CN105203111B - A kind of martian atmosphere approach section Combinated navigation method of dynamic pressure auxiliary - Google Patents

A kind of martian atmosphere approach section Combinated navigation method of dynamic pressure auxiliary Download PDF

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CN105203111B
CN105203111B CN201510580209.4A CN201510580209A CN105203111B CN 105203111 B CN105203111 B CN 105203111B CN 201510580209 A CN201510580209 A CN 201510580209A CN 105203111 B CN105203111 B CN 105203111B
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mrow
msub
detector
density
dynamic pressure
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CN105203111A (en
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崔平远
邓剑峰
高艾
朱圣英
徐瑞
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Beijing Institute of Technology BIT
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/24—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 specially adapted for cosmonautical navigation

Abstract

A kind of martian atmosphere approach section Combinated navigation method of dynamic pressure auxiliary disclosed by the invention, is related to martian atmosphere approach section Combinated navigation method, belongs to field of deep space exploration.The present invention establishes the plasma density that plasma model estimates detector stationary point in real time on the basis of position recursion air navigation aid of navigating.When density is less than communication critical electron density, the state estimation deviation of detector is modified by measuring the relative distance information between detector and radio beacon；When density is more than communication critical electron density, the dynamic pressure value that the 3-axis acceleration and Mars of Inertial Measurement Unit output obtain into air data system measurement is considered as externally measured, and the state of detector is estimated with reference to non-linear filtering method, improve air approach section air navigation aid reliability and precision of state estimation.The present invention can effectively suppress the problem that diverging when Radio Measurement is interrupted for a long time using the state estimation deviation of single boat position recursion air navigation aid detector be present.

Description

A kind of martian atmosphere approach section Combinated navigation method of dynamic pressure auxiliary
Technical field
The present invention relates to a kind of martian atmosphere approach section Combinated navigation method, more particularly to a kind of Mars of dynamic pressure auxiliary are big Gas approach section Combinated navigation method, belongs to field of deep space exploration.
Background technology
Following Mars sampling return and manned mars exploration mission requirements detector have the ability of accuracy, pinpoint Lu Yaoqiu carries out accurate Navigation, Guidance and Control in air approach section to detector, it is ensured that detector can accurately reach pre- and open Umbrella point.Accurately determine that the status information of detector is the precondition of accuracy detection in martian atmosphere approach section.
In the mars exploration task that success was landed in the past, martian atmosphere approach section all uses and is based on Inertial Measurement Unit Boat position recursion (Dead Reckoning, DR) air navigation aid of (Inertial Measurement Unit, IMU) output.Due to Boat position recursion air navigation aid can not be modified to original state deviation, and be difficult to elimination sensor system deviation and state is estimated The influence of precision is counted, causes state estimation deviation to be dissipated with the time, it is difficult to meet the navigation accuracy demand of following accuracy.And It is currently based in radio and the Combinated navigation method of Inertial Measurement Unit output, because radio signal is quick to external environment Sense, especially at hypersonic section, detector can cause surrounding air to ionize with Aerodynamic Heating caused by martian atmosphere severe friction.Deng Plasma density exceedes can cause radio communication to be interrupted corresponding to radio-communication frequencies during critical electron density, produce communication " black barrier ".Prolonged communication " black barrier " can cause approach section state estimation deviation to be dissipated with the time.
By the plasma density around the online detector of estimation in real time, the navigation of martian atmosphere approach section is divided into communication Normal and communication " black barrier " two parts.When plasma density is less than radio communication critical electron density, radio communication is just Often, by measuring the relative distance between detector and radio beacon, the state of detector can be estimated；Work as plasma When density is higher than radio communication critical electron density, radio communication " black barrier ", (Dynamic aided in using dynamic pressure Pressure Measurement Aid, DA) air navigation aid, stationary point dynamic pressure measurement value and Inertial Measurement Unit 3-axis acceleration Information is considered as externally measured, and the state of detector is estimated.
