Navigation method based on combination of multiple accelerometers and GPS

Abstract

The application discloses a navigation method based on combination of multiple accelerometers and GPS, which comprises the following steps: calculating the angular velocity of a carrier according to a measurement formula of a gyro-free inertial measurement system; calculating the attitude information, the speed information and the position information of the carrier by using the calculated angular velocity and the output value of a three-axis accelerometer at the center of the measurement system; obtaining the speed information and the position information of the carrier by using a GPS system; subtracting the obtained speed information and position information respectively to obtain the speed difference value and the position difference value, and inputting the speed difference value and the position difference value into a combined navigation filter; obtaining the error estimation value of the navigation parameters based on the speed difference value and the position difference value by the combined navigation filter; and correcting the navigation parameters of the carrier by using the error estimation value of the navigation parameters. The application reduces the dependence on high-precision gyroscopes by adopting multiple accelerometers to construct the gyro-free inertial measurement system, thereby reducing the hardware cost of the system; meanwhile, the overall precision and stability of the navigation system are improved by combining with the GPS system.

Description

Technical Field

[0001] This invention relates to the field of navigation technology, and in particular to a navigation method based on a combination of multiple accelerometers and GPS. Background Technology

[0002] Common inertial navigation systems typically consist of gyroscopes and accelerometers. Gyroscopes measure angular velocity, while accelerometers acquire linear acceleration information. However, in environments with high overload or strong impacts, gyroscopes are easily affected, leading to decreased measurement accuracy or even damage, thus impacting the stability of the navigation system. Furthermore, errors in traditional inertial navigation systems accumulate over time, making it difficult to maintain high accuracy when used alone. Although some research has proposed combining inertial navigation systems with GPS, some methods still have shortcomings in angular velocity estimation and error modeling for gyroscope-less inertial measurement systems, easily leading to navigation error divergence. Therefore, a simple, low-cost, and highly accurate integrated navigation method is still needed. Summary of the Invention

[0003] Purpose of the invention: The purpose of this invention is to provide a low-cost and high-precision navigation method based on a combination of multiple accelerometers and GPS.

[0004] Technical Solution: To achieve the above objectives, the present invention provides a navigation method based on a combination of multiple accelerometers and GPS, comprising the following steps:

[0005] Step 1: Calculate the angular velocity of the carrier according to the measurement formula of the gyroscope-less inertial measurement system. Use the calculated angular velocity and the output value of the central three-axis accelerometer of the measurement system to calculate the navigation parameters of the carrier, including attitude information, velocity information and position information.

[0006] Step 2: Use the GPS system to obtain the vehicle's speed and location information;

[0007] Step 3: Subtract the speed information and position information obtained in Step 1 and Step 2 respectively to obtain the speed difference and position difference, and input them into the integrated navigation filter;

[0008] Step 4: The combined navigation filter calculates the error estimate of the navigation parameters mentioned in Step 1 based on the velocity difference and position difference;

[0009] Step 5: Correct the navigation parameters of the vehicle using the estimated navigation parameter error values.

[0010] Preferably, the gyroscope-free inertial measurement system is a 9-axis accelerometer-free gyroscope inertial measurement system, and the combined navigation filter is a strong tracking Kalman filter.

[0011] Preferably, the method for calculating the attitude information, velocity information, and position information of the carrier is as follows:

[0012] Step 1.1: Obtain the parameters output by the gyroscope-free inertial measurement system, including the linear acceleration of the shell {s} relative to the relative inertial frame {o}. angular velocity and angular velocity Projection in the shell coordinate system {s} ) s and attitude matrix ;

[0013] Step 1.2: Convert the data obtained in Step 1.1 into motion parameters of system {b}, and obtain the acceleration of system {b} relative to the absolute inertial frame {i}. ;

[0014] Step 1.3: Using parameter values Calculate the navigation acceleration of the vehicle. ;

[0015] Step 1.4, utilizing carrier navigation acceleration The navigation speed and position of the vehicle are obtained through numerical integration, namely the speed information and position information of the vehicle.

[0016] Step 1.5: Based on the attitude equations of the navigation system, calculate the attitude matrix of the carrier system {b} relative to the navigation system {n}. The values ​​of each element;

[0017] Step 1.6: Solve the expression of the attitude matrix, and match the expression of the attitude matrix with the values ​​of each element to calculate the navigation attitude angle of the vehicle, that is, the attitude information of the vehicle.

