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1 INTRODUCTION

Paradoxically, the ubiquity of and trust in GNSS makes

these systems vulnerable to interference. Signals

transmitted by satellites reach Earth with a power of

the order of picowatts - making them easily drowned

out by stronger radio emissions [4]. In addition, open

civilian GNSS signals (GPS, Galileo, GLONASS,

BeiDou) are not encrypted or authenticated, which

means there are no built-in safeguards against

imitation. This raises two main threats: jamming and

spoofing. Jamming involves intentionally generating

radio interference on GNSS frequencies so that the

receiver is unable to receive the true signal from the

satellites [10]. The result of such an action is the loss or

severe degradation of satellite navigation performance

- the receiver may report a missing signal or determine

a position with very low accuracy. Spoofing, on the

other hand, is a more sophisticated attack in which an

attacker broadcasts falsified signals that mimic real

GNSS messages so that the receiver assumes them to

be authentic [10]. In this way, erroneous location or

time information can be fed to the receiver, potentially

directing the “victim” to the wrong location or

misinforming time-dependent systems (such as power

grids or financial networks). Interference with GNSS

signals is not just a theoretical threat, but a real

problem noted with increasing frequency around the

world. Reports from the maritime and aviation services

indicate an increasing number of jamming and

spoofing incidents, especially in geopolitically unstable

regions [10]. For example, numerous GPS signal

disruptions have been reported in recent years for

ships in the Eastern Mediterranean, the Black Sea or the

Persian Gulf. Civil aviation has also seen an alarming

increase in spoofing attacks, with pilots reporting

The Use of Artificial Intelligence in Enhancing

Navigation Safety in Case of GNSS Signal Fading

or Interference

M. Chrzan

Kazimierz Pulaski University in Radom, Radom, Poland

ABSTRACT: Global Navigation Satellite Systems (GNSS) play a key role in modern navigation and transportation

service delivery. Today it is difficult to imagine the daily operation of land, sea or air transportation without the

positioning and timing provided by satellite systems [6, 8, 11]. In civil aviation, GNSS provides precision landing

approaches and support for safety systems, in maritime navigation it enables open sea course determination and

maneuvering, and on land it directs vehicle navigation and synchronization of telecommunications networks.

Many of these applications are so-called PNT (Positioning, Navigation and Timing) systems, where uninterrupted

and accurate position and timing information is critical to safe operations [8]. Unfortunately, satellite systems

have recently become the target of hacking attacks. This paper will present AI methods for detecting GNSS

anomalies, the role of inertial systems as an independent navigation source, and position correction techniques

(e.g., using Kalman filters) supported by intelligent algorithms. An overview of current research and experiments

in this field will also be presented, as well as conclusions on the effectiveness and development prospects of the

technologies discussed.

http://www.transnav.eu

the International Journal

on Marine Navigation

and Safety of Sea Transportation

Volume 19

Number 2

June 2025

DOI: 10.12716/1001.19.02.31

590

instances where onboard systems gave incorrect

coordinates or altitude, posing an obvious risk to flight

safety. Spoofing applied to an aircraft can result in

erroneous navigation, and in extreme cases - if the crew

does not figure it out in time - even lead to a violation

of airspace or an attempted landing on a false path. In

military applications, the consequences are equally

serious: a spoofed signal can result in military units

losing orientation or taking control of the unmanned

aircraft, which is a significant breach of operational

security [8, 10].

The reason for the vulnerability of GNSS systems to

attacks is the lack of mechanisms to verify the

reliability of the signal - most receivers trust the data

received from satellites implicitly. Unlike, for example,

computer networks, where there are firewalls and

authentication systems or protocol verification

procedures, a typical GNSS receiver has no way to

distinguish a genuine signal from a crafted one until

additional detection methods are put in place. The fact

that full documentation of GNSS protocols is publicly

available makes it easier for potential attackers to

prepare hardware and software for an attack. What's

more, advances in technology and engineering have

made the “barrier to entry” for attackers significantly

lower - nowadays, for a few hundred dollars, one can

get a software-defined radio (SDR) capable of

generating signals that interfere with or mimic GNSS

[11]. While this used to require specialized knowledge

and expensive equipment, today there are open-source

tools and instructions available on the Internet. All of

this demonstrates the importance of ensuring

navigation safety despite GNSS interference.

Improving the resilience of navigation systems to

GNSS interference has thus become a research and

engineering priority in recent years. Multi-layered

strategies are being introduced: from improving the

receivers themselves (e.g., anti-jam antennas, signal

authentication in new systems) to system approaches

using redundant sources of position information and

artificial intelligence algorithms to detect and

compensate for anomalies. Particularly promising is

the use of artificial intelligence (AI) - machine learning

and deep learning techniques - to analyze navigation

data to quickly catch unusual system behavior and

sustain navigation in the event of satellite signal loss.

