CN106885577A - Lagrangian aeronautical satellite autonomous orbit determination method - Google Patents

Abstract

The invention discloses a method for autonomous orbit determination of a Lagrangian navigation satellite, comprising the following steps: obtaining three groups of inter-satellite ranging information through a navigation constellation containing at least four satellites; using the inter-satellite ranging information to update neural network weights ; Estimate the nonlinear perturbation item according to the above neural network weights; use the nonlinear perturbation item obtained above to construct a neural network state observer, and estimate the orbit information of the Lagrangian satellite. The present invention is based on the ellipse-shaped restrictive three-body problem, accurately estimates the perturbation force of the Lagrange navigation satellite through the neural network, improves the model accuracy of orbit determination, and uses the state observer to analyze the Lagrangian navigation satellite. The state is accurately estimated without any restrictions on system noise and observation noise, and has good versatility.

Description

Lagrangian Navigation Satellite Autonomous Orbit Determination Method

technical field

The invention belongs to the technical field of positioning, navigation and control, and specifically refers to a method for autonomous orbit determination of a Lagrangian navigation satellite based on a neural network state observer.

Background technique

Deep space exploration is currently a research hotspot in the aerospace field. Since deep space probes are far away from the earth, it is difficult to rely on ground station navigation to meet the real-time and high precision requirements of deep space probes. The special dynamic properties of the Lagrangian points of the Earth-Moon system determine that the deployment of navigation satellite constellations at Lagrangian points can provide powerful navigation support for deep space exploration. The prerequisite for Lagrangian navigation satellite constellation to provide accurate navigation information is that Lagrangian navigation satellite itself can achieve precise orbit determination.

At present, the research on the technology of autonomous orbit determination of Lagrangian navigation satellites is mainly based on the circular restricted three-body problem, and combined with filtering algorithms to realize the estimation of Lagrangian navigation satellite orbits. The circular restricted three-body problem is an approximate model that completely ignores the eccentricity of the moon's orbit around the earth and the perturbation effect of the gravitational force of the sun and other large planets on the Lagrangian navigation satellite. The simplification of the dynamic model will inevitably affect the accuracy of the autonomous orbit determination of Lagrangian navigation satellites. In addition, the current filtering algorithms all assume the types of system noise and observation noise, which also limits the application range of filtering algorithms.

Contents of the invention

At the problems referred to above, the object of the present invention is to provide a kind of Lagrangian navigation satellite autonomous orbit determination method, by improving the precision of Lagrangian navigation satellite dynamics model, utilize state observer to Lagrangian navigation satellite The state is estimated in real time, and then the high-precision autonomous orbit determination of Lagrangian navigation satellites is realized.

In order to achieve the above object, a kind of Lagrangian navigation satellite autonomous orbit determination method of the present invention comprises steps as follows:

Obtain three sets of inter-satellite ranging information through a navigation constellation containing at least four satellites;

Utilize inter-satellite ranging information to update neural network weights;

Estimate the nonlinear perturbation term according to the above neural network weights;

The neural network state observer is constructed by using the nonlinear perturbation term obtained above, and the orbit information of the Lagrangian satellite is estimated.

Preferably, the neural network weight estimation update law is designed as:

In the formula, is a known bounded basis vector, is the observation residual, is the estimated state, and σ is the correction coefficient.

Preferably, the observer is designed as follows:

Among them, K is a user-defined gain matrix, v(f) is a robust term, is the estimated vector of the nonlinear perturbation term, calculated as follows:

In the formula, is the estimated value of neural network weights, is a known bounded basis vector, D and ε _max are positive scalars.

Beneficial effects of the present invention:

The present invention realizes the autonomous orbit determination of Lagrangian navigation satellites by designing a neural network state observer, uses the neural network to approach all the perturbation forces received by the Lagrangian navigation satellites, improves the model accuracy of autonomous orbit determination, and utilizes state observation The device can accurately estimate the state of Lagrangian navigation satellites, without any restrictions on system noise and observation noise, and has good versatility. At present, the research on the autonomous orbit determination technology of Lagrangian navigation satellites is mainly based on the circular restricted three-body problem, completely ignoring the eccentricity of the moon's orbit around the earth and the impact of large planets such as the sun on Lagrangian navigation satellites. The perturbing effects of gravity.

The invention directly estimates the state of the Lagrangian navigation satellite by only using the inter-satellite ranging information through the neural network state observer, has simple measuring means and high orbit determination precision.

Description of drawings

Figure 1a is a schematic diagram of the X-axis of the satellite 1 orbit determination error curve.

Fig. 1b is a schematic diagram of the Y-axis of the satellite 1 orbit determination error curve.

Fig. 1c is a schematic diagram of the Z-axis of the satellite 1 orbit determination error curve.

Fig. 2a is a schematic diagram of the X-axis of the satellite 2 orbit determination error curve.

Fig. 2b is a schematic diagram of the Y-axis of the satellite 2 orbit determination error curve.

Fig. 2c is a schematic diagram of the Z-axis of the satellite 2 orbit determination error curve.

Fig. 3a is a schematic diagram of the X-axis of satellite 1 perturbation acceleration estimation.

Fig. 3b is a schematic diagram of the Y-axis of satellite 1 perturbation acceleration estimation.

Fig. 3c is a schematic diagram of Z-axis for satellite 1 perturbation acceleration estimation.

Fig. 4a is a schematic diagram of the X-axis of satellite 2 perturbation acceleration estimation.

Fig. 4b is a schematic diagram of the Y-axis of satellite 2 perturbation acceleration estimation.

Fig. 4c is a schematic diagram of Z-axis estimation of satellite 2 perturbation acceleration.