[0018] Preferably, the angular velocity =[ ] T The solution formula is:

[0019] ,

[0020] ,

[0021] ,

[0022] in, The first of the estimated angular velocity values row elements in The value at time; The x-axis component is the output of the central accelerometer. The y-axis component is the output of the central accelerometer. The z-axis component is the output of the central accelerometer; Sampling time, J1 and J2 are system side lengths; J1 and J2 are system configuration matrices; and A is the input vector.

[0023] Preferably, the acceleration Represented as:

[0024] ,

[0025] ,

[0026] In the formula, Let {n} and {b} be the accelerations of the navigation coordinate system and the vehicle coordinate system, respectively, relative to the absolute inertial frame {i}. Let be the orientation matrix between the absolute inertial frame {i} and the relative inertial frame {o}. The installation position vector of the inertial system. Let be the projection of the angular velocity of system {b} relative to the absolute inertial frame {i} onto the loaded system {b}; This represents the acceleration of the shell coordinate system {s} relative to the relative inertial frame {o}; This represents the orientation matrix between the relative inertial frame {o} and the shell coordinate system {s}; This represents the projection of the angular velocity of the carrying system {b} relative to the relative inertial frame {o} onto the carrying system {b}. This represents the projection of the angular velocity of the shell coordinate system {s} relative to the relative inertial frame {o} onto the shell system {s}.

[0027] Preferably, the navigation acceleration Represented as

[0028] ,

[0029] ,

[0030] In the formula, Let be the orientation matrix of the navigation frame {n} relative to the inertial frame {i}. For navigation position matrix, This is the Earth's rotation matrix. For navigation speed, The angular velocity of Earth's rotation. The position angular velocity of the carrier, Let $e$ be the position vector from Earth system $e$ to navigation system $n$.

[0031] Preferably, the attitude matrix The values ​​of each element are represented as follows:

[0032] ,

[0033] In the formula, Let be the orientation matrix of the shell system {s} relative to the relative inertial frame {o}; Let {i} represent the orientation matrix of the absolute inertial frame of reference {i} relative to the Earth frame of reference {e}; This represents the orientation matrix of the Earth system {e} relative to the navigation system {n}; Let {i} be the orientation matrix between the absolute inertial frame {i} and the relative inertial frame {o}.

[0034] Preferably, the attitude matrix of the carrier The attitude of the carrier satisfies the following transformation relationship:

[0035] ,

[0036] ,

[0037] In the formula, Main heading angle, Main roll angle, The pitch angle.

[0038] Preferably, the method for obtaining the error estimate of the navigation parameters obtained in step 1 is as follows:

[0039] Step 4.1: Derive the error equations for navigation attitude, velocity, and position;

[0040] Step 4.2: Select the state variable x of the multi-accelerometer and GPS integrated navigation system as 12-dimensional;

[0041] Step 4.3: Establish the state space model and measurement space model of the multi-accelerometer and GPS integrated navigation system. Based on the error equation in Step 4.1 and the state variables in Step 4.2, solve the state matrix, system noise matrix, measurement matrix and measurement noise matrix in the model respectively to obtain the state equation and measurement equation of the integrated navigation system.

[0042] Step 4.4: Establish the time update equation and measurement equation of the combined navigation filter based on the state equation and measurement equation;

[0043] Step 4.5: The combined navigation filter calculates the optimal estimate of the state error based on the velocity difference and position difference obtained in Step 3.

[0044] Preferably, the attitude error equation is:

[0045] ,

[0046] In the formula, ε is the attitude error angular vector. Let be the attitude matrix of the carrier system {b} relative to the navigation system {n}. Let be the projection of the angular rate of navigation frame {n} relative to absolute inertial frame {i} onto navigation coordinate system {n}. Let be the projection of the angular velocity of system {b} relative to the absolute inertial frame {i} onto the loaded system {b}. Information The error value;

[0047] The velocity error equation is:

[0048]

[0049] In the formula, β is the error angle vector of the actual navigation system {n} deviating from the ideal navigation system {geographic coordinate system {G}}; This represents the projection of the angular velocity of the Earth system {e} relative to the absolute inertial frame {i} onto the navigation frame {n}. δ represents the projection of the angular velocity of navigation frame {n} relative to Earth frame {e} onto navigation frame {n}. n V represents the speed error; Let be the orientation matrix of the navigation frame {n} relative to the inertial frame {i}; These are the accelerations of the navigation coordinate system {n} and the vehicle system {b} relative to the absolute inertial frame {i}, respectively. The angular velocity of Earth's rotation. The position angular velocity of the carrier; Position matrix for navigation;

[0050] The position error equation is:

[0051]

[0052] In the formula, λ, Φ, and h represent the longitude, latitude, and altitude of the carrier's location on Earth, respectively, and V E V N V U These represent the speeds of the carrier along the east, north, and sky directions, respectively, and R is the Earth's radius.