2 LITERATURE RESEARCH AND REVIEW

2.1 Application of artificial intelligence in GNSS anomaly

detection

Effectively recognizing that a GNSS signal has been

disturbed or falsified is the first step to ensuring

navigation safety. Traditional GNSS receivers have

limited mechanisms to warn of anomalies - Receiver

Autonomous Integrity Monitoring (RAIM) systems,

for example, can detect that a pseudo-distance

measurement deviates from others, but against

specialized spoofing attacks they are sometimes

powerless. Therefore, more advanced detection

methods are being developed, often using multi-sensor

analysis and intelligent algorithms. In general, GNSS

anomaly detection approaches can be divided into

several categories: signal-based methods, bit/data-

based methods, positional methods, and methods

using machine learning [11].

Signal methods involve monitoring the parameters

of the GNSS signal received by the antenna - such as

signal power, signal-to-noise ratio (C/N0), or reception

characteristics on multiple antennas. Jamming

interference often manifests itself as a sharp drop in

C/N0 across all channels and loss of satellite tracking,

while spoofing can cause unnatural changes in power

(e.g., a sudden increase in signal strength seemingly

from all satellites simultaneously) or abnormal

behavior of the receiver's synchronization block. Signal

detection can use simple threshold tests or more

complex signal processing algorithms - such as

observing the signal spectrum in the GNSS band to

identify additional unwanted signals.

Bitwise methods focus on the content of navigation

data demodulated from the signal. The receiver can

verify that the almanac/efemerid data or time marks

are consistent and as expected. False signals may

contain minor deviations in the data (e.g., invalid

satellite identifier, repeated data string - characteristic

of meaconing, i.e., retransmission of a real signal with

a delay). Analysis of this data, supported, for example,

by correlation techniques between multiple signals,

makes it possible to detect certain types of attacks. For

example, one method uses monitoring the cross-

correlation of multiple GNSS observations (pseudo-

distance, carrier phases, etc.) and looking for statistical

outliers, which then serve as input features to a

machine-learned detector [12]. In experiments, it has

been shown that a trained classifier (e.g., SVM -

Support Vector Machine) fed with such features can

distinguish spoofing/meaconing situations from

normal ones, effectively alerting to an attack.

Importantly, this approach was verified on real

incident data - the algorithm learned on simulation

data also recognized recordings of real disturbances

with high efficiency [12].

Positional methods are based on checking the

consistency of the determined position with other

information. For example, a vessel equipped with

GNSS and radar or lidar can compare independent

position measurements: if the GPS shows that the

vessel has moved a few hundred meters, while the

radar still sees the shore at a constant distance - that's a

sign of a problem. Another approach is dynamic

control: monitoring whether the calculated movement

trajectory is physically possible (e.g., no sudden

“jumps” in position that exceed the vehicle's

achievable acceleration). In practice, many such

symptoms are used: a loss-of-position alarm, sudden

course deviations observed on an electronic map

compared to the course from radar, jumps in speed or

coordinate readings while the HDOP is low (which

normally means good satellite geometry) - all of these

warning signals can indicate GNSS interference [3].

Operators and systems can also cross-check position

from different systems (e.g., GNSS vs. local systems

like LORAN or cellular network position) to look for

discrepancies.

Methods using artificial intelligence (AI) often

combine elements of the above approaches,

simultaneously analyzing multiple parameters and

signals to detect subtle anomalies invisible to the naked

eye. Machine learning, particularly deep learning (DL),

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has proven to be extremely effective in GNSS

interference detection tasks in recent years [8, 11].

These algorithms can learn from large data sets

characteristic patterns indicative of jamming or

spoofing. For example, a neural network can

simultaneously take into account temporal changes in

signal power, pseudo-distance errors, trajectory

deviations, and other characteristics, and on this basis

classify the state of the system as normal or attacked.

Various machine learning (ML) models have been

compared in the literature for spoofing detection -

results indicate that already relatively simple models,

such as decision trees (CART), achieve very good

performance in identifying attacks, outperforming

classical methods based on rigid thresholds [11]. More

advanced approaches use convolutional or recurrent

Long Short-Term Memory (LSTM) networks to analyze

raw streams of signals or strings of observations. The

latest experiments using deep networks have already

achieved nearly 99% success rate in detecting jamming

attacks on available datasets, a few percent

improvement over earlier algorithms. Such high

results show that AI is capable of very accurately

distinguishing between real and jamming signals

based on even small deviations in patterns.

In practice, AI-based GNSS anomaly detection

systems can operate in continuous receiver monitoring

mode. For example, on board an aircraft, an intelligent

module analyzes the data stream from a GPS receiver

(position, speed, time, signal parameters) and

compares it with data from an inertial navigation

system or other sensors. If the AI detects discrepancies

beyond normal conditions (e.g., much larger

differences between the position from GPS and inertial

than usual, or the simultaneous shift of all pseudo-

distances characteristic of spoofing), it can alert the

system to a suspected attack in a fraction of a second.

This approach is much faster and more reliable than

manual observation by an operator, especially since

combined attacks (e.g., simultaneous jamming and

spoofing) can manifest themselves in complex ways

that are difficult to catch with traditional methods [11].

Artificial intelligence enables learning by example in

this context - the system can be trained on a variety of

attack scenarios, so it will know what the symptoms of

a given threat look like.