The content of the invention
It is " black that the Combinated navigation method exported for current radio and Inertial Measurement Unit there may be radio communication Diverging problem be present using the state estimation deviation of single boat position recursion air navigation aid detector in barrier ", and " black barrier " section.The present invention A kind of martian atmosphere approach section Combinated navigation method technical problems to be solved of disclosed dynamic pressure auxiliary are that solve existing combination Above-mentioned technical barrier present in air navigation aid, and then improve the reliability and state estimation of martian atmosphere approach section air navigation aid Precision.
The purpose of the present invention is achieved through the following technical solutions：
The martian atmosphere approach section Combinated navigation method of a kind of dynamic pressure auxiliary disclosed by the invention, in boat position recursion navigation side On the basis of method, the plasma density in detector stationary point is estimated by the plasma model of foundation in real time, according to online real-time The plasma density for estimating to obtain independently switches air navigation aid.When plasma density is less than communication critical electron density, When i.e. radio communication is normal, using radio and the Combinated navigation method of Inertial Measurement Unit output, by measuring detector Relative distance information between radio beacon is modified to the state estimation deviation of detector；When plasma density is more than During radio communication critical electron density, that is, communicate " black barrier " when, using dynamic pressure aid in air navigation aid, Inertial Measurement Unit The 3-axis acceleration and Mars of output enter the obtained dynamic pressure value of air data system measurement and are considered as externally measured, and combine non-thread Property filtering method the state of detector is estimated, and then improve martian atmosphere approach section air navigation aid reliability and state Estimated accuracy.
A kind of martian atmosphere approach section Combinated navigation method of dynamic pressure auxiliary disclosed by the invention, can effectively suppress wireless The problem of diverging when electrical measurement is interrupted for a long time using the state estimation deviation of single boat position recursion air navigation aid detector be present, It ensure that the reliability and precision of state estimation of air navigation aid.
Described non-linear filtering method uses EKF (Extend Kalman Filter, EKF), no mark Kalman filtering (Unscented Kalman Filter, UKF) algorithm.
A kind of martian atmosphere approach section Combinated navigation method of dynamic pressure auxiliary disclosed by the invention, comprises the following steps：
Step 1：Plasma density model is established, estimates the plasma density in detector stationary point in real time.
Enter hypersonic section in martian atmosphere, detector can cause to visit with Aerodynamic Heating caused by martian atmosphere severe friction The air ionization surveyed around device produces plasma, and the radio-communication frequencies that detector is exceeded when the density of plasma is corresponding Critical electron density when, radio communication can be caused to interrupt, produce communication " black barrier ".Therefore, detector week is estimated in real time The plasma density enclosed is the precondition that dynamic pressure auxiliary navigation method independently switches.Plasma density around detector Mainly determined by the relatively areographic speed of detector and martian atmosphere density, detector stationary point etc. is obtained by formula (1) The estimate of ion concentration：
ne=c ρaVb(1) wherein, a, b, c are model coefficient, and V is that detector is relative to areographic speed, unit Km/s, ρ are martian atmosphere density, it is assumed that martian atmosphere density p exponentially formal distribution, are calculated by formula (2)：
Wherein, ρ0=2e-4kg/m3Represent martian atmosphere reference density, r0=3,437,200m represent reference altitude, hs= 7500m martian atmosphere absolute altitudes.
Step 2：Plasma density model according to step 1 can estimate the plasma around detector in real time Density.When plasma density is less than critical electron density corresponding to detector radio-communication frequencies, radio communication is normal, The Combinated navigation method that system is exported using radio and inertia measurement, when plasma density is more than the critical electricity of radio communication During sub- density, radio communication " black barrier ", detector uses the air navigation aid of dynamic pressure auxiliary.Described dynamic pressure measurement auxiliary is led Boat method refers to the stationary point dynamic pressure value that Mars is obtained into air data system measurement and three axles of Inertial Measurement Unit output add Velocity amplitude is considered as externally measured, and the state of detector is estimated by nonlinear filtering algorithm.According to radionavigation side Method or dynamic pressure Assisted Combinatorial air navigation aid establish corresponding Radio Measurement model and dynamic pressure measurement model respectively.