[0053] Beneficial effects: The present invention has the following advantages: By using multiple accelerometers to construct a gyroscope-free inertial measurement system, the present invention reduces the dependence on high-precision gyroscopes, thereby reducing the system hardware cost; at the same time, by combining navigation with the GPS system, the overall accuracy and stability of the navigation system are improved. Attached Figure Description

[0054] Figure 1 This is a schematic diagram of the method flow of the present invention;

[0055] Figure 2For the spatial configuration of multiple accelerometers in the navigation system, 1-9 are accelerometer numbers, and in particular, 7-8 are the numbers of the center accelerometer. Detailed Implementation

[0056] The technical solution of the present invention will be described in detail below with reference to the embodiments and accompanying drawings.

[0057] like Figure 1 As shown, a high-precision navigation method based on a combination of multiple accelerometers and GPS includes the following steps:

[0058] Step 1: Calculate the carrier's angular velocity using the measurement formula of the gyroscope-less inertial measurement system. Then, use the calculated angular velocity and the output value of the central three-axis accelerometer of the measurement system to calculate the carrier's attitude, velocity, and position information. The gyroscope-less inertial measurement system used is a 9-axis accelerometer-based system. The specific calculation process is as follows:

[0059] Step 1.1: Obtain the parameters output by the gyroscope-free inertial measurement system, including the linear acceleration of the shell {s} relative to the relative inertial frame {o}. angular velocity angular acceleration and angular velocity Projection in the shell coordinate system {s} ) s and attitude matrix ;

[0060] The angular velocity mentioned =[ ] T The solution formula is:

[0061]

[0062]

[0063]

[0064] in, The first of the estimated angular velocity values row elements in The value at time; The x-axis component is the output of the central accelerometer. The y-axis component is the output of the central accelerometer. The z-axis component is the output of the central accelerometer; Sampling time, J1 and J2 are the system side lengths; J1 and J2 are the system configuration matrices; and A is the input vector, defined as follows:

[0065] ,

[0066] ,

[0067] ,

[0068] ,

[0069] Where the subscripts j=1,2,…,6 represent the accelerometer numbers. Let the measurement direction vector of the j-th accelerometer be denoted as, for example Figure 2 As shown;

[0070] Step 1.2: Convert the data obtained in Step 1.1 into motion parameters for system {b}:

[0071]

[0072]

[0073] In the formula, , Let {n} and {b} be the accelerations of the navigation coordinate system and the vehicle coordinate system, respectively, relative to the absolute inertial frame {i}. Let be the orientation matrix between the absolute inertial frame {i} and the relative inertial frame {o}. The installation position vector of the inertial system. Let be the projection of the angular velocity of system {b} relative to the absolute inertial frame {i} onto the loaded system {b}; This represents the acceleration of the shell coordinate system {s} relative to the relative inertial frame {o}; This represents the orientation matrix between the relative inertial frame {o} and the shell coordinate system {s}; This represents the projection of the angular velocity of the carrying system {b} relative to the relative inertial frame {o} onto the carrying system {b}. This represents the projection of the angular velocity of the shell coordinate system {s} relative to the relative inertial system {o} onto the shell system {s}.

[0074] Step 1.3: Derive the basic equations of the strapdown inertial navigation system, and apply the parameter values ​​obtained in Step 1.2. Calculate the navigation acceleration of the vehicle. :

[0075] ,

[0076] ,

[0077] In the formula, Let be the orientation matrix of the navigation frame {n} relative to the inertial frame {i}. For navigation position matrix, This is the Earth's rotation matrix. For navigation speed, The angular velocity of Earth's rotation. The position angular velocity of the carrier, Let {e} be the position vector from Earth system {e} to navigation system {n};

[0078] Step 1.4: Utilize the carrier navigation acceleration obtained in Step 1.3. The navigation speed and position of the vehicle are obtained by numerical integration.

