CN103245962A - Reconnaissance satellite positioning and estimating method - Google Patents

Abstract

The present invention proposes a reconnaissance satellite positioning estimation method, which uses the Beidou satellite to obtain the initial position and initial velocity of the target reconnaissance satellite at zero time, establishes the simplified motion equation of the target reconnaissance satellite, and converts the simplified motion equation of the target reconnaissance satellite to Decompose and establish a nonlinear differential equation model that can determine the estimated position of the target reconnaissance satellite; solve the established nonlinear differential equation model to obtain the estimated position of the reconnaissance satellite to be observed at each time point, and perform positioning estimation. The present invention can perform more accurate, reliable and autonomous positioning estimation on reconnaissance satellites, and can provide a better information basis for judging and mastering the flight intention, flight state and flight trend of target reconnaissance satellites. The method is simple and practical. Very strong.

Description

A Method for Reconnaissance Satellite Positioning Estimation

technical field

The invention relates to the technical field of satellite positioning, in particular to a reconnaissance satellite positioning estimation method.

Background technique

The Beidou satellite navigation system is a self-developed and independently operated global satellite navigation system that is being implemented in my country. It can provide users with all-weather, all-time high-precision and high-reliability positioning services, and has short message communication functions. The Beidou satellite navigation system consists of three parts: the space terminal, the ground terminal and the user terminal. The Beidou satellite navigation system has great strategic and economic significance for promoting the development of my country's satellite navigation and positioning business and meeting the needs of my country's military and national economy. However, the Beidou satellite navigation system can only perform real-time positioning of the objects to be observed, but cannot estimate the positioning of the time when it does not occur.

Reconnaissance satellites refer to special satellites used to obtain intelligence. Some countries will launch special-purpose reconnaissance satellites, and it is of great strategic significance to implement positioning estimation, monitoring and rapid response to hostile reconnaissance satellites launched by other countries.

The traditional reconnaissance satellite positioning estimation method detects and acquires the initial position and initial velocity of the target reconnaissance satellite at zero time, and generally uses an infrared optical detector to detect and acquire, but only receives the infrared radiation information of the target, which can be oriented but not ranged. , and is susceptible to climate influence and cloud interference, and its reliability is not good enough. In addition, traditional reconnaissance satellite positioning estimation methods still have disadvantages such as the need for coordinate transformation, too many variables to be obtained, complex calculations, and insufficient estimation accuracy.

Contents of the invention

The technical problem to be solved by the present invention is to overcome the deficiencies of the prior art, and propose a reconnaissance satellite positioning estimation method. The method can estimate the positioning of the reconnaissance satellite more accurately, more reliably and more autonomously, and the method is simple and easy to implement, and has strong practicability.

In order to solve the above-mentioned technical problems, the technical solution adopted in the present invention is: a method for reconnaissance satellite positioning estimation, comprising the steps of:

Step A, use the Beidou satellite to obtain the initial position and initial velocity of the target reconnaissance satellite in the basic coordinate system at zero time:

x _c (0)=x ₀ , y _c (0)=y ₀ , z _c (0)=z ₀

${\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 00</span>}}<span\; class="notranslate">\; ,</span>{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 00</span>}}<span\; class="notranslate">\; ,</span>{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; z</span>}}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; 00</span>}}$

表示零时刻侦察卫星在基础坐标系下的初始速度；x₀、y₀、z₀为利用北斗卫星获取的目标侦察卫星在零时刻在基础坐标系下的初始位置值，x₀₀、y₀₀、z₀₀为利用北斗卫星获取的目标侦察卫星在零时刻在基础坐标系下的初始速度值；Among them, x _c (0), y _c (0), z _c (0) represent the initial position of the target reconnaissance satellite in the basic coordinate system at zero time;

Indicates the initial velocity of the reconnaissance satellite in the basic coordinate system at zero time; x ₀ , y ₀ , z ₀ are the initial position values of the target reconnaissance satellite in the basic coordinate system at zero time obtained by the Beidou satellite; x ₀₀ , y ₀₀ , z ₀₀ is the initial velocity value of the target reconnaissance satellite in the basic coordinate system at zero time obtained by the Beidou satellite;

