric altitude readings,

− telemetry and navigation data (including GPS,

which was used for reference only).

The Yuneec H520 platform allows for data export in

standard formats and ensures proper time

synchronization of onboard sensors, making it a

suitable testbed for evaluating alternative GNSS-

independent navigation algorithms.

5 EXPERIMENTAL RESULTS

5.1 Experiment No. 1

The test flight was conducted over flat, open terrain

with sparse vegetation (individual trees not exceeding

30 meters in height) and good visual texture. The

mission duration was 129 seconds, consisting of 3885

frames, with an average flight altitude of 61 meters.

Weather conditions were sunny with light wind.

Table 1. Position error metrics compared to GNSS

(Experiment 1)

Mean error (MAE) [m]

RMSE [m]

Maximum error [m]

17,82

19,80

33,65

Table 2. Velocity error metrics compared to GNSS

(Experiment 1)

Mean error (MAE) [m/s]

RMSE [m/s]

Maximum error [m/s]

0,25

0,32

1,36

The obtained results indicate high effectiveness of

the proposed navigation method in open-space

conditions. The estimated position trajectory without

the use of GNSS shows a moderate mean error (17.82

m) and a relatively low maximum error (33.65 m),

which can be considered acceptable given the absence

of satellite-based positioning. The nature of the error

suggests a stable, systematic drift caused by motion

integration through dead reckoning without external

position correction.

Velocity estimation using optical flow

demonstrated very good agreement with GPS data.

The low mean error of 0.25 m/s and a maximum

deviation of 1.36 m/s confirm the validity of the applied

algorithm in a well-textured environment with stable

lighting conditions. Minor discrepancies may have

resulted from brief overflights of taller vegetation or

transitions over less distinct surfaces (e.g., uniform

greenery).

Figure 3. Experiment 1: Trajectory comparison – GPS vs

estimated (GNSS-free navigation)

Figure 4. Experiment 1: Velocity over time – Optical Flow vs

GPS

5.2 Scenario No. 2

The test flight was conducted over flat, open terrain

with isolated trees up to a maximum height of 30

meters and good visual texture. The mission duration

was 120 seconds, comprising 3619 frames, with an

average flight altitude of 120 meters. Weather

conditions were sunny with light wind.

Table 3. Position error metrics relative to GNSS

(experiment 2)

Mean error (MAE) [m]

RMSE [m]

Maximum error [m]

38,67

47,10

85,67

Table 4. Velocity error metrics relative to GNSS

(experiment 2)

Mean error (MAE) [m/s]

RMSE [m/s]

Maximum error [m/s]

1,16

1,22

2,51

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Compared to the previous scenario, both position

and velocity estimation errors are noticeably higher.

The average position error exceeds 38 meters, with a

maximum error over 85 meters, indicating a significant

deviation of the estimated trajectory relative to the

GNSS reference. The most probable factor contributing

to this accuracy degradation is the increased flight

altitude. At 120 meters, ground texture becomes

significantly less distinct in the camera image, which

negatively affects the quality of optical flow

calculations. In addition, suboptimal camera alignment

relative to the flight direction may have introduced

distortions in the motion vector field.

Velocity estimation errors are also more

pronounced—an average difference of 1.16 m/s and a

maximum deviation of 2.51 m/s. This confirms that for

flights at higher altitudes, or when the camera is not

properly aligned, a drop in estimation quality should

be expected. Such conditions highlight the importance

of future work focused on error compensation and

adaptive calibration of input parameters.

Figure 5. Experiment 2: Trajectory comparison – GPS vs

estimated (GNSS-free navigation)

Figure 6. Experiment 2: Velocity over time – Optical Flow vs

GPS

5.3 Scenario No. 3

The test flight was conducted partially over flat, open

terrain with good visual texture, and partially over

densely forested areas. The mission lasted 190 seconds

and included 5712 frames, with an average flight

altitude of 60 meters. Weather conditions were sunny

with light wind.