[0079] Step 1.5: Calculate the attitude matrix based on the navigation attitude equations. The values ​​of each element:

[0080]

[0081] In the formula, Let be the attitude matrix of the carrier, and let be the orientation matrix of the carrier system {b} relative to the navigation system {n}; Let be the orientation matrix of the shell system {s} relative to the relative inertial frame {o}; Let {i} represent the orientation matrix of the absolute inertial frame of reference {i} relative to the Earth frame of reference {e}; This represents the orientation matrix of the Earth system {e} relative to the navigation system {n};

[0082] Step 1.6: Solve for the expression of the attitude matrix, and correlate the expression of the attitude matrix with the element values ​​in Step 1.5 to calculate the navigation attitude angles of the vehicle, as follows:

[0083] The attitude matrix of the carrier The attitude of the carrier satisfies the following transformation relationship:

[0084] ,

[0085] ,

[0086] Heading angle ψ and roll angle The truth values ​​are determined according to Table 1 and Table 2:

[0087] Table 1 Truth table of heading angle ψ

[0088]

[0089] Table 2 Roll Angle truth table

[0090] .

[0091] Step 2: Use the GPS system to obtain the vehicle's speed and location information;

[0092] Step 3: Subtract the velocity and position information obtained in Step 1 and Step 2 respectively to obtain the velocity difference and position difference, and input them into the integrated navigation filter; the integrated navigation filter adopts a strong tracking Kalman filter;

[0093] Step 4: Based on the velocity difference and position difference, the combined navigation filter calculates the error estimate of the navigation parameters obtained in Step 1. The specific process is as follows:

[0094] Step 4.1: Establish the error model of the strapdown inertial navigation system and derive the error equations for navigation attitude, velocity, and position:

[0095] The attitude error equation is:

[0096]

[0097] In the formula, ε is the attitude error angular vector. Let be the projection of the angular rate of navigation frame {n} relative to absolute inertial frame {i} onto navigation coordinate system {n}. Information The error value; Let be the projection of the angular velocity of system {b} relative to the absolute inertial frame {i} onto the loaded system {b};

[0098] The velocity error equation is:

[0099]

[0100] In the formula, β is the error angle vector of the actual navigation system {n} deviating from the ideal navigation system {geographic coordinate system {G}}; This represents the projection of the angular velocity of the Earth system {e} relative to the absolute inertial frame {i} onto the navigation frame {n}. δ represents the projection of the angular velocity of navigation frame {n} relative to Earth frame {e} onto navigation frame {n}. n V represents the speed error; Let be the orientation matrix of the navigation frame {n} relative to the inertial frame {i}; These are the accelerations of the navigation coordinate system {n} and the vehicle system {b} relative to the absolute inertial frame {i}, respectively. The angular velocity of Earth's rotation. The position angular velocity of the carrier; Position matrix for navigation;

[0101] The position error equation is:

[0102]

[0103] In the formula, λ, Φ, and h represent the longitude, latitude, and altitude of the carrier's location on Earth, respectively, and V E V N V U These represent the speeds of the carrier along the east, north, and sky directions, respectively, and R is the Earth's radius.

[0104] Step 4.2: Select the following for the state variable x of the multi-accelerometer and GPS integrated navigation system as 12-dimensional, the state noise variable w as 6-dimensional, the measurement noise variable Z as 6-dimensional, and the measurement noise variable ρ as 6-dimensional:

[0105]

[0106]

[0107]

[0108]

[0109] In the formula, , , To assist in the constant drift of the three axes of the accelerometer; For attitude angle error The amount, satisfying ; , , For speed error The amount, satisfying , , , for The amount, satisfying , , , for The amount, satisfying , , , GPS speed measurement error The amount, satisfying , This is the measurement error of GPS on the longitude of the carrier. This is due to the GPS measurement error of the latitude of the carrier, and This represents the GPS error in measuring the altitude of the carrier.

[0110] Step 4.3: Establish the state space model and measurement space model of the multi-accelerometer and GPS integrated navigation system. The state space model is used to describe the evolution of various error states (including attitude error, velocity error, position error and sensor error, etc.) in the integrated navigation system over time. The measurement space model is used to describe the correspondence between the position and velocity information provided by the GPS system and the inertial navigation solution results.

[0111] Based on the error equation in step 4.1 and the state variables in step 4.2, solve the state matrix, system noise matrix, measurement matrix and measurement noise matrix in the model respectively to obtain the state equation and measurement equation of the integrated navigation system.