Fig. 5 is a schematic flow chart of the orbit determination method.

detailed description

In order to facilitate the understanding of those skilled in the art, the present invention will be further described below in conjunction with the embodiments and accompanying drawings, and the contents mentioned in the embodiments are not intended to limit the present invention.

With reference to shown in Fig. 5, a kind of Lagrangian navigation satellite autonomous orbit determination method of the present invention comprises steps as follows:

Obtain three sets of inter-satellite ranging information through a navigation constellation containing at least four satellites;

Utilize inter-satellite ranging information to update neural network weights;

Estimate the nonlinear perturbation term according to the above neural network weights;

The neural network state observer is constructed by using the nonlinear perturbation term obtained above, and the orbit information of the Lagrangian satellite is estimated.

In the embodiment, a dynamic model is established based on the elliptical restricted three-body problem and _a perturbation term is added; under the elliptical restricted three _- body problem model, the spacecraft is linearized in the L1 or L2 central rendezvous coordinate system The kinetic equation for is as follows:

define a new state vector

Then formula (1) can be written in the following form:

in,

In addition to the gravitational force from the two main celestial bodies, the spacecraft is also affected by other perturbations. When these perturbations are taken into account, the formula (1) will become as follows:

in,

represents the nonlinear perturbed acceleration in the directions of the three coordinate axes, and

In this embodiment, the observations are ranging information between satellites, and the relationship between the observations and the state variables is:

Where [xyz] ^T and [x ₂ y ₂ z ₂ ] ^T are the coordinates of satellite 1 and satellite 2 in the L ₁ or L ₂ center rendezvous coordinate system, respectively.

Equation (9) carries out Taylor series expansion near the estimated state, ignoring higher-order terms, and the linear relationship between the observed quantity and the state can be obtained:

Define the state estimation error as:

Define the observation residuals as:

and then get:

in,

Usually only the estimated value of the position state of satellite 2 can be obtained, so the matrix C is often calculated by the following formula:

In the present invention, three groups of ranging information are needed to realize Lagrangian satellite orbit determination, that is, the navigation constellation needs to include four satellites; at this time, the C matrix is re-expressed as the following formula:

in, with are the estimated positions of satellite 3 and satellite 4, respectively.

In order to estimate the state of Lagrangian satellites only by using inter-satellite ranging observations, the observer is designed as follows:

where K is a user-defined gain matrix, v(f) is a robust term, is the estimated vector of the nonlinear perturbation term, calculated as follows:

In the formula, is the estimated value of neural network weights, is a known bounded basis vector, D and ε _max are positive scalars.

In order to ensure the stability of the estimation error, the above neural network weight estimation update law is designed as:

In the formula, is a known bounded basis vector, is the observation residual, is the estimated state, and σ is the correction coefficient.

Figures 1a-1c and Figures 2a-2c are respectively the orbit determination position error curves of Lagrangian satellite 1 and satellite 2 on each coordinate axis in the experiment. It can be seen from the figure that the neural network state observer can perform well Realize that Lagrangian satellites only use inter-satellite ranging for autonomous orbit determination.

Figures 3a-3c and Figures 4a-4c are the perturbation acceleration estimates of satellite 1 and satellite 2 on each coordinate axis in the experiment, respectively. It can be seen that the neural network can estimate the perturbation force very well.

There are many specific application approaches of the present invention, and the above description is only a preferred embodiment of the present invention. It should be pointed out that for those of ordinary skill in the art, some improvements can also be made without departing from the principles of the present invention. Improvements should also be regarded as the protection scope of the present invention.

Claims (3)

1. An autonomous orbit determination method for a Lagrange navigation satellite is characterized by comprising the following steps:

obtaining three groups of inter-satellite ranging information through a navigation constellation at least comprising four satellites;

updating the weight of the neural network by using the inter-satellite ranging information;

estimating a nonlinear perturbation item according to the weight of the neural network;

and constructing a neural network state observer by using the obtained nonlinear perturbation term, and estimating the orbit information of the Lagrange satellite.

2. The autonomous orbit determination method of the lagrangian navigation satellite according to claim 1, wherein the neural network weight estimation update law is designed as:

$\stackrel{\·}{\hat{W}}=F\left(\mathrm{\φ}\right(\widehat{\stackrel{\‾}{X}}){\tilde{Y}}^T-\mathrm{\σ}\hat{W})$

in the formula,for a known bounded basis vector to be,in order to observe the residual error,to estimate the state, σ is a correction coefficient.

3. The autonomous orbit determination method for Lagrangian navigation satellites according to claim 1, characterized in that the observer is designed as follows:

$\stackrel{\·}{\widehat{\stackrel{\‾}{X}}}=A\widehat{\stackrel{\‾}{X}}+B\[\hat{g}\left(\widehat{\stackrel{\‾}{X}}\right)-v\left(f\right)\]+K(\stackrel{\‾}{Y}-\widehat{\stackrel{\‾}{Y}})$

where K is a user-defined gain matrix, v (f) is a robust term,for the estimated vector of the non-linear perturbation term, the calculation is as follows:

$\hat{g}\left(\widehat{\stackrel{\‾}{X}}\right)={\hat{W}}^T\mathrm{\φ}\left(\widehat{\stackrel{\‾}{X}}\right)$

$v\left(f\right)=-D\frac{\tilde{Y}}{\left|\right|\tilde{Y}\left|\right|}-{\mathrm{\ϵ}}_{max}\tilde{Y}$

in the formula,is an estimate of the weights of the neural network,for a known bounded basis vector to be,d and_maxis a positive scalar.