Academic Journal of Science and Technology 
ISSN: 2771-3032 | Vol. 14, No. 3, 2025 

 

168 

Application	of	Square‐Root	Information	Kalman	
Filtering	to	Combined	Navigation	Systems	
Yifan Yang, Yanmin Luo 

Xi 'an Shiyou University, Xi 'an 710065, China 

 

Abstract: With the rapid development of modern science and technology, navigation technology plays a crucial role in 
transportation, aerospace, military and other fields. At present, a single navigation technology has been difficult to meet the 
complex navigation needs of high mobility carriers or special environments. Aiming at the above problems, this paper carries 
out an in-depth study on the tightly coupled navigation system of Strapdown Inertial Navigation System (SINS) and Global 
Navigation Satellite System (GNSS), and introduces the square-root information Kalman filtering algorithm. The algorithm takes 
the information matrix (the inverse of the mean square error matrix) as the updating object, which effectively avoids the 
numerical instability and non-positive characterization problems that may occur in the iterative process of the mean square error 
matrix. Compared with the traditional extended Kalman filter, the square-root information Kalman filter has higher numerical 
stability and computational efficiency in dealing with nonlinear systems, which is especially suitable for multi-sensor fusion 
scenarios. 

Keywords: Inertial navigation; Tight coupling navigation; Extended Kalman filter; Square-root information Kalman filtering. 
 

1. Introduction 
With the rapid development of modern navigation 

technology, the demand for high-precision and high-
reliability navigation and localization is growing in military, 
civil and industrial fields. In complex environments such as 
urban canyons, tunnels, underground spaces or 
electromagnetic interference scenarios, it is often difficult for 
a single navigation system to meet the actual needs. For 
example, global navigation satellite systems rely on external 
signals and are susceptible to occlusion or interference, while 
inertial navigation systems, though autonomous, accumulate 
errors over time[1]. Combining the Strapdown Inertial 
Navigation System with the global navigation satellite 
systems can combine the advantages of inertial navigation's 
strong anti-jamming ability and the advantages of satellite 
navigation's high long-term accuracy to form a 
complementary system. 

There are three main combinations of current combined 
inertial/satellite navigation systems, namely loose coupling[2], 
tight coupling[3] and deep coupling[4]. The loose combination 
approach simply fuses the outputs of an inertial navigation 
system and a satellite navigation system, usually by 
correcting the errors of the inertial navigation system through 
a Kalman filter. In the tight coupling approach, the 
pseudorange and Doppler shift of the satellite navigation 
system are directly fused with the state quantities of the 
inertial navigation system, enabling better utilization of 
satellite navigation information. The deep combination 
approach, on the other hand, deeply integrates the receiver of 
the satellite navigation system with the inertial navigation 
system, and even fuses them at the signal processing level to 
further improve the system's anti-interference capability and 
reliability. 

Kalman filtering is the core algorithm for state estimation, 
the traditional Kalman filtering algorithm assumes that the 
system is linear and the noise is Gaussian distribution, in 
order to the nonlinear system model and non-Gaussian noise, 

the researchers proposed the extended Kalman filtering 
algorithm, which linearizes the nonlinear model through the 
Taylor Expansion[5], but it is prone to dispersion in the strong 
nonlinear scenario. Some scholars have proposed several 
adaptive algorithms, such as the Sage-Husa algorithm, which 
can dynamically adjust the noise covariance matrix R to 
improve the robustness to abrupt noise, and is suitable for 
intermittent satellite signal scenarios. Aiming at the 
limitations of the EKF algorithm, based on the filtering 
method of nonlinear transformation, the vast number of 
scholars have also proposed the traceless Kalman filter and 
the volumetric Kalman filter. UKF approximates the 
nonlinear distribution through the traceless transformation, 
avoids the calculation of Jacobi matrix, and improves the 
positioning accuracy by about 20% compared with the EKF 
in the inertial/satellite tight coupling. 

