Inertial navigation system error observability quantitative analysis method and system

Abstract

The invention discloses an inertial navigation system error observability quantitative analysis method and system. According to the method, aiming at the problem of observability analysis of error parameters of the composite optical fiber inertial navigation system in a dynamic environment, a complete error model is established, and a time-varying system is converted into a piecewise linear steady system by adopting a piecewise steady system theory; and constructing a segmented observability matrix and calculating an observability quantitative index of each error parameter through singular value decomposition. According to the method, the observability degree of each error parameter in a high-dimensional state can be accurately evaluated, a scientific basis is provided for calibration track optimization and filter parameter configuration, and the calibration efficiency and precision of the inertial navigation system are remarkably improved. Experimental results show that under the seven-position uniform acceleration scheme, the condition number of the observability matrix of the system is reduced from 105 magnitude to 103 magnitude, the calibration time is shortened by 75%, the precision is improved by 30%, and reliable technical support is provided for long-endurance high-precision navigation of the inertial navigation system in a satellite denial environment.

Description

Technical Field

[0001] This invention relates to the field of inertial navigation technology, and in particular to a method and system for quantitative analysis of the observability of inertial navigation system errors based on piecewise steady system theory. Background Technology

[0002] As the core equipment for autonomous navigation, the accuracy of inertial navigation systems is directly affected by various error parameters of the inertial measurement unit. These error parameters include gyroscope drift, accelerometer bias, scale coefficient error, and installation error, which propagate and amplify continuously during navigation calculations, ultimately leading to a sharp decline in navigation accuracy. Effective compensation for these errors requires precise analysis of their observability; only observable error states can be accurately estimated and compensated for.

[0003] Traditional error analysis methods for inertial navigation systems are mostly based on the assumption of linear, time-invariant systems. However, in practical applications, especially when composite inertial navigation systems provide maneuvers via centrifuges or rotation mechanisms, the systems exhibit significant time-varying characteristics. While existing observability analysis methods based on the covariance matrix can provide intuitive quantitative indicators, they rely on the convergence process of Kalman filtering and cannot pre-analyze system observability before filtering. Nonlinear observability analysis methods based on Lie derivatives, although theoretically more rigorous, have high computational complexity, require extensive derivation, and lack scalability when the state dimension is very high.

[0004] In the calibration process of composite fiber optic inertial navigation systems, numerous system error parameters arise, including zero bias of accelerometers and gyroscopes, calibration coefficient errors, installation errors, higher-order error terms, and axis non-orthogonality errors, resulting in dozens or even hundreds of error parameters in total. Accurately analyzing the observability of each error parameter under such high-dimensional conditions and optimizing the calibration trajectory design accordingly has become a key technical challenge for improving the calibration efficiency and accuracy of inertial navigation systems. Summary of the Invention

[0005] This invention proposes a method and system for quantitative analysis of error observability of inertial navigation systems based on piecewise steady system theory. The time-varying system is approximated as a linear steady system over several time periods. By constructing a piecewise observability matrix and performing singular value decomposition, the observability of each error parameter is quantitatively analyzed.

[0006] The technical solution to achieve the objective of this invention is: a method for quantitative analysis of the observability of inertial navigation system errors, comprising the following steps:

[0007] An error model for a composite fiber optic inertial navigation system is established, including basic error terms, higher-order error terms, and axis non-orthogonality error terms for the accelerometer and gyroscope.

[0008] The piecewise time-invariant system theory is used to approximate the time-varying system as a linear time-invariant system in multiple sub-intervals;

[0009] Construct a piecewise observability matrix and calculate the observability metrics of each error parameter through singular value decomposition;

[0010] The calibration trajectory design and filter parameter configuration were optimized based on the observability analysis results.

[0011] Furthermore, the error model includes accelerometer bias, scale coefficient error, installation error, and higher-order nonlinear error terms; gyroscope bias, scale coefficient error, installation error, acceleration-sensitive error, and higher-order angular motion-related error terms; and axis non-orthogonal error terms. The total error parameter dimension can reach 42 to 102 dimensions.

[0012] Furthermore, the application of the piecewise steady-state system theory includes dividing the entire calibration time into multiple sub-intervals, approximating the system state matrix and observation matrix as constant values ​​in each sub-interval, and constructing the overall piecewise observability matrix by splicing the observability matrices of each sub-interval.