[0112] Step 4.4: Establish the time update equation and measurement equation of the discrete combined navigation filter according to the formula in Step 4.3. That is, discretize the continuous time state space model established in Step 4.3 to obtain the discrete state equation and measurement equation, and construct the time update equation of the combined navigation filter based on it, including the state prediction equation and the covariance prediction equation, which are used to realize the prior estimation of the system state.

[0113] Step 4.5: Input the measurement difference between the inertial navigation system and the GPS system into the combined navigation filter to solve for the optimal estimate of the state error. Specifically, calculate the measurement residual based on the measurement equation and use a navigation filtering algorithm (such as the Kalman filter algorithm) to solve for the optimal estimate of the system state error, thereby correcting the inertial navigation error.

[0114] Step 5: Using the error estimate of the navigation parameters obtained in Step 4, correct the navigation parameters of the vehicle.

[0115] The high-precision navigation method based on the combination of multiple accelerometers and GPS provided by this invention can be applied to the fields of aerospace vehicles, high-G aircraft, unmanned systems and intelligent equipment navigation, and has good engineering application prospects.

[0116] Compared with existing technologies, this invention utilizes the high operating frequency of the inertial gyroscope-less system for real-time updating of the carrier's motion parameters, and uses GPS information with a lower operating frequency but higher accuracy to correct the carrier's motion parameters, thus limiting the growth of errors and meeting the requirements of high-precision navigation. The auxiliary inertial measurement system used consists of 9-axis accelerometers, which has the advantages of low cost and convenient design and maintenance. The angular velocity estimation of the carrier is more accurate, and the error of the angular velocity estimation is only related to the carrier's motion state and acceleration noise. The strong tracking Kalman filter has strong robustness, so when combined with the GPS system for navigation, the error will not diverge and the stability is high.

Claims

1. A navigation method based on a combination of multiple accelerometers and GPS, characterized in that, Includes the following steps: Step 1: Calculate the angular velocity of the carrier according to the measurement formula of the gyroscope-less inertial measurement system. Use the calculated angular velocity and the output value of the central three-axis accelerometer of the measurement system to calculate the navigation parameters of the carrier, including attitude information, velocity information and position information. Step 2: Use the GPS system to obtain the vehicle's speed and location information; Step 3: Subtract the speed information and position information obtained in Step 1 and Step 2 respectively to obtain the speed difference and position difference, and input them into the integrated navigation filter; Step 4: The combined navigation filter calculates the error estimate of the navigation parameters mentioned in Step 1 based on the velocity difference and position difference; Step 5: Correct the navigation parameters of the vehicle using the estimated navigation parameter error values.

2. The navigation method according to claim 1, characterized in that, The gyroscope-free inertial measurement system is a 9-axis accelerometer-based gyroscope-free inertial measurement system, and the integrated navigation filter is a strong-tracking Kalman filter.

3. The navigation method according to claim 1, characterized in that, The method for calculating the attitude, velocity, and position information of the computing vehicle is as follows: Step 1.1: Obtain the parameters output by the gyroscope-free inertial measurement system, including the linear acceleration of the shell {s} relative to the relative inertial frame {o}. angular velocity and angular velocity Projection in the shell coordinate system {s} ) s and attitude matrix ; Step 1.2: Convert the data obtained in Step 1.1 into motion parameters of system {b}, and obtain the acceleration of system {b} relative to the absolute inertial frame {i}. ; Step 1.3: Using parameter values Calculate the navigation acceleration of the vehicle ; Step 1.4, utilizing carrier navigation acceleration The navigation speed and position of the vehicle are obtained through numerical integration, namely the speed information and position information of the vehicle. Step 1.5: Based on the attitude equations of the navigation system, calculate the attitude matrix of the carrier system {b} relative to the navigation system {n}. The values ​​of each element; Step 1.6: Solve the expression of the attitude matrix, and match the expression of the attitude matrix with the values ​​of each element to calculate the navigation attitude angle of the vehicle, that is, the attitude information of the vehicle.

4. The navigation method according to claim 3, characterized in that, The angular velocity =[ ] T The solution formula is: ， ， ， in, The first of the estimated angular velocity values row elements in The value at time; The x-axis component is the output of the central accelerometer. The y-axis component is the output of the central accelerometer. The z-axis component is the output of the central accelerometer; Sampling time, J1 and J2 are system side lengths; J1 and J2 are system configuration matrices; and A is the input vector.