In recent years, deep learning has been used to combine 
with traditional Kalman filtering algorithms to produce neural 
network-assisted Kalman filtering methods, which utilize 
LSTM networks to predict inertial device errors, and end-to-
end filtering networks that directly model the observation of 
noise characteristics through CNN-Transformer networks, 
which can replace the manual noise modeling of traditional 
Kalman filtering, and show stronger Adaptability in dynamic 
interference scenarios. Aiming at the problem that the mean 
square error matrix in Kalman filtering tends to lose its 
positive definiteness and the demand of multi-sensor fusion, 
square-root filtering and information filtering are proposed in 
this paper. Square-root filtering updates the square-root of the 
mean square error matrix by Cholesky decomposition or QR 
decomposition to improve numerical stability. Information 
filtering takes the information matrix, which is the inverse of 
the mean square error matrix, as the updating object to avoid 
matrix inversion, making it more suitable for multi-sensor 
data fusion. 



 

169 

2. SINS/GNSS Tightly Coupled 
Navigation System 

In the tight coupling system, the global satellite receiver 
provides the raw information pseudorange and pseudorange 
rate used for localization to the Kalman filter, and the errors 
of each pseudorange and pseudorange rate are independent of 
each other. The strapdown inertial navigation system (SINS) 
solution module receives the specific force and angular rate 
information output from the IMU, generates the navigation 
output position and velocity information for the SINS, and 
calculates the pseudorange and pseudorange rate by 
combining this information with the ephemeris generated by 
the satellite receiver. The differences in pseudorange and 

pseudorange rate between those derived from the strapdown 
inertial navigation system (SINS) information and those 
generated by the satellite receiver are used as inputs to the 
Kalman filter to obtain the state error estimate of the SINS. 

The gyro drift and accelerometer bias in this state error 
estimate are fed back to the strapdown inertial navigation 
system (SINS) for correction. The position and velocity errors 
in the SINS, after being corrected using the position and 
velocity errors from this state error estimate, are then used as 
the final results of the tightly coupled SINS/GNSS navigation 
system[6]. The architecture of the tightly coupled system is 
shown in Figure 1. 

 

IMU
SINS 

computation

Satellite signal 
preprocessing

Kalman filter

Satellite 
receiver

Position, velocity, attitude 
Angle correction

Pseudorange, 
pseudorange rate

ephemeris
+

-

Position, velocity, 
attitude Angle

Pseudorange, 
pseudorange rate  

Figure 1. The architecture of SINS/GNSS tightly coupled system 

 

(1) SINS/GNSS error update equation 

The SINS error state consists of the position error 𝜹𝒑, the 
velocity error 𝜹𝒗𝒏 , the attitude error Angle 𝝋𝒏 , the 
gyroscope error 𝜺𝒃 and the accelerometer error 𝜵𝒃. 

The error state vector[7] is 
𝑿𝑰 𝛿𝐿  𝛿𝜆  𝛿ℎ  𝛿𝑣   𝛿𝑣   𝛿𝑣   𝜑   𝜑   𝜑   𝜀   𝜀   𝜀   𝛻   𝛻   𝛻 . 

In the equation, 𝛿𝐿  is the latitude error, 𝛿𝜆  is the 
longitude error, 𝛿ℎ is the altitude error. The b-frame is the 
body frame, and the n-frame is the navigation frame. 

The error state equation of the SINS is expressed as: 

 

 𝑿𝑰 𝑭𝑰𝑿𝑰 𝑮𝑰𝑾𝑰 (1) 

 

In the equation, the system noise 𝑾𝑰

𝑤   𝑤   𝑤   𝑤   𝑤   𝑤  , represents the components 
of the gyroscope angular velocity measurement noise and the 
accelerometer specific force measurement noise in the three 
coordinate directions of the b-frame[8]. 𝑭𝑰  is the inertial 
navigation state matrix, and 𝑮𝑰  is the inertial navigation 
noise matrix. 

The main errors in satellite navigation systems are clock 
bias and clock drift. Equivalent range errors and velocity 
errors are selected as the error states of the satellites in the 
tightly coupled system.The GNSS error state equation is 
expressed as: 

 

 𝛿𝑡 𝛿𝑡 𝑤  (2) 

 

 𝛿𝑡 𝑤  (3) 

 

In the equation, 𝛿𝑡   and 𝛿𝑡   represent the range and 
range rate corresponding to the receiver clock bias and clock 
drift, respectively[9]. 𝑤   and 𝑤   are white nois. The 
equation can be represented in matrix form as: 

 

 𝑿𝑩 𝑭𝑩𝑿𝑩 𝑮𝑩𝑾𝑩 (4) 

 

In the equation, 𝑿𝑩 𝛿𝑡   𝛿𝑡 ，𝑾𝑩 𝑤 𝑤 . 