Table 5. Position error metrics relative to GNSS

(experiment 3)

Mean error (MAE) [m]

RMSE [m]

Maximum error [m]

59,84

74,44

116,40

Table 6. Velocity error metrics relative to GNSS

(experiment 3)

Mean error (MAE) [m/s]

RMSE [m/s]

Maximum error [m/s]

0,97

1,78

6,07

The results of the experiment show a significant

increase in estimation errors in the second half of the

flight. The primary cause is not directly related to the

forested terrain itself, but rather to the fact that the tree

canopies were much closer to the camera than assumed

based on the flight altitude obtained from the

magnetometer.

As a result, the optical flow was incorrectly scaled,

leading to an overestimation of speed and,

consequently, a substantial trajectory deviation. This

phenomenon is clearly visible in the velocity plot (Fig.

8), where sudden spikes in speed appear during the

middle segment of the mission. Future improvements

should include consideration of relative height above

the observed surface, for instance by integrating

additional depth sensors or analysing scene structure.

Figure 7. Experiment 3: Trajectory comparison – GPS vs

estimated (GNSS-free navigation)

Figure 8. Experiment 3: Velocity over time – Optical Flow vs

GPS

5.4 Scenario No. 4

The test flight was conducted over flat, open terrain

with sparse vegetation (individual trees up to 30

meters in height) and good visual texture. The mission

lasted 138 seconds and consisted of 4,143 frames, with

an average flight altitude of 119 meters. Weather

conditions were sunny with light wind.

Table 7. Position error metrics relative to GNSS

(experiment 4)

Mean error (MAE) [m]

RMSE [m]

Maximum error [m]

11,17

12,34

20,81

Table 8. Velocity error metrics relative to GNSS

(experiment 4)

Mean error (MAE) [m]

RMSE [m]

Maximum error [m]

0,46

0,65

2,92

Despite the relatively high flight altitude (119 m),

the system demonstrated very good accuracy in both

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position and velocity estimation. The average position

error was only 11.17 meters, and the maximum

deviation did not exceed 21 meters. The velocity

estimated via the optical flow method closely matched

the GPS data, with an average error below 0.5 m/s.

These results suggest that, given sufficient visual

texture and uniform terrain, the system can operate

reliably even at higher altitudes. A key factor was the

homogeneous and well-defined surface structure (e.g.,

fields, roads, low vegetation), which enabled stable

optical flow analysis and minimized disturbances in

metric scaling.

Figure 9. Experiment 4: Trajectory comparison – GPS vs

estimated (GNSS-free navigation)

Figure 10. Experiment 4: Velocity over time – Optical Flow vs

GPS

6 CONCLUSION

This work presented a prototype navigation system for

an unmanned aerial vehicle (UAV) designed to

estimate its position in environments where GNSS

signals are unavailable. The proposed method relies on

optical flow analysis from a nadir-facing camera and a

simplified fusion with spatial orientation data. The

implemented model was evaluated in a simulated

environment using real flight data, and the results

indicate that it is possible to maintain consistent

trajectory and velocity estimation even under

challenging observational conditions.

The key advantages of the presented approach

include its resilience to temporary GNSS signal loss

and the smoothness of the estimated trajectory—

enabled by velocity estimation derived from optical

flow. The method is characterized by low

computational complexity, making it suitable for on-

board implementation in resource-constrained UAV

platforms.

The observed limitations—particularly positional

drift over time, sensitivity to heterogeneous terrain

structure, and distortion caused by objects such as trees

or buildings—highlight the need for further

development. Specifically, errors resulting from

inaccurate estimation of the UAV's height above

ground can be mitigated using additional sensors such

as laser rangefinders. Alternatively, more advanced

fusion with classical inertial navigation methods could

be implemented, incorporating airspeed

measurements and inertial sensor data.

The results obtained in this study provide a

promising foundation for future work toward a

lightweight, GNSS-independent positioning system,

intended for use in environments with limited satellite

visibility.

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