Step B, establish the simplified motion equation of the target reconnaissance satellite in the basic coordinate system:

$\left\{\begin{array}{c}{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span>}{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; r</span>}}}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; f</span>}}}_{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}}{{<span\; class="notranslate">\; |</span>{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; r</span>}}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 3</span>}}}{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; r</span>}}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\sqrt{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}\\ {\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 3.986005</span>}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; 10</span>}}^{\mathrm{<span\; class="notranslate">\; 14</span>}}\end{array}\right.$

为飞行器所受的外力加速度之和，G_m为地球引力常数，

为在基础坐标系下的位置矢量，为

对时间t的二阶导数，即加速度，r_c(t)为

的绝对值，即

x_c(t)、y_c(t)、z_c(t)为t时刻目标侦察卫星在基础坐标系下的位置；in,

is the sum of the accelerations of external forces suffered by the aircraft, G _m is the gravitational constant of the earth,

is the position vector in the base coordinate system, for

The second derivative with respect to time t, namely the acceleration, r _c (t) is

the absolute value of

x _c (t), y _c (t), z _c (t) are the positions of the target reconnaissance satellite in the basic coordinate system at time t;

Step C, decomposing the simplified motion equation of the target reconnaissance satellite into the following equations:

$\left\{\begin{array}{c}{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}}{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 3</span>}}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\\ {\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}}{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 3</span>}}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\\ {\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; z</span>}}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}}{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 3</span>}}}{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\end{array}\right.$

为t时刻目标侦察卫星在基础坐标系下的加速度；in,

is the acceleration of the target reconnaissance satellite in the basic coordinate system at time t;

Step D, combining the equations of the initial position and initial velocity of the target reconnaissance satellite in the basic coordinate system with the decomposed simplified motion equation to establish a nonlinear differential equation model for determining the estimated position of the target reconnaissance satellite:

$\left\{\begin{array}{c}{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}}{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 3</span>}}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\\ {\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}}{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 3</span>}}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\\ {\stackrel{<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; z</span>}}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}}{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 3</span>}}}{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 3.986005</span>}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; 10</span>}}^{\mathrm{<span\; class="notranslate">\; 14</span>}}\\ {\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\sqrt{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}\\ {\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; the\; <figure-callout\; id="0"\; label="y"\; filenames="HDA00003088791900012.png"\; state="\{\{state\}\}">y</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\\ {\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 00</span>}}<span\; class="notranslate">\; ,</span>{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 00</span>}}<span\; class="notranslate">\; ,</span>{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; z</span>}}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; 00</span>}}\end{array}\right.$

Step E, solving the established nonlinear differential equation model to obtain the estimated position of the target reconnaissance satellite in the basic coordinate system at each time point, so as to realize the positioning estimation.

The beneficial effect of the present invention is: the present invention proposes a kind of reconnaissance satellite positioning estimation method, described method utilizes Beidou satellite to obtain the initial position and the initial speed of target reconnaissance satellite at zero time, establishes the simplified motion equation of target reconnaissance satellite, and Decompose the simplified motion equation of the target reconnaissance satellite to establish a nonlinear differential equation model that can determine the estimated position of the target reconnaissance satellite; solve the established nonlinear differential equation model to obtain the estimation of the reconnaissance satellite to be observed at each time point position, for positioning estimation. The present invention can perform more accurate, reliable and autonomous positioning estimation on reconnaissance satellites, and can provide a better information basis for judging and mastering the flight intention, flight state and flight trend of target reconnaissance satellites. The method is simple and practical. Very strong.

Description of drawings

Figure 1 is a schematic diagram of the basic coordinate system established to describe the motion of the reconnaissance satellite.

Fig. 2 is a schematic diagram of trajectory positioning estimation of a target reconnaissance satellite.

Detailed ways

A reconnaissance satellite positioning estimation method of the present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

As shown in Figure 1, in order to describe the movement of the target reconnaissance satellite, it is necessary to establish its basic coordinate system, take the center of the earth _Oc as the origin, the earth’s rotation axis as the z-axis, pointing to the North Pole as the positive direction, and the x-axis from _Oc to zero The 0 longitude line at the moment, and then determine the y-axis according to the right-hand system, so as to establish its basic coordinate system O _c -X _c Y _c Z _c .