By combining the SINS error state equation (1) with the 
GNSS error state equation (4), the tightly coupled navigation 
system state equation can be obtained[10]: 

 

 
𝑿𝑰

𝑿𝑩

𝑭𝑰 𝑶
𝑶 𝑭𝑩

𝑿𝑰
𝑿𝑩

𝑮𝑰 𝑶
𝑶 𝑮𝑩

𝑾𝑰
𝑾𝑩

 (5) 

 

That is: 

 

 𝑿𝒕 𝑭𝒕𝑿𝒕 𝑮𝒕𝑾𝒕 (6) 

 

(2) System Measurement Equation 

In the tightly coupled navigation system, the measurement 
information mainly consists of the differences in pseudorange 
and pseudorange rate. Specifically, the system employs the 
differences between the pseudoranges and pseudorange rates 



 

170 

calculated by the SINS and those measured by the GNSS as 
the measurement information[11]. This measurement approach 
enables the direct utilization of raw GNSS observations, 
thereby facilitating more precise error modeling and higher 
navigation accuracy. The measurement equation of the tightly 
coupled system is given by: 

 

 𝒁𝒕
𝑯𝝆

𝑯𝝆
𝑿𝒕

𝑽𝝆

𝑽𝝆
𝑯𝒕𝑿𝒕 𝑽𝒕 (7) 

 

The pseudorange and pseudorange rate measurement 
equations play a significant role in the tightly coupled inertial 
and satellite navigation system. By integrating data from the 
inertial navigation system, they notably enhance navigation 
accuracy and reliability. 

3. Extended Kalman Filter 
The core idea of the Extended Kalman Filter (EKF) is to 

linearize the nonlinear system through a Taylor series 
expansion, ignoring higher-order terms. In this paper, the 
Taylor series is expanded to the first order. Assume the 
discrete-time state-space nonlinear model is given by: 

 

 
𝑿𝒌 𝒇 𝑿𝒌 𝟏 𝜞𝒌 𝟏𝑾𝒌 𝟏

𝒁𝒌 𝒉 𝑿𝒌 𝑽𝒌
 (8) 

 

In the equations, 

𝐸 𝑾𝒌 0，𝐸 𝑾𝒌𝑾𝒋 𝑸𝒌𝛿

𝐸 𝑽𝒌 0，𝐸 𝑽𝒌𝑽𝒌 𝑹𝒌𝛿

𝐸 𝑾𝒌𝑽𝒋 0

 , 

where 𝑿𝒌  is the n-dimensional state vector, 𝒇 𝑿𝒌
𝑓 𝑿𝒌   𝑓 𝑿𝒌  … 𝑓 𝑿𝒌   is the n-dimensional nonlinear 

vector function, 𝒁𝒌  is the m-dimensional measurement 
vector, 𝒉 𝑿𝒌 ℎ 𝑿𝒌   ℎ 𝑿𝒌  … ℎ 𝑿𝒌   is the m-
dimensional nonlinear vector function, 𝜞   is the system 
noise distribution matrix, 𝑾𝒌 𝟏 is the system noise vector, 
and 𝑽𝒌 is the m-dimensional measurement noise vector. 

The EKF filtering equations for the nonlinear system with 
state 𝑋  are given by[12]: 

 

 

⎩
⎪
⎨

⎪
⎧

𝑿𝒌 𝒌⁄ 𝟏 𝒇 𝑿𝒌 𝟏

𝑷𝒌 𝒌⁄ 𝟏 𝜱𝒌 𝒌⁄ 𝟏𝑷𝒌 𝟏𝜱𝒌 𝒌⁄ 𝟏 𝜞𝒌 𝟏𝑸𝒌 𝟏𝜞𝒌 𝟏

𝑲𝒌 𝑷𝒌 𝒌⁄ 𝟏𝑯𝒌 𝑯𝒌𝑷𝒌 𝒌⁄ 𝟏𝑯𝒌 𝑹𝒌
𝟏

𝑿𝒌 𝑿𝒌 𝒌⁄ 𝟏 𝑲𝒌 𝒁𝒌 𝒉 𝑿𝒌 𝒌⁄ 𝟏

𝑷𝒌 𝑰 𝑲𝒌𝑯𝒌 𝑷𝒌 𝒌⁄ 𝟏

 (9) 