It is worth noting that the effectiveness of AI

methods strongly depends on the availability of

adequate training data. The scientific community has

several public GNSS attack datasets (e.g., TEXBAT and

OAKBAT containing recordings of various spoofing

scenarios) used for algorithm validation [11]. However,

there is still a lack of open datasets covering a wider

range of situations (different types of simultaneous

interference, other environmental conditions, etc.),

which is the subject of active work. Despite these

challenges, current research results show that the

application of AI significantly improves the ability of

navigation systems to quickly detect and classify GNSS

anomalies, thus providing a foundation for activating

emergency mechanisms to protect traffic safety.

2.2 Role of the inertial systems in navigation

When a GNSS signal fades, the natural salvation is to

resort to other sources of motion information. For

decades, a standard component of professional

navigation systems has been an inertial system (INS) -

that is, a device that measures vehicle acceleration and

angular velocity based on a set of motion sensors [6].

A typical INS consists of an inertial measurement

unit (IMU) containing a three-axis accelerometer and a

three-axis gyroscope, whose readings are processed in

real time by a navigation computer. Operating

completely independent of external signals, the INS

performs so-called dead-reckoning navigation - from a

known initial position, using measurements of

acceleration and rotation, it calculates the new position,

speed and orientation of the vehicle in real time

through a process of integrating (integrating) these

accelerations over time [2]. As a result, INS provides

continuous navigation information even in the

complete absence of external signals (GPS, radio

beacons, etc.), making it invaluable in conditions of

interference or where satellite systems do not reach

(e.g. underwater, in tunnels) [6].

Inertial systems come in different classes of

accuracy. High-end INS, used, for example, in

commercial aviation or submarines, are based on laser

or fiber-optic gyroscopes and have very low drift - their

position error builds up slowly, on the order of a meter

every few minutes or an hour. Low-cost INS based on

MEMS technologies (micro-mechanical sensors used,

for example, in smartphones or drones) unfortunately

have much worse stability - errors in acceleration

measurements mean that after just a few tens of

seconds without correction, the position can have an

error of several meters, and after a few minutes even

hundreds of meters. In general, a fundamental

limitation of any INS is that its accuracy decreases over

time due to the accumulation of measurement errors

during integration [2]. Even the most accurate inertial

systems suffer from a certain level of bias (drift) of

accelerometers and gyroscopes, which, if not

periodically corrected, leads to an increasing deviation

of the calculated position from the actual position. In

the literature, this phenomenon is referred to as

unbounded growth of error - without external

correction, the INS will sooner or later “lose its way” to

the point where its indications become navigationally

useless [2].

Despite this disadvantage, autonomy and

immunity to external interference make INS serve as a

key backup navigation source. For example, in modern

passenger aircraft, several inertial navigation

platforms (IRS) are installed to determine the

machine's movement parameters throughout the

flight. When a GPS signal is available, the data from the

INS is calibrated and corrected on an ongoing basis, but

if it is lost, it is the INS that assumes the burden of

maintaining knowledge of the flight's position and

direction for the time needed, for example, to return

safely to the airport [9]. Similarly, in maritime

navigation - modern ships are equipped with

AHRS/INS systems that can navigate without GPS for

a period of time, relying solely on gyroscopes and

speed logs. In autonomous vehicles, INS (sometimes in

a reduced form, the so-called RISS - Reduced Inertial

Sensor System, e.g., with the replacement of some of

the sensors with a wheel odometer) assists in

maintaining traffic awareness in dense urban areas

where the GNSS signal is weak or fades among tall

buildings [9].

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However, practice shows that GNSS and INS are

complementary - they have complementary properties

[2]. GNSS provides absolute position reference with a

current time-independent error (e.g., a few meters

horizontally), but is susceptible to interference and

fading. INS, on the other hand, is continuous and

difficult to disturb, but its relative error increases over

time. For this reason, the integrated use of GNSS and

INS has become standard, so as to combine the

advantages of both. In a typical navigation system,

GNSS provides periodic accurate position and velocity

corrections, resetting INS's growing error, while INS

provides a bridge during periods when current GNSS

data is unavailable [2]. This approach creates a

navigation system that is both accurate in the long run

(thanks to GNSS) and resilient to short-term reception

problems (thanks to INS).

The disadvantage of integration based solely on

occasional “resetting” of the INS with GPS data (the so-

called loosely coupled system) is that when the GNSS

signal interruption lasts too long or the number of

available satellites falls below the minimum (e.g., less

than 4, making it impossible to determine the position),

the system switches to a standalone INS anyway and

the error starts to grow rapidly [2]. This is why tightly

integrated GNSS/INS systems are used in practice,

where the two systems work together continuously -

the INS continuously corrects itself even with partial

GNSS data, and in return can help track satellite signals

during difficult conditions (e.g., in tightly coupled

systems, the INS can help sustain satellite tracking

when the signal is on the verge of fading). Regardless

of the detailed integration architecture, however, the

role of the INS is crucial as a navigation safeguard: it is

through it that the system is able to sustain position

determination when GNSS signals are disrupted or

lost. Sections 2.3 and 2.4 discuss how artificial

intelligence can further enhance this integration,

reducing INS errors and effectively extending the time

for safe navigation without GNSS.