[0013] Furthermore, the observability quantification analysis includes performing singular value decomposition on the overall piecewise observability matrix and calculating the ratio of the singular value corresponding to each state component to the maximum singular value as an observability index. This index reflects the coupling strength between each error parameter and the observed quantity and the ease of estimation.

[0014] Furthermore, the segmented motion trajectory design includes a multi-position rotation scheme, comprising at least a four-position basic scheme and a seven-position enhanced scheme. Each position segment is configured with different rotation axis directions, angular velocity magnitudes, and rotation directions, including uniform speed, uniform acceleration, and variable acceleration motion modes.

[0015] Furthermore, the seven-position enhancement scheme adds three coordinate axis pairs coupled positions to the four-position basic scheme, and uses bidirectional rotation to decouple the symmetric and asymmetric components in the scaling factor error.

[0016] Furthermore, the filter parameter optimization includes setting an initial covariance matrix based on the observability of each error parameter, using a smaller initial variance for error parameters with high observability to accelerate convergence, and using a larger initial variance for error parameters with low observability to avoid filter divergence.

[0017] Furthermore, it also includes a simulation experiment verification stage. By setting different rotational angular velocities, angular accelerations, and position schemes, the variation patterns of the rank, condition number, and observability of each error parameter of the system's observability matrix are compared and analyzed to provide guidance for actual calibration experiments.

[0018] A system for quantifying the observability of errors in an inertial navigation system, comprising:

[0019] Error modeling module, used to establish a complete error model of the composite fiber optic inertial navigation system;

[0020] The piecewise processing module is used to perform mathematical processing of piecewise time-invariant system theory; the observability analysis module is used to construct the piecewise observability matrix and perform singular value decomposition.

[0021] The trajectory optimization module optimizes the design of the calibration trajectory based on the observability analysis results; the filter configuration module is used to optimize the parameter configuration of the calibration filter.

[0022] Furthermore, the observability analysis module can calculate and display the observability change curves of each error parameter in real time, provide overall indicators such as the rank and condition number of the system observability matrix, and generate an observability analysis report to provide decision support for calibration experiments.

[0023] Based on the differential influence of rotational speed on the observability of various error parameters, a segmented calibration strategy is adopted: zero-bias type error is calibrated in the low-speed rotation stage, installation error type parameters are calibrated in the medium-speed rotation stage, and higher-order error terms are calibrated in the high-speed rotation stage.

[0024] The specific implementation of the bidirectional rotation includes setting two rotation directions, clockwise and counterclockwise, within each position segment, with the rotation speed covering a rotational speed range of 0.5-3 rad / s, and maintaining sufficient stabilization time at each speed point to ensure sufficient excitation of the error parameters.

[0025] Compared with the prior art, the method of the present invention has the following outstanding advantages: (1) It can handle the observability analysis problem of high-dimensional state systems and is suitable for the observability evaluation of time-varying systems; (2) It provides quantitative indicators of observability to provide a basis for filter optimization, has high computational efficiency and is easy to apply in engineering, and has a wide application prospect in the field of inertial navigation system calibration. Attached Figure Description

[0026] Figure 1 This is a schematic diagram of the inertial navigation error observability analysis process based on PWCS.

[0027] Figure 2 This is a schematic diagram of the observable quantification analysis process.

[0028] Figure 3 This is a graph showing the results of the error observability analysis.

[0029] Figure 4 This is a graph showing the results of the error observability analysis.

[0030] Figure 5 This is a graph showing the results of the error observability analysis.

[0031] Figure 6 This is a graph showing the results of the error observability analysis.

[0032] Figure 7 This is a graph showing the results of the error observability analysis.

[0033] Figure 8 This is a graph showing the results of the error observability analysis.

[0034] Figure 9 This is a flowchart of the inertial navigation error observability analysis algorithm based on PWCS.

[0035] Figure 10 This is a flowchart of the optimization process for an inertial navigation calibration system based on observability analysis. Detailed Implementation

[0036] Combination Figure 1 This invention provides a method for quantitative analysis of the observability of errors in inertial navigation systems, comprising the following steps:

[0037] An error model for a composite fiber optic inertial navigation system is established, including basic error terms, higher-order error terms, and axis non-orthogonality error terms for the accelerometer and gyroscope.