 

In the equations, 𝜱𝒌 𝒌⁄ 𝟏  is the system Jacobian matrix, 
𝜱𝒌 𝒌⁄ 𝟏 𝑱 𝒇 𝑿𝒌 𝟏 , and 𝑯𝒌 is the measurement Jacobian 
matrix, 𝑯𝒌 𝑱 𝒉 𝑿𝒌 𝒌⁄ 𝟏  . If the nonlinear functions are 
complex to differentiate or even non-differentiable, the first-
order partial derivatives can be approximated using the 
central difference method. 

4. Square-Root Information Kalman 
Filter Algorithm 

(1) Potter Square-Root Filtering 

The Potter square-root filtering decomposes the mean 
square error matrix 𝑃 into the product of a lower triangular 
matrix Δ  , that is, 𝑃 ΔΔ   , and operates solely on these 
lower triangular matrices during the filtering process. This 
approach reduces numerical errors caused by the ill-
conditioning of the mean square error matrix. 

Assume the square-roots of the mean square error matrices 
𝑷𝒌 𝟏，𝑷𝒌/ 𝒌 𝟏   , and 𝑷𝒌   are ∆𝒌 𝟏，∆𝒌/ 𝒌 𝟏   , and ∆𝒌  , 
respectively. The measurement update of the state estimation 
mean square error matrix and its corresponding square-root 
filtering equations are given by: 

 
𝑷𝒌 𝑷𝒌/ 𝒌 𝟏 𝑷𝒌/ 𝒌 𝟏 𝑯𝒌 𝑯𝒌𝑷𝒌/ 𝒌 𝟏 𝑯𝒌 𝑹𝒌

𝟏𝑯𝒌𝑷𝒌/ 𝒌 𝟏   (10) 

 

𝚫𝒌 𝚫𝒌/ 𝒌 𝟏 𝑰 𝚫𝒌/ 𝒌 𝟏 𝑯𝒌 𝝆𝒌𝝆𝒌 𝑹𝒌𝝆𝒌
𝑻 𝟏𝑯𝒌𝚫𝒌/ 𝒌 𝟏

   (11) 

In the equations, 𝑹𝒌  denotes the square-root matrix of 
𝑹𝒌 . The matrix 𝝆𝒌 satisfies𝝆𝒌𝝆𝒌 𝑯𝒌𝑷𝒌/ 𝒌 𝟏 𝑯𝒌 𝑹𝒌

𝑯𝒌𝚫𝒌/ 𝒌 𝟏 𝑹𝒌

𝚫𝒌/ 𝒌 𝟏 𝑯𝒌

𝑹𝒌

. The square-root matrix 𝜌  

is obtained using the 𝑄𝑅 decomposition method. 

(2) Information Filtering and Information Fusion 

The information matrix is the inverse of the mean square 
error matrix[13], while the information vector is the product of 
the state estimate and the information matrix. This 
representation makes information filtering more efficient and 
intuitive when dealing with multi-sensor data fusion and 
distributed systems. Let 𝕀𝒌 𝑷𝒌

𝟏 [14]. Then, the so-called 
information filtering equations expressed in terms of the 
information matrix are given by: 

 

⎩
⎪⎪
⎨

⎪⎪
⎧𝕀𝒌/ 𝒌 𝟏 𝚽𝒌/ 𝒌 𝟏 𝕀𝒌 𝟏

𝟏 𝚽𝒌/ 𝒌 𝟏 𝚪𝒌 𝟏𝑸𝒌 𝟏𝚪𝒌 𝟏
𝟏

𝕀𝒌 𝕀𝒌/ 𝒌 𝟏 𝑯𝒌𝑹𝒌
𝟏𝑯𝒌

𝑲𝒌 𝕀𝒌
𝟏𝑯𝒌𝑹𝒌

𝟏

𝑿𝒌/ 𝒌 𝟏 𝚽𝒌/ 𝒌 𝟏 𝑿𝒌 𝟏

𝑿𝒌 𝑿𝒌/ 𝒌 𝟏 𝑲𝒌 𝒁𝒌 𝑯𝒌𝑿𝒌/ 𝒌 𝟏

 (12) 