When plasma density is less than communication critical electron density, radio communication is normal, by measuring detector and nothing Relative distance between line telecommunications mark is modified to the state deviation of detector.
Depending on navigation accuracy needs, radio beacon is more for described aerogram target quantity and position, measurement Information is abundanter, and navigation accuracy is higher.Assuming that detector has three beacons in visible range during entrance：One track Device and two martian surface beacons.Aerogram target position is accurately surveyed before detector enters martian atmosphere by ground Deep Space Network It is fixed.The distance between detector and i-th beacon are calculated by formula (3)：
Wherein, r, riDetector and the i-th position vector of (i=1,2, the 3) beacon under Mars inertial system are represented respectively, εRiRepresent Radio Measurement noise, Gaussian distributed.
When plasma density is more than radio communication critical electron density, radio communication " black barrier ", detector leads to Cross the 3-axis acceleration value of inertia measurement output and Mars enters detector stationary point in air data system acquisition flight course and moved Pressure value, the state of detector is estimated by non-linear estimation algorithm.The measurement mould of the air navigation aid of described dynamic pressure measurement auxiliary Type is established such as formula (4)：
Wherein, εDARepresent measurement noise, Gaussian distributed；A represents detector 3-axis acceleration value, is determined by formula (5)：
q∞Detector stationary point dynamic pressure value is represented, is determined by formula (6)：
Wherein,Represent expression of the velocity coordinate system unit vector under Mars inertial system；σ represents tilt Angle, it is system control variables, it is assumed that angle of heel σ is constant value；D, L represents resistance acceleration and lift acceleration, is determined by formula (7)：
Wherein, CD, CLThe resistance coefficient and lift coefficient of detector are represented, S represents detector area of reference, and m represents detection Device quality, parameter CD, CL, S, m are considered as constant value.
The definition of the axle of velocity coordinate system three is determined by formula (8) and formula (9)：
Wherein,For the relatively areographic speed of detector, Ω=[0,0,7.095e-5]Trad/s Represent expression of the Mars spin velocity under Mars inertial system.
Then the measurement model of whole air navigation aid is as follows：
When plasma density is less than radio communication critical electron density, that is, when communicating normal：
When plasma density is more than radio communication critical electron density, that is, communicate " black barrier " when：
The plasma density that martian atmosphere approach section navigation system is estimated to obtain online in real time according to system independently switches Air navigation aid, it is ensured that the metrical information that martian atmosphere approach section navigation system can obtain during entrance maximizes.
Step 3：The plasma density model obtained according to step 1, and the Radio Measurement model established of step 2 and dynamic Measurement model is pressed, the state of detector is estimated by nonlinear filtering algorithm, and then improves martian atmosphere approach section and leads The reliability and precision of state estimation of boat system.
Beneficial effect：
1st, the martian atmosphere approach section Combinated navigation method of a kind of dynamic pressure auxiliary disclosed by the invention, can estimate to visit in real time Device stationary point plasma density is surveyed, it is autonomous by contrasting stationary point plasma density and the size of radio communication critical electron density Switch radionavigation and dynamic pressure auxiliary navigation method.
2nd, the martian atmosphere approach section Combinated navigation method of a kind of dynamic pressure auxiliary disclosed by the invention, by increasing capacitance it is possible to increase when wait from Martian atmosphere approach section metrical information when daughter density is more than radio communication critical electron density, suppress single boat position recursion and lead There is diverging in the state estimation deviation of boat method detector, the reliability and state for improving martian atmosphere approach section air navigation aid are estimated Count precision.