2.3 Position correction mechanisms using AI and filtering

For years, the Kalman filter has been the primary

mathematical tool used to combine GNSS and INS data

into coherent navigation information. A Kalman filter

is a state estimation algorithm that, based on a motion

model and a measurement model, can optimally

estimate the current error and correction based on the

available data, even if it is subject to noise [6]. In the

context of GNSS/INS integrated navigation, the

Kalman filter usually acts as an INS error estimator - it

compares the position and velocity calculated by the

INS with GNSS measurements and calculates

corrections to the inertial solution based on this [1, 2].

In other words, when a GNSS signal is available, the

filter continuously corrects INS drift, minimizing the

differences between the two sources. At times when

the GNSS signal dies, the filter enters predictive mode:

it continues to estimate the state based only on the INS

model, and its uncertainty gradually increases, but

thanks to the earlier calibration of INS errors, it slows

the accumulation of these errors compared to the

stand-alone INS [15].

A key challenge is maintaining accuracy during

longer GNSS signal gaps. The standard Kalman filter

assumes a specific INS error model (e.g., gyro drift

modeled as a first-order Gauss-Markov process, etc.)

and uses limited information for prediction, so that at

long gaps (tens of seconds or more) its predictions

begin to diverge from reality. In recent years, however,

ideas have emerged to support classical filtering with

artificial intelligence methods that can learn more

complex error and motion patterns than the simple

linear model used in the Kalman filter. AI can be

involved in several ways: to predict corrections during

periods of GNSS absence, to adaptively tune filter

parameters, or as a separate sensory fusion module

parallel to the classical approach.

One interesting strategy is to predict GNSS

observations from INS data using machine learning

models. Such a mechanism has been proposed, among

others, by Chen et al. (2022), where they used a hybrid

method based on partial least squares regression

(PLSR) and regression with Gaussian process (GPR)

[5]. The model learns the relationship between INS

errors and GNSS observations (when these are

available) to predict, during satellite fading, what the

GNSS data (e.g., pseudo-distance or position) would

look like based on INS alone. These “synthetic”

observations are then fed into the Kalman filter instead

of real GNSS data, allowing it to continue to correct INS

errors despite the absence of an actual satellite signal.

In experiments with four GNSS fades during a test

flight, it was shown that the use of such prediction

significantly improved navigation accuracy compared

to the usual mode without corrections - the Kalman

filter “supported” by PLSR/GPR prediction

maintained smaller trajectory deviations than the

traditional one, proving the effectiveness of the

approach. In other words, the intelligent module

learned to predict certain GNSS receiver behavior

based on traffic history and INS errors, thus filling in

data gaps during disturbances.

Another line of research focuses on directly

correcting INS readings using AI algorithms. An

example is the use of adaptive neuro-fuzzy systems

(ANFIS) to calibrate lower-cost inertial systems. In the

work of Mahdi et al. (2024) presented a system in which

a reduced RISS inertial system (using, among other

things, an odometer and one gyroscope) was

integrated with GNSS using ANFIS as an error

correction learning block [9]. ANFIS, combining

elements of neural network and fuzzy logic, was

trained to predict INS-generated position errors based

on vehicle movement patterns and previous

differences between INS and GNSS. As a result, the INS

so calibrated provides much more accurate

information during interruptions in GPS reception.

Tests using actual vehicle runs, during which GNSS

signal fades lasting between 50 and 150 seconds were

simulated, showed a reduction in 2D position error

(RMSE) of about 43.8% relative to traditional

RISS/GNSS integration without such calibration [9].

Maximum position deviations were also reduced by

about 47%, meaning that the vehicle, even for two

minutes without GNSS, stayed much closer to the

actual trajectory than would have been possible with

the classical system [9]. This is a big step forward, given

that we're talking about a system made of low-cost

MEMS sensors - thanks to AI, precision close to that

which would be provided by much more expensive

inertial systems was achieved.

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Also, deep neural networks are finding applications

in improving inertial navigation in the absence of

GNSS. Long Short-Term Memory (LSTM) models, a

variation of recurrent neural networks capable of

learning temporal dependencies, have been used to

predict vehicle movements and trajectories based on

history from inertial sensors. Research indicates that

LSTM networks can effectively stabilize INS drift error:

in field tests, it was shown that the use of such a model

can significantly improve positioning accuracy during

GNSS fading (e.g., 30 or 90 seconds) compared to

unassisted stand-alone INS. A network learned from

data from periods when GNSS is operational can then

predict on-the-fly corrections to the INS-calculated

position when GNSS fades. In practice, this can look

like this: an autonomous vehicle equipped with an

LSTM network, when the GPS signal is lost, switches

to a mode where each new position from the INS is

corrected by a neural network predicting how much

error is likely to have occurred. It's a bit like a virtual

GPS acting on past experience. Such an approach,

while sounding futuristic, is already yielding tangible

results, and further development of the models (e.g.,

combining LSTM with convolutional networks that

analyze camera data - which combines inertial and

visual navigation) could further improve the reliability

of GNSS-free navigation.

Artificial intelligence can also support position

correction more indirectly - for example, through

adaptive tuning of the Kalman filter. Filter parameters

(covariances of model and measurement noise) are

often fixed rigidly or according to simple adaptations,

which do not always reflect the actual error dynamics.

