A combined navigation positioning method and system, electronic equipment and storage medium

Abstract

The application belongs to navigation positioning technology, and discloses a combined navigation positioning method, a combined navigation positioning system, an electronic device and a storage medium, comprising the following steps: constructing a measurement vector according to the difference between preprocessed Loran-C positioning data and INS positioning data; constructing a state equation taking inertial navigation error and Loran-C positioning systematic deviation as state variables, and constructing a measurement equation taking the measurement vector as an observation variable; performing state estimation based on the state equation and the measurement equation by using Kalman filtering to obtain an inertial navigation error estimation value; and correcting the calculation process of the INS based on the inertial navigation error estimation value to obtain a combined navigation positioning result. According to the application, the systematic deviation of the Loran-C is expanded into the state vector, and the systematic deviation is separated from the position difference measurement in the filtering process, and is estimated by Kalman filtering together with the inertial navigation error, so that the interference of the systematic deviation on the inertial error estimation is inhibited.

Description

Technical Field

[0001] This application pertains to navigation and positioning technology, specifically relating to a combined navigation and positioning method, system, electronic device, and storage medium. Background Technology

[0002] Inertial Navigation Systems (INS) are autonomous navigation systems that continuously provide navigation parameters such as attitude, velocity, and position of a vehicle without relying on external signal reception and transmission. They possess excellent independence and stealth capabilities, making them widely used in aviation, maritime, and underwater vehicles. However, INS positioning errors accumulate over time, making it difficult to maintain high accuracy independently for extended periods. Therefore, they typically need to be combined with other navigation systems, employing information fusion techniques to suppress errors. Currently, existing technology combines INS with Global Navigation Satellite Systems (GNSS), leveraging GNSS's all-weather, high-precision positioning capabilities to correct the accumulated errors of INS, achieving complementary advantages. However, in adversarial environments, satellite signals are susceptible to interference or spoofing, and signal attenuation or even complete rejection is severe in concealed spaces such as underground, underwater, and indoors. Therefore, the Loran-C (Long Range Navigation System C) long-range radio navigation system serves as an alternative or backup to GNSS, possessing strong anti-interference capabilities, the ability to penetrate water layers of a certain depth, and its positioning error does not accumulate over time.

[0003] However, the Loran-C positioning results contain a systematic bias with a non-zero mean. This systematic bias causes the zero-mean statistical assumption of measurement noise to be invalid. If the conventional filtering model is used, biased estimation will be produced, which will directly affect the positioning accuracy of the integrated navigation. Summary of the Invention

[0004] This application addresses the technical problem of systematic bias with non-zero mean in existing Loran-C positioning results, which affects navigation and positioning accuracy, by providing a combined navigation and positioning method, system, electronic device, and storage medium.

[0005] To achieve the above objectives, this application adopts the following technical solution: Firstly, a combined navigation and positioning method includes: Obtain INS location data and Loran-C location data; Eliminate the initial positional deviation of the Loran-C positioning data to obtain preprocessed Loran-C positioning data; Based on the difference between the preprocessed Loran-C positioning data and the INS positioning data, a measurement vector is constructed; Constructing based on inertial navigation error and Loran C. The systemic deviation of the positioning system is used as the state equation, and the measurement equation is used as the observation. Kalman filtering is used for time update to obtain the one-step predicted state value and the one-step predicted mean square error matrix at the current time. The innovation sequence is calculated based on the measurement vector, the one-step predicted state value and the measurement equation. After adaptive update of the measurement noise based on the innovation sequence, the updated Kalman gain is calculated in combination with the one-step predicted mean square error matrix. Based on the state equation and measurement equation, the inertial navigation error estimate and the Loran-C positioning system deviation estimate are obtained by updating the measurement according to the updated Kalman gain. The INS solution process is corrected based on the inertial navigation error estimate to obtain the integrated navigation and positioning result. The corresponding inertial navigation error component in the state vector is then set to zero. This is achieved using the Loran... The estimated systematic bias of C positioning for Loran C-positioning performance is monitored and evaluated online.

[0006] In some implementations, eliminating the initial positional deviation of the Loran-C positioning data to obtain preprocessed Loran-C positioning data includes: Obtain initial position data; The initial position deviation is obtained by subtracting the Loran-C positioning data from the initial position data; The Loran-C positioning data are all subtracted from the initial position deviation to obtain the preprocessed Loran-C positioning data.