[0038] The piecewise time-invariant system theory is used to approximate the time-varying system as a linear time-invariant system in multiple sub-intervals;

[0039] Construct a piecewise observability matrix and calculate the observability metrics of each error parameter through singular value decomposition;

[0040] The calibration trajectory design and filter parameter configuration were optimized based on the observability analysis results.

[0041] Furthermore, the error model includes accelerometer bias, scale coefficient error, installation error, and higher-order nonlinear error terms; gyroscope bias, scale coefficient error, installation error, acceleration-sensitive error, and higher-order angular motion-related error terms; and axis non-orthogonal error terms. The total error parameter dimension can reach 42 to 102 dimensions.

[0042] Furthermore, the application of the piecewise steady-state system theory includes dividing the entire calibration time into multiple sub-intervals, approximating the system state matrix and observation matrix as constant values ​​in each sub-interval, and constructing the overall piecewise observability matrix by splicing the observability matrices of each sub-interval.

[0043] Furthermore, the observability quantification analysis includes performing singular value decomposition on the overall piecewise observability matrix and calculating the ratio of the singular value corresponding to each state component to the maximum singular value as an observability index. This index reflects the coupling strength between each error parameter and the observed quantity and the ease of estimation.

[0044] Furthermore, the segmented motion trajectory design includes a multi-position rotation scheme, comprising at least a four-position basic scheme and a seven-position enhanced scheme. Each position segment is configured with different rotation axis directions, angular velocity magnitudes, and rotation directions, including uniform speed, uniform acceleration, and variable acceleration motion modes.

[0045] Furthermore, the seven-position enhancement scheme adds three coordinate axis pairs coupled positions to the four-position basic scheme, and uses bidirectional rotation to decouple the symmetric and asymmetric components in the scaling factor error.

[0046] Furthermore, the filter parameter optimization includes setting an initial covariance matrix based on the observability of each error parameter, using a smaller initial variance for error parameters with high observability to accelerate convergence, and using a larger initial variance for error parameters with low observability to avoid filter divergence.

[0047] Furthermore, it also includes a simulation experiment verification stage. By setting different rotational angular velocities, angular accelerations, and position schemes, the variation patterns of the rank, condition number, and observability of each error parameter of the system's observability matrix are compared and analyzed to provide guidance for actual calibration experiments.

[0048] The present invention also provides a system for quantitative analysis of the observability of errors in inertial navigation systems, comprising:

[0049] Error modeling module, used to establish a complete error model of the composite fiber optic inertial navigation system;

[0050] The piecewise processing module is used to perform mathematical processing of piecewise time-invariant system theory; the observability analysis module is used to construct the piecewise observability matrix and perform singular value decomposition.

[0051] The trajectory optimization module optimizes the design of the calibration trajectory based on the observability analysis results; the filter configuration module is used to optimize the parameter configuration of the calibration filter.

[0052] Furthermore, the observability analysis module can calculate and display the observability change curves of each error parameter in real time, provide overall indicators such as the rank and condition number of the system observability matrix, and generate an observability analysis report to provide decision support for calibration experiments.

[0053] Based on the differential influence of rotational speed on the observability of various error parameters, a segmented calibration strategy is adopted: zero-bias type error is calibrated in the low-speed rotation stage, installation error type parameters are calibrated in the medium-speed rotation stage, and higher-order error terms are calibrated in the high-speed rotation stage.

[0054] The specific implementation of the bidirectional rotation includes setting two rotation directions, clockwise and counterclockwise, within each position segment, with the rotation speed covering a rotational speed range of 0.5-3 rad / s, and maintaining sufficient stabilization time at each speed point to ensure sufficient excitation of the error parameters.

[0055] This invention addresses the problem of error parameter observability analysis for composite fiber optic inertial navigation systems under dynamic environments, providing a complete system for mathematical modeling, analysis, calculation, and experimental verification.