 

(3) Square-Root Information Extended Kalman Filter 

Let the square-roots of the information matrices 𝕀𝒌  and 
𝕀𝒌/ 𝒌 𝟏   be denoted as 𝕀𝒌 𝝃𝒌𝝃𝒌  and 𝕀𝒌/ 𝒌 𝟏

𝝃𝒌/ 𝒌 𝟏 𝝃𝒌/ 𝒌 𝟏  , respectively. 

The information prediction equation is given by: 

 

𝕀𝒌/ 𝒌 𝟏 𝚽𝒌/ 𝒌 𝟏 𝕀𝒌 𝟏𝚽𝒌/ 𝒌 𝟏
𝟏

𝚽𝒌/ 𝒌 𝟏 𝕀𝒌 𝟏𝚽𝒌/ 𝒌 𝟏
𝟏 𝚪𝒌 𝟏 𝚪𝒌 𝟏𝚽𝒌/ 𝒌 𝟏 𝕀𝒌 𝟏𝚽𝒌/ 𝒌 𝟏

𝟏 𝚪𝒌 𝟏

𝑸𝒌 𝟏
𝟏 𝟏 𝚪𝒌 𝟏𝚽𝒌/ 𝒌 𝟏 𝕀𝒌 𝟏𝚽𝒌/ 𝒌 𝟏

𝟏   (13) 

 

Analogous to the mean square error matrix update in the 
standard Kalman filter, the square-root information Kalman 



 

171 

filter time update algorithm can be obtained by replacing the 
symbols 𝚫𝒌 → 𝝃𝒌/ 𝒌 𝟏 ，𝚫𝒌/ 𝒌 𝟏 → 𝚽𝒌/ 𝒌 𝟏 𝝃𝒌 𝟏，𝑯𝒌 →

𝚪𝒌 𝟏及𝑹𝒌 → 𝑸𝒌 𝟏 . 

 

𝝃𝒌/ 𝒌 𝟏 𝚽𝒌/ 𝒌 𝟏 𝝃𝒌 𝟏 𝑰 𝝃𝒌 𝟏𝚽𝒌/ 𝒌 𝟏
𝟏 𝚪𝒌 𝟏 𝝆𝒌𝝆𝒌

𝑻

𝑸𝒌 𝟏 𝝆𝒌

𝟏

𝚪𝒌 𝟏𝚽𝒌/ 𝒌 𝟏 𝝃𝒌 𝟏  (14) 

 

In the equation, 𝝆𝒌  is obtained by performing 𝑄𝑅 

decomposition on
𝝃𝒌 𝟏𝚽𝒌/ 𝒌 𝟏

𝟏 𝚪𝒌 𝟏

𝑸𝒌 𝟏

. 

The measurement update algorithm for the Square-Root 
Information Kalman Filter can be derived from the equation 
𝕀𝒌 𝕀𝒌/ 𝒌 𝟏 𝑯𝒌𝑹𝒌

𝟏𝑯𝒌 . Performing QR decomposition 

on 
𝝃𝒌/ 𝒌 𝟏

𝑹𝒌 𝑯𝒌

 yields 𝝃𝒌. 

In the Square-Root Information Kalman Filter, the initial 
state estimation mean square error matrix can be set to infinity, 
corresponding to the information matrix being a zero matrix. 
Consequently, the initial square-root matrix 𝝃𝟎  can also be 
set to the zero matrix, indicating a lack of initial information 
about the state. 

5. Simulation Analysis 
To verify the effectiveness of the Square-Root Information 

Kalman Filter in the SINS/GNSS integrated navigation 
system, a set of experimental data, including approximately 
15 minutes of IMU and satellite receiver data, was selected 
for MATLAB simulation. 