[0007] In some implementations, the state vector of the state equation includes: three-dimensional attitude angle error, three-dimensional velocity error, three-dimensional position error, three-axis gyroscope zero bias error, three-axis accelerometer zero bias error, Loran-C positioning latitude deviation, and Loran-C positioning longitude deviation; In the state transition matrix of the state equation, the diagonal elements corresponding to the Loran-C positioning latitude deviation and Loran-C positioning longitude deviation are 1, and the other elements are set to 0; The system noise vector of the state equation includes the driving noise for the Loran-C positioning latitude deviation and Loran-C positioning longitude deviation; In the noise control matrix of the state equation, the elements at the corresponding noise component positions in the rows corresponding to the Loran-C positioning latitude deviation and Loran-C positioning longitude deviation are set to 1, and the remaining elements are set to 0.

[0008] In some embodiments, the measurement matrix of the measurement equation includes columns corresponding to the Loran-C positioning latitude deviation and Loran-C positioning longitude deviation, with non-zero elements set to -1.

[0009] In some implementations, the step of performing measurement noise adaptive updates based on the innovation sequence and then calculating the updated Kalman gain in conjunction with the one-step prediction mean square error matrix includes: Based on the innovation sequence, the adaptive measurement noise covariance matrix is ​​calculated; based on the measurement matrix corresponding to the measurement equation, combined with the one-step prediction mean square error matrix and the adaptive measurement noise covariance matrix, the updated Kalman gain is calculated.

[0010] In some implementations, the method further includes: when there is no valid Loran-C positioning data, switching to pure inertial navigation mode and directly obtaining the INS solution result through the INS solution process as the integrated navigation positioning result.

[0011] Secondly, a combined navigation and positioning system includes: The data acquisition module is used to acquire INS positioning data and Loran-C positioning data; The data preprocessing module is used to eliminate the initial position deviation of the Loran-C positioning data to obtain preprocessed Loran-C positioning data; The measurement vector construction module is used to construct a measurement vector based on the difference between the preprocessed Loran-C positioning data and the INS positioning data; The measurement noise adaptive update module is used to construct the state equation and the measurement equation. Based on the state equation, it uses Kalman filtering to perform time update to obtain the one-step predicted state value and the one-step predicted mean square error matrix at the current time. It calculates the innovation sequence according to the measurement vector, the one-step predicted state value and the measurement equation. After the measurement noise adaptive update is performed based on the innovation sequence, the updated Kalman gain is calculated in combination with the one-step predicted mean square error matrix. The measurement update module is used to update the measurement based on the state equation and the measurement equation, and according to the updated Kalman gain, to obtain the estimated value of the inertial navigation error. The INS correction module is used to correct the INS solution process based on the inertial navigation error estimate to obtain the integrated navigation positioning result.

[0012] Thirdly, a computer device includes: a processor and a computer-readable storage medium; A processor, adapted to execute computer programs; A computer-readable storage medium storing a computer program, which, when executed by the processor, implements the aforementioned integrated navigation and positioning method.

[0013] Fourthly, a computer-readable storage medium storing a computer program adapted to be loaded by a processor and executed as described in the section on latitude, is also provided.

[0014] Fifthly, a computer program product comprising a computer program that, when executed by a processor, implements the aforementioned integrated navigation and positioning method.

[0015] Compared with the prior art, this application has the following beneficial effects: This application provides a combined navigation positioning method. After acquiring INS positioning data and Loran-C positioning data, the initial position deviation of the Loran-C positioning data is eliminated to obtain preprocessed Loran-C positioning data, thereby eliminating the relatively fixed systematic deviation in the Loran-C positioning result and making the preprocessed Loran-C positioning data closer to the true position. Based on the difference between the preprocessed Loran-C positioning data and the INS positioning data, a measurement vector is constructed. This measurement vector reflects the comprehensive information of INS error and residual Loran-C deviation. A state equation and a measurement equation are constructed. Based on the state equation, a Kalman filter is used for time updating to obtain the one-step predicted state value and the one-step predicted mean square error matrix at the current time. An innovation sequence is calculated based on the measurement vector, the one-step predicted state value, and the measurement equation. After adaptive updating of the measurement noise based on the innovation sequence, the updated Kalman gain is calculated using the one-step predicted mean square error matrix. Based on the state equation and the measurement equation, the measurement is updated according to the updated Kalman gain to obtain an estimated inertial navigation error. The inertial navigation error estimate is used to correct the INS solution process to obtain the integrated navigation and positioning result. Through the above steps, this application explicitly models the systematic bias of Loran-C through state vector expansion, so that it is no longer treated as indistinguishable noise interference, but is incorporated into the state estimation system. This allows for separate estimation during the filtering process, satisfying the assumption of zero-mean measurement noise in subsequent measurement update stages. This fundamentally solves the problem of biased filtering estimation caused by the systematic bias of Loran-C. Simultaneously, the correction of the INS solution by the inertial navigation error estimate effectively suppresses the accumulation of INS errors.

