WO-2026091186-A1 - NULL-SPACE DIMENSIONALITY-REDUCTION COVARIANCE ESTIMATION METHOD AND SYSTEM FOR HIGH-DIMENSIONAL SEQUENTIAL GRAPH OPTIMIZATION

Abstract

Disclosed in the present invention are a null-space dimensionality-reduction covariance estimation method and system for high-dimensional sequential graph optimization. The null-space dimensionality-reduction covariance estimation method comprises: acquiring measurement data of a sliding window, wherein the measurement data comprises data within the sliding window that is collected by several sensors; establishing a factor graph optimization estimation of the measurement data, wherein the factor graph optimization estimation comprises parameters to be estimated; performing dimensionality-reduction processing on said parameters; and executing a covariance solution on the dimensionality-reduced factor graph optimization estimation. In the present invention, a high-dimensional space is linearized, and a covariance solution problem is mapped to a low-dimensional space by means of solving a null space for high-dimensional parameters, thereby greatly reducing the covariance solution time while ensuring the optimality of covariance estimation.

Inventors

• CHI, Cheng
• HUANG, Ce
• WEN, Xiaohua

Assignees

• 苏州天硕导航科技有限责任公司

Dates

Publication Date

20260507

Application Date

20241115

Priority Date

20241030

Claims (10)

1. A zero-space dimensionality reduction covariance estimation method for high-dimensional sequential graph optimization, characterized in that the zero-space dimensionality reduction covariance estimation method includes: Acquire measurement data of a sliding window, the measurement data including data collected by several sensors within the sliding window; Establish a factor graph optimization estimate of the measurement data, wherein the factor graph optimization estimate includes the parameters to be estimated; The parameters to be estimated are then subjected to dimensionality reduction processing; The covariance of the optimized estimation of the dimensionality-reduced factor graph is solved.
2. The zero-space dimensionality reduction covariance estimation method for high-dimensional sequential graph optimization as described in claim 1 is characterized in that the zero-space dimensionality reduction covariance estimation method includes: Obtain the covariance component to be solved from the parameters to be estimated; The covariance is solved for the part that needs to be solved for.
3. The method for zero-space dimensionality reduction and covariance estimation of high-dimensional sequential graph optimization as described in claim 1 is characterized in that the factor graph optimization estimation is expressed using a nonlinear equation, and the dimensionality reduction processing of the parameters to be estimated includes: The nonlinear equation is linearized using a transformation matrix to obtain a linearized equation. The linearized equation is divided into a covariance part to be solved and a covariance part that does not need to be solved. Obtain the left null space of the transformation matrix corresponding to the covariance component of the solution without requirements; The left null space is used to reduce the dimensionality of the parameters to be estimated in the factor graph optimization estimation.
4. The method for zero-space dimensionality reduction and covariance estimation of high-dimensional sequential graph optimization as described in claim 3 is characterized in that the nonlinear equation is: Where χ represents all parameters to be estimated. χ _p represents the state-updated sensor-related parameters to be estimated at time k ₀, and χ_p represents the state-transferred sensor-related parameters to be estimated. The sensor-related parameters to be estimated are passed to the state at time k0 , and χ_i is used to update the sensor-related parameters to be estimated at time i. Let χ _i-1 be the state-transfer sensor-related parameters to be estimated at time i, χ_i-1 be the state-update sensor-related parameters to be estimated at time i-1, ρ represent the robust kernel function, ρ _m be the robust kernel function for marginalizing parameters, Z be the measurement of the sliding window, z_m be the marginalized pseudo-measurement, zi be the sensor measurement at time i, z _p,i be the measurement from the state-transfer sensor, and zi |i-1 be the parameter transfer model that the state-transfer sensor cannot measure. R represents the covariance of the measurement, used to assign the weight of the measurement in the system within a given sliding window.
5. The zero-space dimensionality reduction covariance estimation method for high-dimensional sequential graph optimization as described in claim 4 is characterized in that the zero-space dimensionality reduction covariance estimation method includes: For a target parameter to be estimated, determine whether there is a state transfer sensor measurement between the target parameters to be estimated. If not, use the dynamic model corresponding to the target parameter to be estimated as the parameter transfer model instead.
6. The method for zero-space dimensionality reduction and covariance estimation of high-dimensional sequential graph optimization as described in claim 4 is characterized in that the formula for solving the covariance of the nonlinear equation parameters is as follows: Where J and R are the global Jacobian matrix and covariance matrix constructed from the Jacobian matrix and covariance matrix of all residuals, and T is the transpose symbol.
7. The method for zero-space dimensionality reduction covariance estimation of high-dimensional sequential graph optimization as described in claim 6 is characterized in that the nonlinear equation is linearized to obtain z = Jχ, where Z is a vector composed of all measurements, χ is a vector composed of all parameters to be estimated, and J is the Jacobian matrix.
8. The method for zero - space dimensionality reduction covariance estimation for high-dimensional sequential graph optimization as described in claim 7 is characterized in that the formula z = Jχ is divided into two parts z = Jaχa + Jbχb , where a is the covariance part to be solved and b is the covariance part that does not need to be solved. Find the left null space of the Jacobian matrix Jb , and use the left null space to obtain L0z = L0Jaχa .
9. The method for zero-space dimensionality reduction covariance estimation of high-dimensional sequential graph optimization as described in claim 8 is characterized in that the covariance of the nonlinear equation parameters is obtained using the formula L _0z = L _0J χ_a .
10. A high-dimensional sequential graph optimization null-space dimension reduction covariance estimation system, the high-dimensional sequential graph optimization null-space dimension reduction covariance estimation system comprising a GNSS receiver, characterized in that the null-space dimension reduction covariance estimation system is used to implement the high-dimensional sequential graph optimization null-space dimension reduction covariance estimation method as described in any one of claims 1 to 9.