The specific embodiment of the present invention provides that the initial position of the known target reconnaissance satellite at time zero is (2043922.166765m, 8186504.631471m, 4343461.714791m) and initial velocity (-5379.544693m/s, -407.095342m/s, 3516.052656m/s ) is a method for estimating the location of reconnaissance satellites, and its specific implementation steps are:

Step A, use the Beidou satellite to obtain the initial position and initial velocity of the target reconnaissance satellite in the basic coordinate system at zero time:

x _c (0)=2043922.166765, y _c (0)=8186504.631471, z _c (0)=4343461.714791

${\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 5379.544693</span>}<span\; class="notranslate">\; ,</span>{\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 407.095342</span>}<span\; class="notranslate">\; ,</span>{\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; z</span>}}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 3516.052656</span>}$

表示零时刻侦察卫星的初始速度；Among them, x _c (0), y _c (0), z _c (0) represent the initial position of the target reconnaissance satellite at zero time;

Indicates the initial velocity of the reconnaissance satellite at zero time;

Step B, establish the simplified motion equation of the target reconnaissance satellite in the basic coordinate system:

$\left\{\begin{array}{c}{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&CenterDot;</span>}{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; r</span>}}}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; f</span>}}}_{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}}{{<span\; class="notranslate">\; |</span>{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; r</span>}}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 3</span>}}}{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; r</span>}}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\sqrt{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}\\ {\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 3.986005</span>}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; 10</span>}}^{\mathrm{<span\; class="notranslate">\; 14</span>}}\end{array}\right.$

为飞行器所受的外力加速度之和，G_m为地球引力常数，

为在基础坐标系下的位置矢量，

为

对时间t的二阶导数，即加速度，r_c(t)为

的绝对值，x_c(t)、y_c(t)、z_c(t)为t时刻目标侦察卫星的位置；in,

is the sum of the accelerations of external forces suffered by the aircraft, G _m is the gravitational constant of the earth,

is the position vector in the base coordinate system,

for

The second derivative with respect to time t, namely the acceleration, r _c (t) is

The absolute value of , x _c (t), y _c (t), z _c (t) is the position of the target reconnaissance satellite at time t;

Step C, decomposing the simplified motion equation of the target reconnaissance satellite into the following equations:

$\left\{\begin{array}{c}{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}}{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 3</span>}}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\\ {\stackrel{<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}}{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 3</span>}}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\\ {\stackrel{<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; z</span>}}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}}{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 3</span>}}}{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\end{array}\right.$

为t时刻目标侦察卫星的加速度，

in,

is the acceleration of the target reconnaissance satellite at time t,

Step D, combining the equations of the initial position and initial velocity of the target reconnaissance satellite with the decomposed simplified motion equation to establish a nonlinear differential equation model capable of determining the estimated position of the target reconnaissance satellite:

$\left\{\begin{array}{c}{\stackrel{<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}}{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 3</span>}}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\\ {\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}}{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 3</span>}}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\\ {\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; z</span>}}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}}{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 3</span>}}}{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 3.986005</span>}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; 10</span>}}^{\mathrm{<span\; class="notranslate">\; 14</span>}}\\ {\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\sqrt{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}\\ {\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 2043922.166765</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 8186504.631471</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 4343461.714791</span>}\\ {\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 5379.544693</span>}<span\; class="notranslate">\; ,</span>{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 407.095342</span>}<span\; class="notranslate">\; ,</span>{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; z</span>}}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 3516.052656</span>}\end{array}\right.$

Step E, use the Simulink toolbox in the MATLAB software to carry out S-function programming, solve the established nonlinear differential equation model, and obtain the estimated position of the target reconnaissance satellite at each time point, such as the three-dimensional position at 50.0s is ( 1.77381×10 ⁶ m, 8.16138×10 ⁶ m, 4.51670×10 ⁶ m), so as to perform position estimation.