[0016] Furthermore, initial position data is acquired; the initial position deviation is obtained by subtracting the Loran-C positioning data from the initial position data; the initial position deviation is subtracted from all Loran-C positioning data to obtain preprocessed Loran-C positioning data. Utilizing the prior condition that the initial position is usually known in actual scenarios, such as docks or ports, or determined in advance by GNSS, the main fixed deviation of Loran-C can be quickly eliminated before filtering starts with simple subtraction and subtraction. This provides a more accurate input for the subsequent construction of measurement vectors and filtering estimation, thereby accelerating filtering convergence, simplifying the preprocessing process, and reducing computational complexity.

[0017] Furthermore, the state vector of the state equation includes: three-dimensional attitude angle error, three-dimensional velocity error, three-dimensional position error, three-axis gyroscope zero bias error, three-axis accelerometer zero bias error, Loran-C positioning latitude deviation, and Loran-C positioning longitude deviation. Compared with the state vector of a conventional integrated navigation system, this application expands the state vector to include the Loran-C positioning deviation in the estimation range, enabling the filter to simultaneously separate the various errors of the INS and the systematic deviation of the Loran-C positioning system from the mixed error observations, thus avoiding the interference of the Loran-C deviation on the INS error estimation. Meanwhile, in the state transition matrix of the state equation, the diagonal elements corresponding to the Loran-C positioning latitude and longitude deviations are set to 1, and the other elements are set to 0; the system noise vector of the state equation includes the driving noise for the Loran-C positioning latitude and longitude deviations; in the noise control matrix of the state equation, the elements at the corresponding noise component positions in the rows corresponding to the Loran-C positioning latitude and longitude deviations are set to 1, and the other elements are set to 0. These three technical features together achieve accurate mathematical modeling of the Loran-C deviation components, making the deviation estimation independent of other state components and not transmitting interference to other states, ensuring the stability of the deviation state estimation during the filtering recursion process, and improving the accuracy and stability of the deviation estimation.

[0018] Furthermore, the measurement matrix of the measurement equation includes columns corresponding to the Loran-C positioning latitude deviation and Loran-C positioning longitude deviation, with its non-zero elements set to -1. This setting establishes a direct correlation between the measurement vector and the deviation components in the state vector within the measurement equation. Since the measurement vector is composed of the difference between the preprocessed Loran-C positioning data and the INS positioning data, it inherently contains mixed information of INS position error and Loran-C systematic deviation. The setting of the corresponding columns and non-zero elements in the measurement matrix allows the two error components to be characterized and separately estimated during measurement updates. This forms the structural basis for achieving joint estimation of INS error and Loran-C deviation, ensuring the feasibility and accuracy of the joint estimation.

[0019] Furthermore, after adaptively updating the measurement noise based on the innovation sequence, the updated Kalman gain is calculated by combining the one-step prediction mean square error matrix. This includes: calculating the adaptive measurement noise covariance matrix based on the innovation sequence; calculating the updated Kalman gain based on the measurement matrix corresponding to the measurement equation, combined with the one-step prediction mean square error matrix and the adaptive measurement noise covariance matrix. The innovation sequence is calculated from the measurement vector, the one-step prediction state value, and the measurement equation, reflecting the degree to which the current measurement deviates from the prediction. The adaptive update of the measurement noise covariance matrix is ​​achieved online through the innovation sequence, ensuring that the statistical characteristics of the noise are determined in real-time by actual operating data, rather than relying on preset fixed values. The Kalman gain is then calculated by combining the one-step prediction mean square error matrix and the measurement matrix, allowing the gain to adaptively adjust with the time-varying characteristics of Loran-C noise. Since the measurement noise of Loran-C is time-varying due to changes in the propagation environment, the above adaptive adjustment allows the filter to automatically correct its dependence weight on measurement information when noise changes, effectively improving the robustness and adaptability of the integrated navigation system in complex environments.

[0020] Furthermore, after the time update step using Kalman filtering, the system further includes: when there is no valid Loran-C positioning data, the INS solution process is used to obtain the INS solution result as the integrated navigation positioning result. This technical feature ensures that the integrated navigation system can still continuously output positioning results under abnormal conditions such as Loran-C signal interruption or data rejection in the preprocessing stage, maintaining the continuity of navigation function and avoiding the problem of navigation interruption due to invalid Loran-C data. After valid Loran-C positioning data is recovered, the system can normally enter the measurement update stage to continue error correction, ensuring the continuity and reliability of the navigation system. Attached Figure Description