The IMU data includes timestamps, three-axis gyroscope 
measurements, and three-axis accelerometer measurements. 
The satellite receiver data includes timestamps, 
pseudorandom noise codes, ionosphere-free pseudorange 
linear combinations, tropospheric delay, ionospheric delay, 
relativistic corrections, satellite clock bias and drift, satellite 
position and velocity in the Earth-Centered Earth-Fixed 
(ECEF) frame, elevation angle, azimuth angle, and user range 
error. Satellite positioning systems employ the pseudorange-
based single-point positioning method, which utilizes 
ionosphere-corrected pseudorange measurements and 
satellite clock bias corrections. By applying the least squares 
method, the three-dimensional position of the receiver is 
computed. Additionally, the residuals from the single-point 
positioning are used to evaluate the accuracy of the solution, 
enabling rapid and effective real-time positioning. 

The system initial state is configured as follows: the initial 
attitude uncertainty is set to 20 °, the initial velocity 
uncertainty is set to 0.1 m/s, and the initial position 
uncertainty is set to 10 m. The initial accelerometer bias 
uncertainty of the IMU is set to 10,000 μm/s², and the initial 
gyroscope bias uncertainty of the IMU is set to 10 °/h. The 
initial clock bias is set to 10 m, and the initial clock drift is set 
to 0.1 m/s. The experimental parameters are configured as 
shown in Table 1 and Table 2. 

Table 1. IMU Module Parameter Configuration 

Parameter Names Value Unit 
Gyroscope Noise Power 

Spectral Density 
0.01 (°/h)2/Hz 

Accelerometer Noise 
Power Spectral Density 

0.1 (μg)2/Hz 

Gyroscope Bias Random 
Walk Power Spectral 

Density 
4.0×10-11 rad2/s3 

Accelerometer Bias 
Random Walk Power 

Spectral Density 
1×10-5 m2/s5 

Table 2. GNSS Receiver Parameter Configuration 

Parameter Names Value Unit 
Observation Time Interval 1 s 

Number of Satellites 30 / 
Mask Angle 10 ° 

Receiver Clock Frequency 
Drift Power Spectral Density 

1 
m2/s3 

Receiver Clock Phase Drift 
Power Spectral Density 

1 
m2/s 

Pseudorange Measurement 
Noise Standard Deviation 

2.5 
m 

Pseudorange Rate 
Measurement Noise Standard 

Deviation 
0.1 

m/s 

 

The system simulation error results of the square-root 
information extended Kalman filter algorithm are shown in 
Figure 2. 

 

 
(a) Simulation Angle Error Plot of Tightly-Coupled 

Navigation System under Square-Root Information 
Kalman Filter 

 
(b) Simulation Velocity Error Plot of Tightly-Coupled 

Navigation System under Square-Root Information 
Kalman Filter 



 

172 

 
(c) Simulation Position Error Plot of Tightly-Coupled 

Navigation System under Square-Root Information Kalman 
Filter 

Figure 2. Simulation Error Plots of the Tightly-Coupled 
Navigation System under Square-Root Information Kalman 

Filter 

 

From the angle error plot, it can be observed that the angle 
errors of the system in all three directions are generally within 
the range of ±0.8 rad. Similarly, the velocity errors in all three 
directions are within the range of ±1 m/s. Nevertheless, the 
position error plot reveals that the Z-direction error surpasses 
±10 meters. This can be addressed by integrating 
supplementary sensors, such as altimeters or barometers, to 
enhance altitude accuracy. Meanwhile, the errors in the X and 
Y directions are maintained within ±5 meters, well within the 
permissible limits of the navigation system. 

The system calculations indicate that the standard 
deviations of the pitch, roll, and heading angle errors for the 
square-root information extended Kalman filter algorithm in 
the tightly-coupled navigation system simulation are 0.0093 
rad, 0.0091 rad, and 0.0082 rad, respectively. Furthermore, 
the standard deviations of the velocity errors in the X, Y, and 
Z directions are 0.1536 m/s, 0.1592 m/s, and 0.1435 m/s, 
respectively, while the standard deviations of the position 
errors in the X, Y, and Z directions are 0.8569 m, 0.9711 m, 
and 1.0618 m, respectively. The navigation accuracy achieved 
by the square-root information extended Kalman filter 
algorithm falls within the acceptable range. The use of the 
square root of the information matrix for filter propagation 
enhances computational efficiency and ensures numerical 
stability. 