3rd, the martian atmosphere approach section Combinated navigation method of a kind of dynamic pressure auxiliary disclosed by the invention, using nonlinear filtering Algorithm, martian atmosphere approach section navigation data computing speed can be improved, meet following martian atmosphere approach section navigation real-time Demand.
Brief description of the drawings
Fig. 1 is dynamic pressure measurement assisting navigation schematic diagram；
Fig. 2 is martian atmosphere approach section navigation calculation flow chart；
Fig. 3 I-VI represent what the integrated navigation that dynamic pressure measurement aids in exported with conventional wireless electricity and Inertial Measurement Unit respectively Integrated navigation position, speed, flight-path angle, azimuth, longitude and latitude estimated bias comparison diagram.Solid line signified symbol a in figure Represent the state estimation deviation that Combinated navigation method of the present invention obtains；Dotted line signified symbol b represents conventional wireless electricity and inertia The state deviation of the integrated navigation of measuring unit output；Dotted line signified symbol c represents state estimation 3sigma curves of the present invention, Dotted line signified symbol d represents that the integrated navigation state estimation 3sigma of conventional wireless electricity and Inertial Measurement Unit output is bent Line.
Embodiment
In order to better illustrate objects and advantages of the present invention, present disclosure is done with example below in conjunction with the accompanying drawings into One step explanation.
This example is directed to the Combinated navigation method of martian atmosphere approach section dynamic pressure measurement auxiliary, when plasma density is less than During radio communication critical electron density formula, radio communication is normal, and detector is exported using radio and Inertial Measurement Unit Combinated navigation method；When plasma density is more than radio communication critical electron density, radio communication " black barrier ", use The Combinated navigation method of dynamic pressure auxiliary.And the state of detector is resolved using EKF wave filters, add Radio Measurement The reliability and precision of state estimation of navigation system when interrupting for a long time.The specific implementation method of this example is as follows：
Step 1：Plasma density model is established, estimates the plasma density in detector stationary point in real time.
Enter hypersonic section in martian atmosphere, detector can cause to visit with Aerodynamic Heating caused by martian atmosphere severe friction The air ionization surveyed around device produces plasma, and the radio-communication frequencies that detector is exceeded when the density of plasma is corresponding Critical electron density when, radio communication can be caused to interrupt, produce communication " black barrier ".Therefore, detector week is estimated in real time The plasma density enclosed is the precondition that dynamic pressure auxiliary navigation method independently switches.Plasma density around detector Mainly determined by the relatively areographic speed of detector and martian atmosphere density, detector stationary point etc. is obtained by formula (12) The estimate of ion concentration：
ne=c ρaVb (12)
Wherein, a, b, c are model coefficient, V be detector relative to areographic speed, unit km/s, ρ are Mars Atmospheric density, it is assumed that martian atmosphere density p exponentially formal distribution, be calculated by formula (13)：
Wherein, ρ0=2e-4kg/m3Represent martian atmosphere reference density, r0=3,437,200m represent reference altitude, hs= 7500m martian atmosphere absolute altitudes.
Step 2：Plasma density model according to step 1 can estimate the plasma around detector in real time Density.When plasma density is less than critical electron density corresponding to detector radio-communication frequencies, that is, when communicating normal, it is The Combinated navigation method that system is exported using radio and inertia measurement, when plasma density is more than the critical electronics of radio communication During density, i.e., radio communication " black barrier " when, detector use dynamic pressure auxiliary air navigation aid.Described dynamic pressure measurement auxiliary Air navigation aid refers to three axles of the stationary point dynamic pressure value that Mars is obtained into air data system measurement and Inertial Measurement Unit output Acceleration magnitude is considered as externally measured, and the state of detector is estimated by nonlinear filtering algorithm.According to radionavigation Method or dynamic pressure Assisted Combinatorial air navigation aid establish corresponding Radio Measurement model and dynamic pressure measurement model respectively.