[0021] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of this application and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0022] Figure 1 A flowchart illustrating a combined navigation and positioning method provided in an embodiment of this application; Figure 2 A structural diagram of a combined navigation and positioning system provided in an embodiment of this application; Figure 3 A flowchart illustrating the technical principle of a combined navigation and positioning method provided in this application embodiment; Figure 4 Latitude error comparison chart provided for embodiments of this application; Figure 5 Longitude error comparison chart provided for embodiments of this application; Figure 6 A comparison diagram of planar position errors provided for embodiments of this application; Figure 7 A structural diagram of a computer device provided for an embodiment of this application. Detailed Implementation

[0023] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0024] like Figure 3As shown, this invention provides a combined navigation and positioning method. First, system initialization is completed, and raw observation data from an inertial navigation system (INS) and a Loran-C long-range radio navigation system are simultaneously acquired. The two types of raw observation data are then processed to obtain INS positioning data and Loran-C positioning data. The Loran-C positioning data is preprocessed to eliminate its initial position deviation. The validity of the preprocessed Loran-C positioning data is then checked. If valid Loran-C positioning data exists, a Kalman filter time update is first performed, followed by adaptive estimation of measurement noise based on the innovation sequence, and then a Kalman filter measurement update is performed to obtain updated inertial navigation error estimates and Loran-C positioning system systematic deviation estimates. The inertial navigation error estimates are fed back to the INS processing module for correction. If valid Loran-C positioning data does not exist, only a Kalman filter time update is performed, and the INS positioning data is directly used as the navigation result for the current moment. Finally, the combined navigation and positioning result is output. The combined navigation and positioning method of this embodiment is described in detail below with reference to the accompanying drawings.

[0025] In one embodiment of this application, such as Figure 1 As shown, a combined navigation and positioning method is provided, including: S1, acquire INS location data and Loran-C location data; Specifically, INS and Loran-C observation data are collected simultaneously, and then processed separately to obtain INS positioning data and Loran-C positioning data. INS positioning data includes longitude, latitude, and altitude. Loran-C positioning data includes longitude and latitude.

[0026] S2, eliminate the initial position deviation of the Loran-C positioning data to obtain preprocessed Loran-C positioning data; Specifically, the initial position of the carrier mounting the INS and Loran-C is known and can be determined in advance or provided by GNSS. After obtaining the first Loran-C positioning data, it is subtracted from the known initial position, or a segment of Loran-C positioning data under static conditions is selected, its average value is taken, and the difference between this average value and the known initial position is calculated to obtain the initial position deviation. Thereafter, this initial position deviation is subtracted from all subsequent Loran-C positioning data to obtain preprocessed Loran-C positioning data. Assuming the initial position is In order to obtain the initial positional deviation, the first Loran-C positioning data was obtained. Alternatively, select a segment of Loran-C positioning data under static conditions and take its average value. The initial position deviation is obtained by subtracting it from the known initial position, as shown in formula (1) or (2): (1) (2) in, Let the initial position vector be... Let the Loran-C position vector be... The initial position is the latitude component. The initial position is the longitude component. This is the first valid Loran-C latitude component. This is the first valid Loran-C longitude component. The average latitude component of Loran-C. For the Loran-C mean longitude component, This is the initial position deviation vector. This is the initial latitude deviation. This represents the initial longitude deviation.

[0027] After obtaining the initial position deviation, all subsequent Loran-C positioning data are subtracted from this initial position deviation to obtain preprocessed Loran-C positioning data.

[0028] S3, construct a measurement vector based on the difference between the preprocessed Loran-C positioning data and the INS positioning data; Specifically, the difference between the INS-calculated position and the preprocessed Loran-C position is used as the measurement vector. The measurement vector includes the latitude and longitude differences. Loran-C positioning does not provide altitude information; altitude is obtained from other sensors, such as barometric altimeters or depth gauges. In application scenarios where no other sensors are available and the vehicle's altitude does not change significantly, the altitude value of the initial position is used as the current altitude.

[0029] S4. Construct the state equation and measurement equation. Based on the state equation, use Kalman filtering to update the time and obtain the one-step predicted state value and one-step predicted mean square error matrix at the current time. Calculate the innovation sequence according to the measurement vector, one-step predicted state value and measurement equation. After adaptive update of the measurement noise based on the innovation sequence, calculate the updated Kalman gain in combination with the one-step predicted mean square error matrix. In conventional INS / GNSS integrated navigation, the Kalman filter state vector is 15-dimensional, including three-dimensional attitude angle error, three-dimensional velocity error, three-dimensional position error, three-axis gyroscope bias error, and three-axis accelerometer bias error. For INS / Loran-C integrated navigation, based on the above 15-dimensional state, the longitude and latitude deviations of Loran-C positioning are introduced as states to be estimated, extending the state vector to 17 dimensions. Based on their variation characteristics, the Loran-C positioning latitude and longitude deviations are modeled as random constants. The three-dimensional attitude angle error includes pitch angle error, roll angle error, and azimuth angle error; the three-dimensional velocity error includes eastward, northward, and azimuth velocity errors; and the three-dimensional position error includes latitude error, longitude error, and altitude error.