[0056] 1. Establishment of System Error Model

[0057] The error model of a composite fiber optic inertial navigation system includes an accelerometer assembly error model and a gyroscope drift error model. The error model for the apparent acceleration measurement unit, composed of three quartz accelerometers, is as follows:

[0058]

[0059] In the formula, The measurement error of the quartz accelerometer assembly is expressed in units of 1. ; The zero bias of the j-axis accelerometer is given by units of 0. ; The scale factor error of the j-axis accelerometer is expressed in units of 1. For i-axis accelerometer winding The installation error angle in the positive direction of the axis, in rad; Let be the apparent acceleration along the j-direction of the table coordinate system, in units of . ; The apparent acceleration along the j-direction of the table coordinate system, in units of 1 / ; The error is the asymmetric scaling factor error of the j-axis accelerometer, reflecting the difference between the positive and negative scaling factors of the j-axis accelerometer measurement. This error is determined by... The equivalent values ​​for the positive and negative channels can be calculated separately. Let be the angular velocity of the platform relative to inertial space. For the internal lever arm error of the accelerometer .

[0060] The drift error model for fiber optic gyroscopes is as follows:

[0061]

[0062] In the formula, Let be the angular velocity of the platform relative to inertial space. Due to gyroscope installation error, This is for gyroscope scaling error. The j-axis gyroscope asymmetric scaling factor error reflects the difference between the positive and negative scaling factors measured by the j-axis gyroscope. This refers to platform constant drift.

[0063] For applications under high dynamic conditions, higher-order error terms also need to be considered. Higher-order error models related to linear motion include quadratic, cross-coupling, and cubic terms for accelerometers. Higher-order error models related to angular motion include squared angular velocity terms, angular velocity cross-coupling terms, and angular acceleration error terms for gyroscopes.

[0064] The non-orthogonal error model of the shaft system describes the small-angle error caused by the assembly accuracy of the frame shaft system. In a dual-axis composite inertial measurement system, the direction cosine matrix from the stage coordinate system to the inertial navigation base can be expressed as:

[0065]

[0066] in and The measured value is from the frame angle sensor. and The frame angle is zero bias and the non-orthogonal error angle.

[0067] 2. Application of Piecewise Steady-Invariant System Theory

[0068] To analyze the time-varying characteristics of the composite fiber optic inertial navigation system during rotation modulation, a piecewise steady system theory is employed. The entire calibration time... Divided into Sub-intervals The system state matrix is ​​approximated within each sub-interval. The observation matrix is ​​constant. .

[0069] Within the subinterval, the system's state equation and observation equation can be expressed as:

[0070]

[0071]

[0072] in This is the state vector, containing all the error parameters to be estimated; For control input; For observation vectors; and These are process noise and observation noise, respectively.

[0073] 3. Construction of piecewise observability matrix

[0074] Within each subinterval, the system's observability matrix can be constructed as follows:

[0075]

[0076] Where n is the dimension of the state vector, and the overall piecewise observability matrix is ​​formed by concatenating the observability matrices of each sub-interval:

[0077]

[0078] The observability of a system can be determined by the rank of the overall piecewise observability matrix. When the system is fully observable; when At that time, the system is not fully observable, and the unobservable state subspace has a dimension of . .

[0079] 4. Observable quantification analysis

[0080] To quantify the observability of each state component, singular value decomposition is performed on the overall piecewise observability matrix:

[0081]

[0082] in and It is an orthogonal matrix. It is a singular value matrix and .

[0083] The observability of each state component is defined as follows:

[0084]

[0085] in Observability Reflects the first The coupling strength between a state component and an observation is such that the closer the value is to 1, the stronger the observability of the state component and the easier it is to estimate accurately; the closer the value is to 0, the weaker the observability and the greater the difficulty in estimation. Figure 2 This is a schematic diagram of the observable quantification analysis process.

[0086] 5. Segmented motion trajectory design

[0087] To improve system observability, it is necessary to design suitable segmented motion trajectories. For composite fiber optic inertial navigation systems, multi-position rotation schemes are typically designed, including rotational motion around different coordinate axes and oblique axis coupled motion. Different rotational angular velocities and rotational directions are set within each position segment to fully excite various error parameters.

[0088] A typical four-position scheme includes rotational motions about the X, Y, Z axes, and oblique axis. A more sophisticated seven-position scheme adds three pairs of coupled coordinate axes to the four-position scheme, further improving system observability. Bidirectional rotations can also be set within each position segment to decouple the symmetric and asymmetric components of the scaling factor error.