Methods of using learning algorithms to continuously

adapt these parameters on the fly are being

investigated, so that the Kalman filter can better

respond to changes in conditions (e.g., rapid vehicle

maneuvers that increase INS model error). For

example, a neural network could learn from observed

deviations between INS and GNSS to adjust the filter's

Q and R covariance matrices, making it more resilient

to unusual situations. Such approaches are at the

research stage, but early results suggest that combining

a physics-based model (Kalman filter) with a learning

model yields better results than each alone. In other

words, AI does not have to replace proven navigation

algorithms - it can complement them, compensating for

their limitations (e.g. nonlinearities, model

uncertainty).

In summary, GNSS interference position correction

mechanisms are increasingly using a hybrid approach:

classical filters and models are combined with AI

components that provide additional information or

adaptivity. Experimental results prove that this makes

it possible to significantly improve the accuracy and

reliability of navigation during prolonged

interruptions in satellite signal reception. As a result,

the navigation system becomes more resilient - it can

rely on itself for longer without external data,

increasing overall safety.

2.4 Overview of actual research, implementation and

experiments

The topic of enhancing the safety of navigation using

AI under GNSS interference is being intensively

researched around the world. A large number of

experimental works, prototype implementations and

simulation studies have appeared in the literature of

the last decade, which confirm the usefulness of the

methods described. The following is an overview of

selected developments and initiatives in this area,

divided into the issues of anomaly detection and

maintaining navigation during signal fading.

GNSS interference detection: As early as around

2015-2020, work began to appear demonstrating the

effectiveness of machine learning in spoofing

detection. The authors in [12] presented a system that

used supervised machine learning algorithms

(including SVM) to detect false GNSS signals. A unique

element was the use of real incident data - the authors

used sets of meaconing and spoofing records from real

tests, which made it possible to test the algorithm

under near-real conditions. The results showed that the

classifier learned from laboratory data recognizes

attacks in field data with high efficiency, which is

significant evidence of the practical usefulness of AI.

Other research teams have also confirmed the

effectiveness of the ML/DL approach: in 2021 and 2022,

research results were published in which various

models (from decision trees, to convolutional neural

networks analyzing the signal, to hybrid methods

based on ensemble learning) achieved efficiencies of

95-99% in detecting GNSS interference on shared

datasets [8]. The ~99% accuracy result mentioned

earlier was achieved on two different jamming and

spoofing datasets, demonstrating the versatility of the

approach used [8]. It is interesting to note that the best

results were obtained by combining different

techniques - the aforementioned work used both deep

learning methods and elements of signal analysis and

even vision techniques (e.g., a camera analyzing the

environment for sources of interference). This indicates

a trend that multi-sensor fusion involving AI can yield

the most reliable sensing systems - for example,

combining data from a GNSS receiver, inertial sensors,

cameras and other sources into a single platform

supervised by learning algorithms. Such solutions are

currently being tested in aeronautical or maritime

applications: next-generation prototype GNSS

receivers can collect dozens of diagnostic parameters,

which are then analyzed by an embedded AI module

and signal the crew or autopilot in real time when a

potential anomaly is detected. For example, research

projects co-funded by European Union agencies are

testing systems where the aircraft is equipped with a

dual GNSS set (one primary, the other monitoring) and

INS - data from both receivers and INS is compared by

an intelligent algorithm that can detect even subtle

attacks (e.g., those that slowly move position, hoping

not to be noticed by standard alarms).

Importantly, the aviation and transportation

industries recognize the seriousness of the problem.

Organizations such as EASA (European Union

Aviation Safety Agency) and IATA are sounding the

alarm about the increasing number of GNSS jamming

incidents and are launching initiatives to make systems

more resilient. Post-conference recommendations

point to the need to equip aircraft with improved GNSS

jamming detection and warning mechanisms, as well

as to maintain traditional navigation aids as back-ups

(e.g., aviation VOR/DME beacons) [7].

As for maintaining navigation during GNSS fading,

numerous experiments have been reported in this area

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as well, confirming the effectiveness of AI methods.

Chen, L., et. all [5] conducted flight tests in which the

aircraft experienced four targeted GNSS signal outages

at different phases of flight. The navigation accuracy of

the GNSS/INS system with a classical Kalman filter and

the system assisted by the AI prediction module

(PLSR/GPR) were compared. The results clearly

showed that the AI-assisted version maintained the

correct trajectory much better - the average position

error during GNSS fading was significantly smaller

than in the traditional system. What's more, the AI

system showed greater stability under different

maneuvers (the flight included both calm stretches and

sharp turns); the classical filter gave a larger deviation

at certain points, while the system with AI prediction

still kept close to the true path. This is important

evidence that intelligent methods improve not only

static accuracy, but also robustness to different

dynamic conditions.