[0030] Accordingly, the state transition matrix, noise control matrix, and system noise vector are expanded in dimension. Based on the assumption of a stochastic constant model for Loran-C bias, the newly added diagonal elements in the state transition matrix are set to 1, and all other elements are set to zero. The two newly added dimensions of the system noise vector represent the driving noise of Loran-C positioning latitude and longitude bias. After expanding the dimension of the noise control matrix, the diagonal elements corresponding to the newly added driving noise are set to 1, and all other elements are set to zero, as follows: Based on the INS error propagation law, the state equation of the system is established as shown in equation (3): (3) In the formula, Represents the rate of change of state. This represents the state variable to be estimated. F Here is the state transition matrix. G For noise control matrix, W The system noise vector is typically 15-dimensional, but after considering the Loran-C positioning bias, it is transformed into 17-dimensional vectors, as shown in (4): (4) In the formula, , and These represent pitch angle error, roll angle error, and azimuth angle error, respectively. , and These represent the velocity errors in the east, north, and sky directions, respectively. , and These represent latitude error, longitude error, and altitude error, respectively. , and They represent the three axes respectively. xThe zero bias error of the gyroscope (axis 1, y-axis, z-axis) , and They represent the three axes respectively. x Accelerometer zero bias error (axis, y-axis, z-axis). and The newly added Loran-C positioning latitude and longitude deviations are modeled as random constants based on their variation characteristics. The state transition matrix, constructed based on the standard INS error equations, describes the dynamic propagation of each error state variable. Simultaneously, the state transition matrix... Noise control matrix System noise vector To expand the dimension, based on the assumption of a stochastic constant model with Loran-C bias, The newly added diagonal element in the matrix is ​​set to 1, and the other elements are set to 0; The newly added two-dimensional representation and Drive noise; After expanding the matrix, the diagonal elements (i.e., the positions of the noise components) corresponding to the newly added driving noise are set to 1, and the other elements are set to zero.

[0031] In the construction of the measurement equation, the measurement matrix is ​​augmented with columns corresponding to the Loran-C positioning deviation status, enabling the measurement values ​​to simultaneously reflect the combined effects of INS position error and Loran-C systematic deviation, as detailed below: After the state equation modeling is completed, measurement equations need to be established to realize the measurement update of Kalman filtering. This embodiment adopts a combined navigation scheme based on location information as the measurement. The measurement vector is composed of the difference between preprocessed Loran-C positioning data and INS positioning data. The measurement equation is defined as: (5) In the formula, Indicates measurement noise. Represents the measurement vector. Represents the measurement matrix. X The state variable to be estimated is represented by the following expression: (6) in, , and The latitude, longitude, and altitude calculated for INS. and These represent the latitude and longitude calculated by Loran-C, respectively. Since Loran-C positioning does not provide altitude information, the figures shown are... Data obtained from other sensors, such as barometric altimeters for land use and depth gauges for underwater use, can be used in application scenarios where no other sensors are available and the carrier's altitude does not change significantly. Set the height value to the initial position. This represents the measurement matrix, taking into account Loran-C positioning bias. Represented as: (7) After constructing the state equation and measurement equation, the process proceeds to the recursive estimation stage of the Kalman filter. In the measurement update stage, based on the time update, the position difference between the INS and Loran-C systems is used as the actual measurement value, and the Kalman gain is calculated. The one-step prediction value is then corrected to obtain the posterior state estimate. This process achieves real-time separation and estimation of the INS error and the systematic bias of the Loran-C positioning system, yielding estimates of the Loran-C positioning system bias and the inertial navigation error.

[0032] S5. Based on the state equation and measurement equation, the inertial navigation error estimate is obtained by updating the measurement according to the updated Kalman gain. Furthermore, an adaptive adjustment strategy for measurement noise is introduced into the Kalman filtering framework. The measurement noise covariance matrix at the current time step is estimated in real time based on the innovation sequence, and the Kalman gain is dynamically adjusted. The innovation is the difference between the actual measurement value and the one-step predicted value. By estimating the measurement noise covariance matrix online in real time, the weights of the filter on the Loran-C measurement information are dynamically adjusted to address the problem of decreased filtering accuracy caused by the time-varying statistical characteristics of measurement noise and the difficulty in accurately modeling it in advance. Specifically: In practical applications, the positioning accuracy of Loran-C is affected by many factors, and its measurement noise has time-varying characteristics, making it difficult to model accurately in advance. Using a fixed measurement noise covariance matrix may lead to performance degradation or even divergence of the filter during actual operation due to model mismatch. Therefore, this invention introduces an adaptive measurement noise adjustment strategy into the Kalman filter framework, improving the filter's adaptability to complex environments by estimating the measurement noise covariance matrix online in real time.