[0089] The setting of the rotational angular velocity needs to take into account the overload capacity range of the centrifuge. For a centrifuge with a rotation radius of 2.5m, the angular velocity setting range is typically 0.5 rad / s to 3 rad / s, corresponding to an overload range of 0.625g to 22.5g. To excite higher-order error terms, uniform acceleration and variable acceleration motion segments also need to be designed.

[0090] 6. Simulation Experiment and Result Analysis

[0091] The effectiveness of the proposed method was verified through simulation experiments. A composite fiber optic inertial navigation system model containing 42 fundamental error parameters was established, including 18 accelerometer errors and 24 gyroscope errors. Four-position and seven-position rotation schemes were designed, and observability analysis was performed under different rotational speeds.

[0092] Simulation results show that under uniform rotation conditions, the observability matrix rank of the four-position scheme is 12 / 42 (28.6%), meaning that 30 error parameters are unobservable or weakly observable. By introducing uniformly accelerated motion (angular acceleration of 0.01 rad / s²), the observability of the system is significantly improved, with the observability matrix rank reaching 36 / 42 (85.7%).

[0093] The seven-position scheme further improves system observability. Under uniform rotation, the rank of the observability matrix increases to 24 / 42 (57.1%); under uniform acceleration, the system becomes fully observable (rank 42 / 42). Considering bidirectional rotation, the observability of all error parameters is further improved.

[0094] The observability analysis of various error parameters shows that the quadratic error coefficients (k2x, k2y, k2z) of the accelerometer have the strongest observability (close to 100%) at higher speeds, while the accelerometer zero bias (n0x, n0y, n0z) and gyroscope installation errors (rx, ry, rz) have relatively high observability under low-speed conditions. The observability of lever errors (dk1x, dk1y, dk1z) and cross-coupling errors (xy, xz, yz) are significantly affected by the direction of the rotation axis.

[0095] For the complete model containing higher-order error terms (a total of 102 error parameters), 67 parameters (65.7%) are observable under the four-position variable acceleration scheme, and this number increases to 77 parameters (75.5%) under the seven-position variable acceleration scheme. This demonstrates that optimizing the motion trajectory design can significantly improve the observability of complex error models.

[0096] Detailed simulation test data analysis

[0097] (1) Simulation experiment of constant overload condition for the error model of the accelerometer assembly foundation:

[0098] Here are the results of Experiment 1: with a rotational angular velocity of 0.5 rad / s:

[0099] Table 1. Statistics on Error Observability

[0100]

[0101] Figure 3 This is the result of the error observability analysis.

[0102] (2) Simulation test of constant overload condition of basic system model

[0103] The rotational angular velocity is given here as 0.5 rad / s. The results are as follows:

[0104] Table 2. Statistics on Error Observability

[0105]

[0106] Figure 4 This is the result of the error observability analysis.

[0107] (3) Simulation test of system model under variable overload conditions

[0108] The angular acceleration is set here. Experimental results at that time:

[0109] Table 3. Statistics on Error Observability

[0110]

[0111] Figure 5 Error observability analysis results.

[0112] (4) Simulation test on the observability of non-orthogonal error of inertial navigation axis system

[0113] The results of singular value calculation for the observability analysis of nonorthogonal error of the inertial navigation system are as follows:

[0114] Table 4. Calculation results of singular values ​​of non-orthogonal error of shaft system

[0115]

[0116] (5) Simulation test of PWCS observability analysis considering the boundary conditions of the test equipment

[0117] Considering the boundary conditions of the centrifuge equipment, the simulation results of the seven-position scheme based on the basic target model are analyzed in detail.

[0118] Considering the boundary conditions of the centrifuge equipment, the simulation results of the seven-position scheme based on the basic target model are analyzed in detail. In the uniform velocity test group, the angular velocity was set to 2 rad / s, and the results are as follows:

[0119] Table 5. Statistics on Error Observability

[0120]

[0121] Figure 6 This is the result of the error observability analysis.

[0122] In the uniform acceleration test group, the centrifuge angular acceleration was set to 2.6° / s². Under this angular acceleration condition, the maximum overload was 10.2g, the centrifuge radius was 2.5m, and the corresponding angular velocity was approximately 2.02 rad / s. The simulation results are as follows:

[0123] Table 6. Statistics on Error Observability

[0124]

[0125] Figure 7 The results are from the error observability analysis.