5. The navigation method according to claim 3, characterized in that, The acceleration Represented as: ， ， In the formula, Let {n} and {b} be the accelerations of the navigation coordinate system and the vehicle coordinate system, respectively, relative to the absolute inertial frame {i}. Let be the orientation matrix between the absolute inertial frame {i} and the relative inertial frame {o}. The installation position vector of the inertial system. Let be the projection of the angular velocity of system {b} relative to the absolute inertial frame {i} onto the loaded system {b}; This represents the acceleration of the shell coordinate system {s} relative to the relative inertial frame {o}; This represents the orientation matrix between the relative inertial frame {o} and the shell coordinate system {s}; This represents the projection of the angular velocity of the carrying system {b} relative to the relative inertial frame {o} onto the carrying system {b}. This represents the projection of the angular velocity of the shell coordinate system {s} relative to the relative inertial frame {o} onto the shell system {s}.

6. The navigation method according to claim 3, characterized in that, The navigation acceleration Represented as ， ， In the formula, Let be the orientation matrix of the navigation frame {n} relative to the inertial frame {i}. For navigation position matrix, This is the Earth's rotation matrix. For navigation speed, This is the Earth's rotational angular velocity. The position angular velocity of the carrier, Let $e$ be the position vector from Earth system $e$ to navigation system $n$.

7. The navigation method according to claim 3, characterized in that, The attitude matrix The values ​​of each element are represented as follows: ， In the formula, Let be the orientation matrix of the shell system {s} relative to the relative inertial frame {o}; Let {i} represent the orientation matrix of the absolute inertial frame of reference {i} relative to the Earth frame of reference {e}; This represents the orientation matrix of the Earth system {e} relative to the navigation system {n}; Let {i} be the orientation matrix between the absolute inertial frame {i} and the relative inertial frame {o}.

8. The navigation method according to claim 3, characterized in that, The attitude matrix of the carrier The attitude of the carrier satisfies the following transformation relationship: ， ， In the formula, Main heading angle, Main roll angle, It is the pitch angle.

9. The navigation method according to claim 1, characterized in that, The method for obtaining the error estimate of the navigation parameters obtained in step 1 is as follows: Step 4.1: Derive the error equations for navigation attitude, velocity, and position; Step 4.2: Select the state variable x of the multi-accelerometer and GPS integrated navigation system as 12-dimensional; Step 4.3: Establish the state space model and measurement space model of the multi-accelerometer and GPS integrated navigation system. Based on the error equation in Step 4.1 and the state variables in Step 4.2, solve the state matrix, system noise matrix, measurement matrix and measurement noise matrix in the model respectively to obtain the state equation and measurement equation of the integrated navigation system. Step 4.4: Establish the time update equation and measurement equation of the combined navigation filter based on the state equation and measurement equation; Step 4.5: The combined navigation filter calculates the optimal estimate of the state error based on the velocity difference and position difference obtained in Step 3.

10. The navigation method according to claim 9, characterized in that, The attitude error equation is as follows: ， In the formula, ε is the attitude error angular vector. Let be the attitude matrix of the carrier system {b} relative to the navigation system {n}. Let be the projection of the angular rate of navigation frame {n} relative to absolute inertial frame {i} onto navigation coordinate system {n}. Let be the projection of the angular velocity of system {b} relative to the absolute inertial frame {i} onto the loaded system {b}. Information The error value; The velocity error equation is: ， In the formula, β is the error angle vector of the actual navigation system {n} deviating from the ideal navigation system {geographic coordinate system {G}}; This represents the projection of the angular velocity of the Earth system {e} relative to the absolute inertial frame {i} onto the navigation frame {n}. δ represents the projection of the angular velocity of navigation frame {n} relative to Earth frame {e} onto navigation frame {n}. n V represents the speed error; Let be the orientation matrix of the navigation frame {n} relative to the inertial frame {i}; These are the accelerations of the navigation coordinate system {n} and the vehicle system {b} relative to the absolute inertial frame {i}, respectively. This is the Earth's rotational angular velocity. The position angular velocity of the carrier; Position matrix for navigation; The position error equation is: ， In the formula, λ, Φ, and h represent the longitude, latitude, and altitude of the carrier's location on Earth, respectively, and V E V N V U These represent the speeds of the carrier along the east, north, and sky directions, respectively, and R is the Earth's radius.

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