Claims (1)

1. A scout satellite positioning estimation method is characterized by comprising the following steps:

step A, acquiring an initial position and an initial speed of a target reconnaissance satellite at zero time under a basic coordinate system by using a Beidou satellite:

x_c(0)=x₀,y_c(0)=y₀,z_c(0)=z₀

${\stackrel{\&CenterDot;}{x}}_c\left(0\right)=x_{00},{\stackrel{\&CenterDot;}{y}}_c\left(0\right)=y_{00},{\stackrel{\&CenterDot;}{z}}_c\left(0\right)=z_{00}$

wherein x is_c(0)、y_c(0)、z_c(0) Representing the initial position of the target reconnaissance satellite at zero time under a basic coordinate system;

representing the initial speed of the reconnaissance satellite at zero time under a basic coordinate system; x is the number of₀、y₀、z₀The initial position value x of the target reconnaissance satellite acquired by the Beidou satellite in the basic coordinate system at zero time₀₀、y₀₀、z₀₀The method comprises the following steps of obtaining an initial speed value of a target reconnaissance satellite in a basic coordinate system at zero time by using a Beidou satellite;

and B, establishing a simplified motion equation of the target reconnaissance satellite in a basic coordinate system:

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;\&CenterDot;}{\stackrel{\&RightArrow;}{r}}}_c\left(t\right)={\stackrel{\&RightArrow;}{F}}_e=-\frac{G_m}{{\left|{\stackrel{\&RightArrow;}{r}}_c\left(t\right)\right|}^3}{\stackrel{\&RightArrow;}{r}}_c\left(t\right)\\ r_c\left(t\right)=\sqrt{x_c^2\left(t\right)+y_c^2\left(t\right)+z_c^2\left(t\right)}\\ G_m=3.986005\&times;{10}^{14}\end{array}\right.$

wherein,

is the sum of the external accelerations to which the aircraft is subjected, G_mIs a constant of the gravity of the earth,

for the position vector in the base coordinate system,

is composed of

Second derivative with respect to time t, i.e. acceleration, r_c(t) is

Absolute value of, i.e.

x_c(t)、y_c(t)、z_c(t) the position of the target reconnaissance satellite in the basic coordinate system at the moment t;

and C, decomposing the simplified motion equation of the target reconnaissance satellite into the following equation sets:

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;\&CenterDot;}{x}}_c\left(t\right)=-\frac{G_m}{r_c{\left(t\right)}^3}{x}_c\left(t\right)\\ {\stackrel{\&CenterDot;\&CenterDot;}{y}}_c\left(t\right)=-\frac{G_m}{r_c{\left(t\right)}^3}{y}_c\left(t\right)\\ {\stackrel{\&CenterDot;\&CenterDot;}{z}}_c\left(t\right)=-\frac{G_m}{r_c{\left(t\right)}^3}{z}_c\left(t\right)\end{array}\right.$

wherein,

detecting the acceleration of the satellite under the basic coordinate system for the target at the time t;

step D, combining the equation of the initial position and the initial velocity of the target scout satellite with the decomposed simplified motion equation, and establishing a nonlinear differential equation model for determining the estimated position of the target scout satellite:

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;\&CenterDot;}{x}}_c\left(t\right)=-\frac{G_m}{r_c{\left(t\right)}^3}{x}_c\left(t\right)\\ {\stackrel{\&CenterDot;\&CenterDot;}{y}}_c\left(t\right)=-\frac{G_m}{r_c{\left(t\right)}^3}{y}_c\left(t\right)\\ {\stackrel{\&CenterDot;\&CenterDot;}{z}}_c\left(t\right)=-\frac{G_m}{r_c{\left(t\right)}^3}{z}_c\left(t\right)\\ G_m=3.986005\&times;{10}^{14}\\ r_c\left(t\right)=\sqrt{x_c^2\left(t\right)+y_c^2\left(t\right)+z_c^2\left(t\right)}\\ x_c\left(0\right)=x_0,y_c\left(0\right)=y_0,z_c\left(0\right)=z_0\\ {\stackrel{\&CenterDot;}{x}}_c\left(0\right)=x_{00},{\stackrel{\&CenterDot;}{y}}_c\left(0\right)=y_{00},{\stackrel{\&CenterDot;}{z}}_c\left(0\right)=z_{00}\end{array}\right.$

and E, solving the established nonlinear differential equation model to obtain the estimated position of the target reconnaissance satellite in the basic coordinate system at each time point, thereby realizing positioning estimation.

Images