Description

A method and system for zero-space dimensionality reduction and covariance estimation of high-dimensional sequential graph optimization Technical Field This invention relates to a method and system for null-space dimensionality reduction covariance estimation in high-dimensional sequential graph optimization. Background Technology In recent years, tilt measurement based on inertial measurement units (INS) has been gradually promoted and applied. By using the inertial orientation and navigation system (INS) built into the GNSS receiver to output the GNSS receiver attitude data in real time, the azimuth angle, tilt angle, and tilt azimuth angle of the centering rod under tilted state can be calculated. Combined with the obtained phase center coordinates of the GNSS receiver antenna, the coordinates of the ground point at the bottom of the tilted centering rod can be calculated. With the development and application of technologies such as high-precision engineering surveying and high-precision navigation, the accuracy consistency and reliability of sensor estimation systems are receiving increasing attention. In this industry, GNSS/INS integrated navigation algorithms, visual VIO algorithms, and LiDAR LIO algorithms, as representative fusion navigation technologies, have been widely used. In recent years, to further improve system reliability, tightly integrating GNSS, INS, visual, and LiDAR sensors has gradually become a mainstream trend. Scientific research and engineering applications have proven that such tightly integrated multi-sensor systems can provide robust pose estimation outputs in complex environments, meeting a wider range of application requirements. Two estimators can be used to solve this multi-sensor fusion problem: the Extended Kalman Filter (EKF) estimator and the Factor Graph Optimization (FGO) estimator. Among them, the FGO estimator, with its superior estimation performance, has gradually become the mainstream. However, for high-dimensional estimation problems such as the aforementioned multi-sensor compact combination problem, it is difficult to estimate the covariance of its parameters using the FGO estimator. In existing technologies, directly estimating the covariance of the FGO estimator is very time-consuming. Therefore, in practical applications, the covariance cannot be estimated directly; instead, it is set empirically, which obviously cannot meet the growing demand for system reliability. Summary of the Invention The technical problem to be solved by this invention is to overcome the shortcomings of existing graph optimization estimators, which take a long time to estimate covariance and cannot estimate its covariance. This invention provides a zero-space dimensionality reduction covariance estimation method and system for high-dimensional sequential graph optimization that significantly reduces the covariance solution time while ensuring the optimality of covariance estimation. The present invention solves the above-mentioned technical problems through the following technical solution: A zero-space dimensionality reduction covariance estimation method for high-dimensional sequential graph optimization is characterized in that the zero-space dimensionality reduction covariance estimation method includes: Acquire measurement data of a sliding window, the measurement data including data collected by several sensors within the sliding window; Establish a factor graph optimization estimate of the measurement data, wherein the factor graph optimization estimate includes the parameters to be estimated; The parameters to be estimated are then subjected to dimensionality reduction processing; The covariance of the optimized estimation of the dimensionality-reduced factor graph is solved. Preferably, the null-space dimensionality reduction covariance estimation method includes: Obtain the covariance component to be solved from the parameters to be estimated; The covariance is solved for the part that needs to be solved for. Preferably, the factor graph optimization estimation is expressed using a nonlinear equation, and the dimensionality reduction processing of the parameters to be estimated includes: The nonlinear equation is linearized using a transformation matrix to obtain a linearized equation. The linearized equation is divided into a covariance part to be solved and a covariance part that does not need to be solved. Obtain the left null space of the transformation matrix corresponding to the covariance component of the solution without requirements; The left null space is used to reduce the dimensionality of the parameters to be estimated in the factor graph optimization estimation. Preferably, the nonlinear equation is: Where χ represents all parameters to be estimated. χ _p represents the state-update sensor-related parameters to be estimated at time k ₀, where χ_p is the state-transferred sensor-related parameter. The sensor-related parameter