[0126] Considering each location, with the centrifuge rotating in both directions, the results are as follows:

[0127] Table 7. Statistics on Error Observability

[0128]

[0129] Figure 8 Error observability analysis results

[0130] (6) Summary of Observability Analysis Simulation Test Results

[0131] Table 8. Statistics on the number of error terms

[0132]

[0133] The complete observability analysis results of typical experiments are summarized in the table below:

[0134] Table 9 Typical experimental results of observability analysis

[0135]

[0136] The simulation results show that, in the simulation experiment of the designed seven-position uniformly accelerated rotation scheme, the observability of different error terms in the calibration target model of the dual-axis composite fiber optic inertial navigation system varies, but all 42 error terms in the inertial navigation system calibration target model have a certain degree of observability. This work is of great significance for further calibration simulation experiments and verification of the error calibration effect.

[0137] Experimental verification and performance evaluation

[0138] The effectiveness of the proposed method was verified on a real centrifuge. Considering the equipment boundary conditions, the maximum angular velocity was set to 3 rad / s (corresponding to an overload of 22.5g), and the maximum angular acceleration was set to 2.6° / s². Uniform velocity and uniform acceleration experiments were conducted, and the output data of the inertial navigation system were collected and observability analysis was performed.

[0139] Experimental results show that under the seven-position uniform acceleration scheme (angular acceleration 2.6° / s²), all 42 error parameters of the basic model have sufficient observability, and the condition number of the observability matrix is ​​reduced from the order of 10^5 under the uniform acceleration condition to the order of 10^3 under the uniform acceleration condition, and the ill-conditioned nature of the system is significantly improved.

[0140] The calibration filter design was optimized based on the observability analysis results. Larger initial variances were used for error parameters with low observability, while smaller initial variances were used for error parameters with high observability. The optimized calibration filter improved convergence speed by approximately 40% and parameter estimation accuracy by approximately 25%.

[0141] Compared to traditional Lie derivative-based methods, the method of this invention improves computational efficiency by two orders of magnitude while maintaining similar analytical accuracy, making it particularly suitable for real-time observability analysis of high-dimensional state systems. Compared to methods based on covariance matrices, this invention does not rely on a filtering convergence process, allowing for pre-analysis of system observability before calibration, thus providing guidance for calibration trajectory optimization.

[0142] The method of this invention has been successfully applied to the calibration of various types of composite fiber optic inertial navigation systems, significantly improving calibration efficiency and accuracy, and providing technical support for long-endurance, high-precision navigation of inertial navigation systems in satellite-denied environments.

[0143] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. The implementation of the method of the present invention mainly includes the steps of establishing a system error model, designing a segmented motion trajectory, constructing a segmented observability matrix, singular value decomposition and observability calculation, result analysis and optimization, etc.

[0144] During the system error model establishment phase, the dimensions and types of the error parameters to be estimated need to be determined based on the specific inertial navigation system type. For the basic model, it typically includes 18 accelerometer errors and 24 gyroscope errors. For high-precision applications, 15 linear motion-related higher-order errors and 27 angular motion-related higher-order errors also need to be considered, bringing the total number of error parameters to 102.

[0145] The segmented motion trajectory design needs to consider the performance limitations of the actual centrifuge equipment. A typical seven-position scheme includes rotational motion around the X, Y, and Z axes, as well as four oblique axes. Different angular velocity curves are set within each position segment, including uniform velocity, uniform acceleration, and variable acceleration segments. To fully excite various error parameters, it is recommended that each position segment include rotational motion in both forward and reverse directions.

[0146] Figure 9 Flowchart of the PWCS-based algorithm for inertial navigation error observability analysis

[0147] The key steps of the algorithm are explained below:

[0148] (1) Input parameter processing

[0149] The input parameter processing stage is the foundation of the entire algorithm, requiring the accurate reception and processing of three key types of parameters. Error model parameters define the error characteristics of the system under analysis, including the accelerometer's zero-bias vector, calibration coefficient error matrix, installation error matrix, and the corresponding error parameters of the gyroscope. Motion trajectory parameters describe the motion state of the carrier during calibration, including the rotation axis direction vector, angular velocity sequence, angular acceleration sequence, and apparent acceleration sequence. The sampling frequency determines the fineness of the time segmentation, directly affecting the accuracy of constructing the segmented observability matrix. These parameters collectively constitute the complete input conditions for observability analysis, and their accuracy and completeness directly determine the reliability of the analysis results.