[0033] In Discrete Kalman filtering, innovation is defined as the difference between the actual measurement and the one-step prediction: (8) In the formula, Indicates new information, Indicates the actual measured value. This represents a one-step prediction value.

[0034] The adaptive estimation formula for measurement noise is as follows: (9) in, (10) In the formula, the subscript Indicates the first time, Indicates the first k The time-adaptive adjusted discrete measurement noise, i.e., the measurement noise covariance matrix. Indicates the first k Discrete measurement noise adaptively adjusted at time -1 For discrete measurement matrices, Represents the mean square error matrix. For the first k Time decay factor, For the first k The decay factor at time -1, initial value , This is called the forgetting factor, and it can take values ​​of... , For the new interest, For the transposition of new information, This is the transpose of the discrete measurement matrix.

[0035] S6. Based on the estimated inertial navigation error, the INS solution process is corrected to obtain the integrated navigation positioning result.

[0036] After each measurement update, the error parameters related to INS in the estimated state variables, including attitude angle error, velocity error, position error, gyroscope bias and accelerometer bias, are fed back to the INS calculation module to correct the navigation output at the current moment and obtain the integrated navigation and positioning result.

[0037] When no valid Loran-C positioning data is available, the state vector is predicted in one step using only the system state equation, and the state covariance matrix is ​​updated. In this case, the filtering result relies entirely on the recursive solution of the INS, providing prior estimation information for subsequent time steps, as detailed below: Kalman filter estimation is divided into time update and measurement update. When there are no measurement values, time update is performed to achieve one-step prediction of state variables and one-step prediction of mean square error. When there are measurement values, measurement update is performed to calculate the filter gain, correct the predicted values ​​of state variables and update the mean square error matrix, and then feed the estimated error back to the INS update solution.

[0038] After establishing the state equation and measurement equation that take into account Loran-C positioning bias, and determining the adaptive adjustment strategy for measurement noise, the process proceeds to the recursive estimation and feedback correction stage of Kalman filtering. This process performs time updates and measurement updates based on the availability of valid Loran-C measurement information at the current time. After state estimation is completed, the estimated error state is fed back to the INS solution module for correction. When there is no valid Loran-C measurement data (e.g., data is removed during preprocessing or the signal is missing), the following formula is used to predict the state vector in one step based solely on the system state equation, and the state covariance matrix is ​​updated: (11) (12) In the formula, superscript Indicates transpose. For the first k State estimate at time -1 This is a one-step prediction value. The mean square error matrix for one-step prediction. This is the discretized state transition matrix. express transpose, Represents the noise driving matrix. Let be the system noise covariance matrix. express The transpose of the INS. At this point, the navigation result depends entirely on the updated solution of the INS, providing prior estimation information for subsequent time steps.

[0039] When valid Loran-C measurement data is available, a measurement update is performed based on the time update, and the one-step prediction value is corrected using the following formula: (13) (14) (15) In the formula, For Kalman filter gain, This represents the adaptive measurement noise covariance matrix. This is the corrected state estimate. This is the corrected mean square error matrix.

[0040] After each measurement update, the error parameters related to the INS in the obtained state estimate are fed back to the INS calculation module in real time for correction. This closed-loop correction method can effectively suppress the accumulation of INS errors over time, ensuring that the integrated navigation system maintains high accuracy during long-term operation.

[0041] In one embodiment of this application, such as Figure 2 As shown, a combined navigation and positioning system is provided, including: The data acquisition module is used to acquire INS positioning data and Loran-C positioning data; The data preprocessing module is used to eliminate the initial position deviation of the Loran-C positioning data to obtain preprocessed Loran-C positioning data; The measurement vector construction module is used to construct a measurement vector based on the difference between the preprocessed Loran-C positioning data and the INS positioning data; The measurement noise adaptive update module is used to construct the state equation and the measurement equation. Based on the state equation, it uses Kalman filtering to perform time update to obtain the one-step predicted state value and the one-step predicted mean square error matrix at the current time. It calculates the innovation sequence according to the measurement vector, the one-step predicted state value and the measurement equation. After the measurement noise adaptive update is performed based on the innovation sequence, the updated Kalman gain is calculated in combination with the one-step predicted mean square error matrix. The measurement update module is used to update the measurement based on the state equation and the measurement equation, and according to the updated Kalman gain, to obtain the estimated value of the inertial navigation error. The INS correction module is used to correct the INS solution process based on the inertial navigation error estimate to obtain the integrated navigation positioning result.

