Manifold based non-linear space object motion state determination method

Abstract

The invention provides a manifold based non-linear space object motion state determination method comprising the following steps: building a space object locus observation equation; using manifold as the basic space and employing a multiple dimensioned analysis manifold method to carry out multiple dimensioned expressions of object state parameters on the manifold according to physics characteristics of the object locus embedded in a low dimension manifold in the space, thus obtaining a multiple dimensioned expression coefficient; using a non-linear iteration method to obtain a manifold multiple dimensioned expression coefficient according to the observation equation and a multiple dimensioned expression formula, thus obtaining an object state parameter estimating value. The novel method can simplify an object state parameter resolving process, thus improving resolving precision; in addition, the method is universal and suitable for high precision estimating problems of motion states of various space objects under various measuring systems in the spaceflight field.

Description

technical field

[0001] The invention belongs to the problem of high-precision estimation of the state of a space target, and relates to a method for determining the motion state of a nonlinear space target based on a manifold, that is, using the distance, azimuth, pitch angle or distance (sum / difference) change rate of the space target and other measurement element information, through the trajectory calculation process on the manifold, the high-precision estimation of the target position and velocity is obtained, which is suitable for high-precision post-processing of measurement data in aerospace measurement and control systems and other technical fields. Background technique

[0002] In the traditional high-precision data processing of aircraft measurement data, the spline constraint solution method is used, that is, the flight trajectory is expressed by the spline function, and the direct estimation of the position and velocity is converted into the estimation of the spli...

Examples

Embodiment Construction

[0063] Generally speaking, the trajectory of the target is a spatial curve, and the entire trajectory is not estimated to be in a plane, so it needs to be projected to a tangent plane in a certain local area to obtain the projected plane curve. Such as figure 1 As shown, specifically: Map some points on a certain part of the space curve to the tangent space to get And there is a set of basis for the vector space (e j ), then there exists (τ 1 ,…,τ d ), such that Using polynomial interpolation or multi-point value averaging (see below) in the multi-scale analysis method on the manifold to obtain the interpolation of the midpoint of each coordinate, and obtain the representation in the tangent space by inverse mapping Get the representation in the manifold.

[0064] The multi-scale representation of the curve in the plane is to take advantage of its smoothness, first perform low-density sampling, and then calculate the "wavelet" coefficients in the process of gradual r...

technical field

[0001] The invention belongs to the problem of high-precision estimation of the state of a space target, and relates to a method for determining the motion state of a nonlinear space target based on a manifold, that is, using the distance, azimuth, pitch angle or distance (sum / difference) change rate of the space target and other measurement element information, through the trajectory calculation process on the manifold, the high-precision estimation of the target position and velocity is obtained, which is suitable for high-precision post-processing of measurement data in aerospace measurement and control systems and other technical fields. Background technique

[0002] In the traditional high-precision data processing of aircraft measurement data, the spline constraint solution method is used, that is, the flight trajectory is expressed by the spline function, and the direct estimation of the position and velocity is converted into the estimation of the spli...

Examples

Embodiment Construction

[0063] Generally speaking, the trajectory of the target is a spatial curve, and the entire trajectory is not estimated to be in a plane, so it needs to be projected to a tangent plane in a certain local area to obtain the projected plane curve. Such as figure 1 As shown, specifically: Map some points on a certain part of the space curve to the tangent space to get And there is a set of basis for the vector space (e j ), then there exists (τ 1 ,…,τ d ), such that Using polynomial interpolation or multi-point value averaging (see below) in the multi-scale analysis method on the manifold to obtain the interpolation of the midpoint of each coordinate, and obtain the representation in the tangent space by inverse mapping Get the representation in the manifold.

[0064] The multi-scale representation of the curve in the plane is to take advantage of its smoothness, first perform low-density sampling, and then calculate the "wavelet" coefficients in the process of gradual r...

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