[0150] (2) Circular processing mechanism

[0151] The loop processing mechanism implements piecewise linearization of the time-varying system. For each segment... The algorithm performs three core computational steps. The state matrix is ​​calculated based on the average motion parameters of the current segment:

[0152]

[0153] in The observation matrix is ​​obtained by averaging the motion data within this segment. Based on the observation type, the structure for the velocity + position observation mode is as follows:

[0154]

[0155] The piecewise observability matrix is ​​constructed using a recursive method:

[0156]

[0157] Among them, the construction depth Based on state dimension Adaptive selection, usually taking To ensure computational efficiency.

[0158] (3) Matrix operations

[0159] The core of matrix operations deals with numerical computation problems involving large-scale matrices. The concatenation of the overall piecewise observability matrices uses a vertical join method:

[0160]

[0161] Matrix dimension is ,in This represents the number of rows in each piecewise observability matrix. Singular value decomposition uses an economical SVD algorithm:

[0162]

[0163] in ,and Observability is calculated through singular value normalization:

[0164]

[0165] System observability assessment is accomplished using the matrix rank and condition number:

[0166]

[0167] Based on tolerance Calculation of the numerical rank;

[0168]

[0169] The condition number reflects the ill-conditioning of the matrix.

[0170] (4) Output results

[0171] The output format provides a complete observability analysis report. Observability vector. Arranged in order of state components, each element The observability of the corresponding error parameters was quantified. Based on engineering experience, observability is divided into three levels: For strongly observable states, the estimation accuracy is high and the convergence is fast; It is in a moderately observable state, requiring a relatively long observation time to make an accurate estimate; This is a weakly observable state, difficult to estimate accurately in practical calibration. The rank of the system observability matrix... It indicates the number of states that can be independently estimated, when The system is fully observable at that time. Condition number. This reflects the stability of numerical computation. This indicates that the system is in a good state. This indicates a moderate pathological condition. This indicates a severe pathological condition, requiring the use of numerical stabilization techniques such as regularization.

[0172] Through rigorous mathematical processing and numerical optimization, this algorithm provides a reliable technical means for the observability analysis of error parameters in composite fiber optic inertial navigation systems, significantly improving the efficiency and success rate of calibration experiments.

[0173] In practical implementation, the following key issues need attention: the segmentation of intervals needs to be sufficiently fine to ensure approximate accuracy, but it should not be too fine to avoid increasing the computational burden. It is generally recommended to divide each rotation cycle into 8-16 segments. Numerical stability issues in singular value decomposition need to be addressed through appropriate regularization methods, especially for systems with high ill-conditioned characteristics.

[0174] Optimizing filter parameters based on observability analysis results is key to improving calibration efficiency. For error parameters with observability higher than 0.8, the initial variance can be set to 1% of the prior variance; for error parameters with observability between 0.3 and 0.8, the initial variance should be set to 10% of the prior variance; and for error parameters with observability lower than 0.3, the initial variance should be set to 50% of the prior variance. This setting ensures both the convergence speed of the filter and avoids filter divergence caused by improper initial variance settings. Figure 10 This is a flowchart of the optimization process for an inertial navigation calibration system based on observability analysis.

[0175] The method of this invention has been verified through practical engineering applications. In the calibration of a certain type of composite fiber optic inertial navigation system, after optimizing the calibration trajectory using the method of this invention, the calibration time was shortened from the traditional 8 hours to 2 hours, and the calibration accuracy was improved by approximately 30%. Especially in the calibration of high-order error parameters, the method of this invention can accurately identify error parameters with low observability, avoiding unnecessary calibration attempts and significantly improving calibration efficiency.