In the field of land navigation, especially for

autonomous vehicles, a number of tests have been

conducted in urban conditions. For example, the

authors [9], in their experiment, drove a vehicle along

urban routes, where GNSS signals were deliberately

turned off for set periods of time (from tens to over a

hundred seconds). The car then relied only on its own

sensors (IMU, odometer) - once with and once without

ANFIS correction enabled. The comparison showed

that without AI the vehicle “lost position” from the real

one quite quickly (the error grew exponentially with

time), while with ANFIS the trajectory reconstructed

by the system remained close to the real one - the

differences in distances of tens of meters were able to

be reduced to a few tens of meters, which can be

decisive for maintaining continuity in the lane or

avoiding a collision at a critical moment [9]. It is worth

mentioning that these tests took into account different

scenarios: straight driving, sharp turns (where INS

errors usually increase faster), and speed changes. In

all cases, neuro-fusion integration improved the

results, making it a promising technique for the

automotive industry. Already, some so-called dead

reckoning GPS systems in cars use simple forms of

machine learning for self-calibration (e.g., learning the

bias of a MEMS gyroscope when the car is at a traffic

light). Future on-board navigation systems can be

expected to incorporate even more advanced learning

algorithms, especially in autonomous vehicles, where

full redundancy (GNSS, INS, lidar, camera) is standard

- AI will play the role of integrator of all these sources.

For ships, systems are being developed that

integrate INS, GNSS and local sensors like logs and

gyrocompasses, where AI manages how much weight

to assign to each source at any given time. Under

conditions of GNSS interference, the system can

automatically switch to “INS + optical” mode, using,

for example, cameras and lidar to track the shoreline

(known as terrestrial navigation), and machine

learning helps compare this information with the map.

These are, however, solutions just crawling in research.

Military projects are more advanced - armies have long

used high accuracy INS, and are now testing AI to

correct these INS without GNSS, such as by matching

observed maneuver runs to known models. The details

are often not public, but it is conceivable that military

vehicle navigation systems will become a testbed for

many of the techniques described (AI for spoofing

detection, fusion with magnetometers, IR cameras,

etc.).

Despite numerous successes, operational

implementations of these technologies are just

beginning. So far, most of the AI systems described

have been demonstrated in test or prototype

conditions. However, there are early swallows: for

example, Honeywell has announced work on a GNSS

receiver integrated with an AI module capable of self-

learning the interference environment for general

aviation. In automotive, manufacturers of GPS systems

for the automotive class are beginning to add learning-

based features (like the aforementioned INS self-

calibration). Commercial software platforms are also

emerging that allow the implementation of custom AI

algorithms on GNSS receiver data (e.g., receivers with

access to raw observations and the ability to upload

user software) - this is important because it will allow

the user community to create dedicated anti-spoofing

solutions for their own needs.

In summary, research and experiments conducted

over the past few years clearly confirm the

effectiveness of using AI both in detecting GNSS

threats and in maintaining navigation when they

occur. Impressive results have been achieved in

laboratory conditions (close to 100% attack detection,

significant increase in safe navigation time without

GNSS). In real-world conditions, the prototypes are

also performing very well, although they are, of course,

still subject to intensive testing in various scenarios.

The next step is to translate these achievements into

industrial standards and procedures, which is already

beginning to happen with the cooperation of scientific

institutions, manufacturers and regulators.

3 MATHEMATICAL MODEL OF GNSS/INS/AI

SYSTEM

GNSS systems are crucial for precise navigation, but

their signals are susceptible to interference (e.g.,

spoofing, jamming) and atmospheric disturbances. To

increase the reliability of position estimation,

additional inertial systems (INS) and adaptive filtering

methods are used. Integration of these systems while

monitoring anomalies in the GNSS signal enables

dynamic error correction. This analysis presents

mathematical modeling of the state estimation process,

an adaptive anomaly detection algorithm and detailed

simulation results.

3.1 The extended state model

Assume that the state of the system is described by a

vector:







where:

pk – position,

vk – speed,

595

– drift (bias) of the accelerometer,

– gyro drift.

For a discrete dynamic system, the model can be

written as:

= + +

k k k

B u w

k k k

x F x

whereby:

Fk – state transition matrix, taking into account the

dynamics of movement and evolution of drifts,

Bkuk – Control model, where uk to controlled

acceleration (e.g., correction from INS),

wk~N(0,Qk)– process noise.

An example of the form of the Fk matrix (for a 1D

model with Δt sampling) might look as follows:

1 0

0 1 0

0 1 1 0

0 0 0 1





−



−





where the negative members associated with drifts

model the systematic effect of INS errors on the

estimation [14].

3.2 Measurement model

The GNSS signal provides the position measurement

directly. We write the measurement model as:

where:

H=[1 0 0 0]– observation matrix,

vk~N(0,Rk)– measurement noise, whose covariance Rk

may undergo adaptive modifications under

anomalous conditionsi.

3.3 Anomaly detection using an AI system

3.3.1 Innovation and statistical test

The basis of anomaly detection in the Kalman filter

is innovation vector analysis:

−

=−

k k k k

v z xH

where:

−kk

is the predicted state. For the standard

Kalman filter, the innovation covariance matrix is:

|1−

k k k k

SPH H R

Anomaly detection test is based on statistics:

21−

k k k k

d v S v

which under normal conditions has a chi-square

distribution with mmm degrees of freedom (where m

is the measurement dimension). Threshold γ is selected

to take care of a certain level of significance of the test

(e.g. α=0.05):

anomaly detected





If an anomaly is detected, the system can modify the

matrix Rk or initiate a filter reset procedure.