[0042] For specific limitations regarding a combined navigation and positioning system, please refer to the limitations regarding a combined navigation and positioning method described above; the corresponding technical effects are equivalent and will not be repeated here. Each module in the aforementioned combined navigation and positioning system can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device, or stored in the memory of a computer device in software form, so that the processor can call and execute the corresponding operations of each module.

[0043] Figure 7 An internal structural diagram of a computer device is shown in one embodiment. This computer device may specifically be a terminal or a server. Figure 7As shown, the computer device includes a processor, memory, network interface, display, camera, and input device connected via a system bus. The processor provides computing and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The network interface is used to communicate with external terminals via a network connection. When the computer program is executed by the processor, it implements a combined navigation and positioning method. The display screen can be an LCD screen or an e-ink display screen. The input device can be a touch layer covering the display screen, buttons, a trackball, or a touchpad located on the computer device's casing, or an external keyboard, touchpad, or mouse.

[0044] As will be understood by those skilled in the art, computer equipment Figure 7 The structure shown is merely a block diagram of a portion of the structure related to the present invention and does not constitute a limitation on the computer device to which the present invention is applied. Specific computing devices may include more or fewer components than those shown in the figure, or combine certain components, or have the same component arrangement.

[0045] In one embodiment, a computer device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the method described above.

[0046] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the steps of the above-described method.

[0047] This embodiment uses onboard INS and Loran-C data for comparative analysis. The test results are shown in the figure below. Figure 4 Indicates latitude error. Figure 5 Indicates longitude error. Figure 6 This indicates that the planar errors of latitude and longitude are taken into account. The figure compares three modes: pure inertial navigation, i.e., pure inertial positioning without Loran-C; 17-dimensional inertial navigation / Loran-C integrated navigation, a combined navigation and positioning method proposed in this embodiment, taking into account Loran-C positioning deviation; and 15-dimensional inertial navigation / Loran-C integrated navigation, a conventional combined navigation and positioning mode, whose processing procedures are consistent with 17-dimensional inertial navigation / Loran-C integrated navigation except that it does not consider Loran-C positioning deviation.

[0048] Depend on Figures 4-6It can be seen that, compared with the results of pure inertial navigation, the 17-dimensional inertial navigation / Loland C integrated navigation significantly suppressed the inertial navigation error. Further statistical analysis of the error was conducted, using the maximum error value as the evaluation index. Since errors can be positive or negative, the absolute value of the error was taken first, followed by the maximum value. The results are shown in Table 1. The maximum latitude error decreased from 1840 meters to 1259 meters, improving accuracy by 31.58%; the maximum longitude error decreased from 3988 meters to 2851 meters, improving accuracy by 28.51%; and the maximum horizontal error decreased from 4363 meters to 3014 meters, improving accuracy by 30.92%. The 15-dimensional inertial navigation / Loland C integrated navigation not only failed to effectively suppress inertial navigation errors but also reduced the accuracy of the original inertial navigation. Comparative analysis demonstrates the effectiveness of the proposed solution in this embodiment.

[0049] Table 1 Error Statistics Results

[0050] In summary, the integrated navigation and positioning method, system, computer device, and storage medium provided in this application preprocess the Loran-C raw positioning data by subtracting the fixed deviation of the initial position, effectively eliminating systematic fixed deviations. Furthermore, addressing the issue that Loran-C positioning errors exhibit non-zero mean characteristics and do not satisfy the normal distribution assumption of standard Kalman filter measurement noise, the conventional 15-dimensional state vector is extended to 17 dimensions, adding the latitude and longitude deviations of Loran-C positioning as states to be estimated, thereby achieving unbiased estimation. In addition, an adaptive adjustment strategy for measurement noise is introduced, further improving the adaptability and stability of the filtering algorithm, significantly enhancing the positioning accuracy and reliability of INS / Loran-C integrated navigation, and providing an effective solution for continuous high-precision navigation in GNSS-denied environments.

[0051] The various embodiments in this specification are described in a progressive manner. For directly identical or similar parts of the embodiments, refer to each other. Each embodiment focuses on its differences from other embodiments. In particular, the system embodiments are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions in the method embodiments. It should be noted that the technical features of the above embodiments can be combined arbitrarily. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as the combination of these technical features does not contradict each other, it should be considered within the scope of this specification.

[0052] The above-described embodiments are merely preferred embodiments of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various improvements and substitutions without departing from the principles of the present invention, and these improvements and substitutions should also be considered within the scope of protection of the present invention. Therefore, the scope of protection of this invention should be determined by the scope of the claims.