The simulation results validate that the tightly-coupled 
navigation system employing the square-root information 
extended Kalman filter algorithm delivers superior estimation 
accuracy and reduced mean square error in nonlinear 
environments, highlighting its significant potential for 
nonlinear system applications. Consequently, integrating 
square-root information filtering into tightly-coupled 
navigation systems maximizes its strengths in managing 
nonlinearities, thereby boosting the system's capability to 
adapt to dynamic variations. 

6. Conclusion 
This paper thoroughly investigates the integrated 

navigation approach of the SINS/GNSS tightly-coupled 
navigation system and introduces the square-root information 
Kalman filter algorithm to enhance the system's accuracy and 

reliability. In summary, the proposed SINS/GNSS tightly-
coupled navigation system based on the square-root 
information Kalman filter algorithm demonstrates significant 
advantages in improving navigation accuracy, suppressing 
error divergence, and enhancing anti-interference capabilities, 
highlighting its important theoretical and practical application 
value. 

References 
[1] Yang, S., Han, Y. K., & Jia, S. (2025). Application of 

GNSS/INS integrated navigation in flight approach and landing. 
Aeronautical Computing Technique, 55(1), 114-118. 

[2] Zhou, Y., Wang, H., & Wang, J. (2025). GNSS/INS integrated 
positioning method in urban occlusion and multipath 
environments. Journal of Navigation and Positioning, 13(1), 
113-118. 

[3] Sun, S. G., Xu, Y. Z., & Wang, H. L. (2025). Research on 
INS/GNSS tightly coupled positioning algorithm for UAVs in 
GNSS-denied environments. Internet of Things Technologies, 
15(1), 44-48. 

[4] Sun, J. R., Meng, F. C., & Wang, D. Y. (2023). Code phase 
fault diagnosis and reconstruction algorithm for SINS/GNSS 
deeply integrated navigation. Journal of Chinese Inertial 
Technology, 31(6), 563-568. 

[5] Cao, C. Y. (2023). Research on GPS/INS integrated navigation 
information fusion based on broad learning method (Doctoral 
dissertation, Dalian Maritime University). 

[6] Jeong, K. Y., Park, D. Y., Kim, S. M., et al. (2021). Design of 
a compact GPS/MEMS IMU integrated navigation receiver 
module for high dynamic environment. The Korean Navigation 
Institute, 25(1). 

[7] Chang, G., Xu, J., Li, A., et al. (2010). Error analysis and 
simulation of the dual-axis rotation-dwell autocompensating 
strapdown inertial navigation system. IEEE. 

[8] Wang, N., & Liu, F. M. (2024). Application of adaptive fading 
memory square root mixed-order cubature particle filter based 
on constrained optimization in inertial/satellite integrated 
navigation. Journal of Jilin University (Engineering and 
Technology Edition), 54(12), 3660-3672. 

[9] Tu, K. P., & Feng, S. J. (2023). A tightly coupled BDS/INS 
filtering method based on sequential processing. Optics & 
Optoelectronic Technology, 21(4), 130-137. 

[10] Christophersen, H. B., Pickell, R. W., Neidhoefer, J. C., et al. 
(2006). A compact guidance, navigation, and control system 
for unmanned aerial vehicles. Journal of Aerospace Computing, 
Information, and Communication, 3(5). 

[11] Wang, J. S., & Wang, X. L. (2013). Performance simulation 
analysis of SINS/GPS tightly coupled and loosely coupled 
navigation systems. Aero Weaponry, (2), 14-19. 

[12] Yildiz, R., Barut, M., & Demir, R. (2020). Extended Kalman 
filter based estimations for improving speed-sensored control 
performance of induction motors. IET Electric Power 
Applications, 14(12), 2471-2479. 

[13] Wang, T., Chen, Q., & Gao, P. (2024). Information filtering 
algorithm for maneuvering target tracking based on unbiased 
measurement conversion. Journal of Ordnance Equipment 
Engineering, 45(11), 19-24. 

[14] Gao, Y. D., Zheng, N. S., Zhang, Y. S., et al. (2024). Phase 
unwrapping method based on phase quality fusion estimation 
and information filtering. Acta Geodaetica et Cartographica 
Sinica, 53(10), 1910-1919.