3.3.2 Adaptive AI-based mechanisms

Machine learning algorithms (e.g., deep neural

networks, SVMs) can be trained on historical data to

classify signals as “normal” or “disturbed.” In a

hybrid approach, the result of the classification

(denoted, for example, as k ∈ {0,1}) affects the filter

parameters:

− if δk=1 (anomaly), element of the matrix increases

Rk, which reduces the weight of measurement

GNSS,

− additionally, it is possible to use adaptive

algorithms (e.g., drift recalibration) to minimize

system errors.

The adaptation model can be formalized by:



adapt

R R I

where:

λ is an adaptive parameter,

I – unit matrix [10].

3.4 Implementation and simulation

The following simulation parameters were assumed:

− Sampling time: Δt=0.1 s,

− Number of steps: 1000 iterations (simulation lasting

100 s),

− Noise parameters:

− The noise of the process: Qk = diag(qp, qv, qb

, qb

)

with typical values e.g.. qp=10

−4

, qv = 10

-4

, qb

=10

−6

, qb

=10

−6

− Measurement noise GNSS: Rk=

GNSSzGNSS1

− Interference conditions: Random interference was

introduced in the simulation to simulate spoofing -

in random iterations, a large deviation was added

to the zk.

3.5 Estimation algorithm

A classical Kalman filter was used for GNSS/INS data

fusion. Stages of the filter:

1. Prediction:

| 1 1| 1 1

ˆˆ

− − − −

k k k

F B u

k k k k

| 1 1| 1− − −

k k k k k k k

P F P F Q

2. Update (with adaptation):

( )

| 1 | 1

| | 1 | 1

| | 1

ˆˆ

−

−−

−

= + −

=−

adapt

k k k k k

k k k k

k k k k k

k k k k

K P H HP H R

x x K H

P I K H P

The anomaly detection module monitors dk

i and, if

the threshold is exceeded, modifies Rk according to the

adaptive model presented earlier.

596

3.6 Simulation results

Simulation conducted using the Monte Carlo method

(500 runs) made it possible to determine the statistical

properties of the estimation. The results are shown in

Table 1:

Table 1. Simulation results

Scenario

Mean position

error [m]

Standard

deviation [m]

GNSS without correction

3.5

1.2

GNSS/INS + classical Kalman filter

1.2

0.5

GNSS/INS + Kalman filter with AI

anomaly detection

0.7

0.3

In addition, analysis of the covariance matrix Pk|k

showed a significant reduction in estimation

uncertainty in the hybrid system. Graphical

presentation of the estimated trajectory as a function of

time showed that at moments of disturbance (detected

by the AI module) there is immediate adaptation of the

system, which minimizes the impact of anomalies on

the estimation.

3.7 Discussion and interpretation of results

INS and GNSS data integration: Data fusion makes

the system resilient to short-term GNSS signal

interference - INS provides continuity of motion

dynamics information.

Adaptive Rk matrix correction: The inclusion of an

anomaly detection module allows the dynamic

increase of measurement uncertainty when a

disturbance is detected, resulting in less impact of

erroneous data on the estimation.

Effectiveness of AI algorithms: Trained models

detect abnormal patterns in the innovation vector,

enabling the system to respond quickly. The use of a

hybrid approach reduces the average position error by

more than 40% compared to a classic filter.

4 CONCLUSIONS

The mathematical analysis and simulations conducted

indicate that:

− GNSS/INS integration using an extended state

model and an adaptive Kalman filter significantly

improves navigation precision even under signal

interference conditions.

− Adaptive anomaly detection mechanisms based on

innovation vector analysis and complemented by

artificial intelligence algorithms enable dynamic

correction of filter parameters.

− Simulation results confirm that the hybrid approach

reduces position error to levels on the order of

0.7 m, which is important for critical applications

(e.g., autonomous systems, aviation, shipping, rail

transportation).

The analyses and examples presented here clearly

indicate that artificial intelligence has great potential

for enhancing navigation safety under unreliable

GNSS systems. AI methods, particularly machine and

deep learning, have proven capable of detecting

satellite interference with a speed and precision

unattainable by traditional algorithms [8]. At the same

time, intelligent data integration techniques allow the

system to maintain correct navigation for much longer

in the absence of a signal - thanks to AI, the system can

adapt to changing conditions and quickly correct

errors before they grow to dangerous proportions. In

other words, AI makes the navigation system more

aware: it can recognize on its own that “something is

wrong” (e.g., that the data being used may be false or

faulty) and react accordingly, whether by alerting the

operator or switching to an alternative mode.

The effectiveness of existing AI solutions has been

confirmed in numerous studies. In the context of GNSS

anomaly detection, the attack classification accuracies

achieved often exceed 95%, and in the best cases

approach 99%. This means that these systems very

rarely mistake normal conditions for an attack (low

false alarm rate) and at the same time almost always

capture the actual threat (high sensitivity). This is

important because in safety-critical applications, while

a false alarm is undesirable, failing to notice an actual

attack is absolutely unacceptable. AI seems to be able

to meet these requirements better than classical

methods - by analyzing multiple sources and features

at once, it is less likely to be fooled by interference

masquerading as a normal signal. In the field of

navigation maintenance (fusion of GNSS/INS and

other sensors), on the other hand, AI has proven that it

can drastically reduce positioning error during long

gaps. Reductions of 30-50% in error achieved in

automotive and aviation tests translate into real

improvements in safety - for example, a ship will stay

in a safe navigation corridor, an aircraft will stay closer

to its intended path, and an autonomous vehicle will

not lose its lane. All this brings us closer to the goal of

resilient navigation (resilient PNT).