Claims

1. A combined navigation and positioning method, characterized in that, include: Obtain INS location data and Loran-C location data; Eliminate the initial positional deviation of the Loran-C positioning data to obtain preprocessed Loran-C positioning data; Based on the difference between the preprocessed Loran-C positioning data and the INS positioning data, a measurement vector is constructed; Construct a state equation and a measurement equation. Based on the state equation, use Kalman filtering to update the time and obtain the one-step predicted state value and the one-step predicted mean square error matrix at the current time. Calculate the innovation sequence according to the measurement vector, the one-step predicted state value and the measurement equation. After adaptively updating the measurement noise based on the innovation sequence, calculate the updated Kalman gain in combination with the one-step predicted mean square error matrix. Based on the state equation and measurement equation, the inertial navigation error estimate is obtained by updating the measurement according to the updated Kalman gain. The inertial navigation error estimate is used to correct the INS solution process to obtain the integrated navigation positioning result. The state vector of the state equation includes: three-dimensional attitude angle error, three-dimensional velocity error, three-dimensional position error, three-axis gyroscope zero bias error, three-axis accelerometer zero bias error, Loran-C positioning latitude deviation and Loran-C positioning longitude deviation; In the state transition matrix of the state equation, the diagonal elements corresponding to the Loran-C positioning latitude deviation and Loran-C positioning longitude deviation are 1, and the other elements are set to 0; The system noise vector of the state equation includes the driving noise for the Loran-C positioning latitude deviation and Loran-C positioning longitude deviation; In the noise control matrix of the state equation, the elements at the corresponding noise component positions in the rows corresponding to the Loran-C positioning latitude deviation and Loran-C positioning longitude deviation are set to 1, and the remaining elements are set to 0. The measurement matrix of the measurement equation includes columns corresponding to the Loran-C positioning latitude deviation and Loran-C positioning longitude deviation, and its non-zero elements are set to -1; After adaptively updating the measurement noise based on the innovation sequence, the updated Kalman gain is calculated by combining the one-step prediction mean square error matrix, including: Based on the innovation sequence, the adaptive measurement noise covariance matrix is ​​calculated; based on the measurement matrix corresponding to the measurement equation, combined with the one-step prediction mean square error matrix and the adaptive measurement noise covariance matrix, the updated Kalman gain is calculated.

2. The integrated navigation and positioning method according to claim 1, characterized in that, The process of eliminating the initial positional deviation of the Loran-C positioning data to obtain preprocessed Loran-C positioning data includes: Obtain initial position data; The initial position deviation is obtained by subtracting the Loran-C positioning data from the initial position data; The Loran-C positioning data are all subtracted from the initial position deviation to obtain the preprocessed Loran-C positioning data.

3. The integrated navigation and positioning method according to claim 1, characterized in that, The step of using Kalman filtering for time update further includes: when there is no valid Loran-C positioning data, obtaining the INS solution result based on the INS solution process, which is used as the integrated navigation positioning result.

4. A combined navigation and positioning system, characterized in that, A combined navigation and positioning method according to any one of claims 1 to 3 includes: The data acquisition module is used to acquire INS positioning data and Loran-C positioning data; The data preprocessing module is used to eliminate the initial position deviation of the Loran-C positioning data to obtain preprocessed Loran-C positioning data; The measurement vector construction module is used to construct a measurement vector based on the difference between the preprocessed Loran-C positioning data and the INS positioning data; The measurement noise adaptive update module is used to construct the state equation and the measurement equation. Based on the state equation, it uses Kalman filtering to perform time update to obtain the one-step predicted state value and the one-step predicted mean square error matrix at the current time. It calculates the innovation sequence according to the measurement vector, the one-step predicted state value and the measurement equation. After the measurement noise adaptive update is performed based on the innovation sequence, the updated Kalman gain is calculated in combination with the one-step predicted mean square error matrix. The measurement update module is used to update the measurement based on the state equation and the measurement equation, and according to the updated Kalman gain, to obtain the estimated value of the inertial navigation error. The INS correction module is used to correct the INS solution process based on the inertial navigation error estimate to obtain the integrated navigation positioning result.

5. A computer device, characterized in that, include: Processor and computer-readable storage media; A processor, adapted to execute computer programs; A computer-readable storage medium storing a computer program that, when executed by the processor, implements a combined navigation and positioning method as described in any one of claims 1 to 3.

6. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program adapted to be loaded by a processor and executed as described in any one of claims 1 to 3.

7. A computer program product, characterized in that, The computer program product includes a computer program that, when executed by a processor, implements a combined navigation and positioning method as described in any one of claims 1 to 3.

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