[0176] The above description is only a preferred embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structural or procedural transformations made based on the content of the present invention specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. A method for quantitative analysis of the observability of errors in an inertial navigation system, characterized in that, Includes the following steps: An error model for a composite fiber optic inertial navigation system is established, including basic error terms, higher-order error terms, and axis non-orthogonality error terms for the accelerometer and gyroscope. The piecewise time-invariant system theory is used to approximate the time-varying system as a linear time-invariant system in multiple sub-intervals; Construct a piecewise observability matrix and calculate the observability metrics of each error parameter through singular value decomposition; The calibration trajectory design and filter parameter configuration were optimized based on the observability analysis results.

2. The method for quantitative analysis of the observability of inertial navigation system errors according to claim 1, characterized in that, The error model includes accelerometer bias, scale coefficient error, installation error, and higher-order nonlinear error terms; gyroscope bias, scale coefficient error, installation error, acceleration-sensitive error, and higher-order angular motion-related error terms; and axis non-orthogonal error terms. The total error parameter dimension can reach 42 to 102 dimensions.

3. The method for quantitative analysis of the observability of inertial navigation system errors according to claim 1, characterized in that, The application of the piecewise steady-state system theory includes dividing the entire calibration time into multiple sub-intervals, approximating the system state matrix and observation matrix as constants within each sub-interval, and constructing the overall piecewise observability matrix by splicing the observability matrices of each sub-interval.

4. The method for quantitative analysis of the observability of inertial navigation system errors according to claim 1, characterized in that, The observability quantification analysis includes performing singular value decomposition on the overall piecewise observability matrix and calculating the ratio of the singular value corresponding to each state component to the maximum singular value as an observability index. This index reflects the coupling strength between each error parameter and the observed quantity and the ease of estimation.

5. The method for quantitative analysis of the observability of inertial navigation system errors according to claim 1, characterized in that, The segmented motion trajectory design includes a multi-position rotation scheme, comprising at least a four-position basic scheme and a seven-position enhanced scheme. Each position segment has different rotation axis directions, angular velocity magnitudes, and rotation directions, including uniform speed, uniform acceleration, and variable acceleration motion modes.

6. The method for quantitative analysis of error observability in inertial navigation systems according to claim 5, characterized in that, The seven-position enhancement scheme adds three coordinate axis pairs coupled to the four-position basic scheme, and uses bidirectional rotation to decouple the symmetric and asymmetric components in the scaling factor error.

7. The method for quantitative analysis of error observability in inertial navigation systems according to claim 1, characterized in that, The filter parameter optimization includes setting the initial covariance matrix based on the observability of each error parameter. A smaller initial variance is used for error parameters with high observability to speed up convergence, while a larger initial variance is used for error parameters with low observability to avoid filter divergence.

8. The method for quantitative analysis of error observability of inertial navigation systems according to claim 1, characterized in that, It also includes a simulation experiment verification stage, which compares and analyzes the changes in the rank, condition number, and observability of the system's observability matrix by setting different rotational angular velocities, angular accelerations, and position schemes, providing guidance for actual calibration experiments.

9. A system for quantitative analysis of the observability of errors in an inertial navigation system, characterized in that, include: Error modeling module, used to establish a complete error model of the composite fiber optic inertial navigation system; The piecewise processing module is used to implement the mathematical processing of piecewise steady system theory; The observability analysis module is used to construct a piecewise observability matrix and perform singular value decomposition. The trajectory optimization module optimizes the design of the calibration trajectory based on the observability analysis results. The filter configuration module is used to optimize the parameter configuration of the calibration filter.

10. The inertial navigation system error observability quantification analysis system according to claim 9, characterized in that, The observability analysis module can calculate and display the observability change curves of each error parameter in real time, provide overall indicators such as the rank and condition number of the system observability matrix, and generate an observability analysis report to provide decision support for calibration experiments. Based on the differential influence of rotational speed on the observability of various error parameters, a segmented calibration strategy is adopted: zero-bias type error is calibrated in the low-speed rotation stage, installation error type parameters are calibrated in the medium-speed rotation stage, and higher-order error terms are calibrated in the high-speed rotation stage. The specific implementation of the bidirectional rotation includes setting two rotation directions, clockwise and counterclockwise, within each position segment, with the rotation speed covering a rotational speed range of 0.5-3 rad / s, and maintaining sufficient stabilization time at each speed point to ensure sufficient excitation of the error parameters.

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