It should be noted, however, that despite promising

results, large-scale implementation of this technology

comes with challenges. First, AI methods must be

properly validated and certified, especially in fields

such as aviation, where safety requirements are very

stringent. It is necessary to prove that the learning

algorithm works reliably under all predicted

conditions, and to understand its behavior in

unforeseen situations. This is not always easy, because

AI models (especially deep neural networks) are

sometimes treated as “black boxes.” That's why one of

the directions of development is so-called XAI

(Explainable AI) - methods to look inside the model

and explain why it made such a decision and not

another. In the context of navigation, this can increase

trust in the system and facilitate certification. Second,

current solutions often require large training data sets

representing a variety of disturbance scenarios.

BIOBLIOGRAPHY

[1] Bonar B., Buratowski T.: Extended Kalman filter

supported by logical conditions for inertial navigation.

W: Systemy mechatroniczne : zagadnienia wybrane :

praca zbiorowa / pod red. Michała Mańka. — Kraków :

Katedra Robotyki i Mechatroniki. Akademia Górniczo-

Hutnicza w Krakowie, 2022. — ISBN: 978-83-965598-2-1.

— S. 51–59.

[2] Boguspayev, N., Akhmedov, D., Raskaliyev, A., Kim, A.,

Sukhenko, A. (2023): A Comprehensive Review of

GNSS/INS Integration Techniques for Land and Air

Vehicle Applications. Applied Sciences, 13(8), 4819.

https://doi.org/10.3390/app13084819

597

[3] Britannia P&I Club - Global Marine P&I Insurance.

https://britanniapandi.com/wp-

content/uploads/2024/10/Navigational-Risks-at-Sea-

Jamming-and-Spoofing.pdf [C: 16 October 2024]

[4] Clausnitzer, Ch., Alexander K,.(2024): GNSS

Jamming/Spoofing and Continued Operational Safety

International Committee on GNSS Interference Detection

&Mitigation Workshop 15 April 2024

[5] Chen, L., Liu, Z., Fang, J.(2022): A novel hybrid

observation prediction methodology for bridging GNSS

outages in INS/GNSS systems. Journal of Navigation.

2022;75(5):1206-1225. doi:10.1017/S037346332200025X

[6] Chrzan, M., Jackowski, S. (2016): Współczesne systemy

satelitarne w transporcie kolejowym. Politechnika

Radomska im. Kazimierza Pułaskiego w Radomiu

[7] EASA partners with IATA to counter aviation safety

threat from GNSS spoofing and jamming | EASA. (b. d.).

EASA. https://www.easa.europa.eu/en/newsroom-and-

events/press-releases/easa-partners-iata-counter-

aviation-safety-threat-gnss-

spoofing#:~:text=“GNSS%20systems%20offer%20tremen

dous%20advantages,is%20a%20priority%20for%20the] –

[C: 10.03.2025]

[8] Ghanbarzade, A., & Soleimani, H. (2025): GNSS/GPS

Spoofing and Jamming Identification Using Machine

Learning and Deep Learning. arXiv preprint

arXiv:2501.02352.

[9] Mahdi AE, Azouz A, Noureldin A, Abosekeen A.(2024):

A Novel Machine Learning-Based ANFIS Calibrated

RISS/GNSS Integration for Improved Navigation in

Urban Environments. Sensors (Basel). 2024 Mar

20;24(6):1985. doi: 10.3390/s24061985.

[10] Pardhasaradhi, B., Yakkati, R. R. Cenkeramaddi, L.

R.(2022): Machine Learning-Based Screening and

Measurement to Measurement Association for

Navigation in GNSS Spoofing Environment in IEEE

Sensors Journal, vol. 22, no. 23, pp. 23423-23435, 1 Dec.1,

2022, doi: 10.1109/JSEN.2022.3214349

[11] Radoš, K., Brkić, M., & Begušić, D. (2024): Recent

Advances on Jamming and Spoofing Detection in GNSS.

Sensors, 24(13), 4210. https://doi.org/10.3390/s24134210

[12] Semanjski, S., Semanjski, I., De Wilde, W., & Muls, A.

(2020): Use of Supervised Machine Learning for GNSS

Signal Spoofing Detection with Validation on Real-World

Meaconing and Spoofing Data—Part I. Sensors, 20(4),

1171. https://doi.org/10.3390/s20041171

[13] Simon, D., "Optimal State Estimation: Kalman, H

Infinity, and Nonlinear Approaches", John Wiley & Sons

2006.

[14] Titterton, D. H. i Weston, J. L., (2004): Strapdown Inertial

Navigation Technology, Radar , Sonar and Navigation

Series 17. 2004.

[15] Zhang, Y., A (2019): Fusion Methodology to Bridge GPS

Outages for INS/GPS Integrated Navigation System. IEEE

Access. 2019;7:61296–61306. doi:

10.1109/ACCESS.2019.2911025