When plasma density is less than communication critical electron density, radio communication is normal, by measuring detector and nothing Relative distance between line telecommunications mark is modified to the state deviation of detector.
Depending on navigation accuracy needs, radio beacon is more for described aerogram target quantity and position, measurement Information is abundanter, and navigation accuracy is higher.Assuming that detector has three beacons in visible range during entrance：One track Device and two martian surface beacons.Aerogram target position is accurately surveyed before detector enters martian atmosphere by ground Deep Space Network It is fixed.The distance between detector and i-th beacon are calculated by formula (14)：
Wherein, r, riDetector and the i-th position vector of (i=1,2, the 3) beacon under Mars inertial system are represented respectively, εRiRepresent Radio Measurement noise, Gaussian distributed.
When plasma density is more than radio communication critical electron density, that is, communicate " black barrier " when, detector passes through The 3-axis acceleration value and Mars of inertia measurement output enter air data system and obtain detector stationary point dynamic pressure in flight course Value, the state of detector is estimated by non-linear estimation algorithm.The measurement model of the air navigation aid of described dynamic pressure measurement auxiliary Establish such as formula (15)：
Wherein, εDARepresent measurement noise, Gaussian distributed；A represents detector 3-axis acceleration value, true by formula (16) It is fixed：
q∞Detector stationary point dynamic pressure value is represented, is determined by formula (17)：
Wherein,Represent expression of the velocity coordinate system unit vector under Mars inertial system；σ represents tilt Angle, it is system control variables, it is assumed that angle of heel σ is constant value；D, L represents resistance acceleration and lift acceleration, can be true by formula (18) It is fixed：
Wherein, CD, CLThe resistance coefficient and lift coefficient of detector are represented, S represents detector area of reference, and m represents detection Device quality, parameter CD, CL, S, m are considered as constant value.
The definition of the axle of velocity coordinate system three is determined by formula (19) and formula (20)：
Wherein,For the relatively areographic speed of detector, Ω=[0,0,7.095e-5]Trad/s Represent expression of the Mars spin velocity under Mars inertial system.
Then the measurement model of whole air navigation aid is as follows：
When plasma density is less than radio communication critical electron density, that is, when communicating normal：
When plasma density is more than radio communication critical electron density, that is, communicate " black barrier " when：
The plasma density that martian atmosphere approach section navigation system is estimated to obtain online in real time according to system independently switches Air navigation aid, it is ensured that the metrical information that martian atmosphere approach section navigation system can obtain during entrance maximizes.
Step 3：The plasma density model obtained according to step 1, and the Radio Measurement model established of step 2 and dynamic Measurement model is pressed, the state of detector is estimated by nonlinear filtering algorithm, and then improves martian atmosphere approach section and leads Navigate precision of state estimation.
Detector original state and deviation are as shown in table 1 in emulation, and other physical parameters are as shown in table 2.
Table 1, detector original state and deviation
Table 2, detector physical parameter
Acceleration sensitive device performance indications are as shown in table 3：
Table 3, LN-200 inertance element performance indications
Two kinds of table 4, " black barrier " end point air navigation aid state estimation deviation contrasts
Table 4 gives the present invention and conventional wireless electricity and the Combinated navigation method parachute-opening point precision pair of inertia measurement output Than when " black barrier " time is 40s, the present invention is compared to conventional wireless electricity and the Combinated navigation method of inertia measurement output " black Barrier " end point can improve the estimated accuracy of an order of magnitude.From figure 3, it can be seen that aided in using the dynamic pressure measurement of the present invention Combinated navigation method state estimation deviation convergence when radio interrupts for a long time is more preferable, and " black barrier " section precision of state estimation is more Height, better reliability.
The scope of the present invention is not only limited to embodiment, and embodiment is used to explaining the present invention, it is all with of the invention identical Change or modification under the conditions of principle and design is within protection domain disclosed by the invention.

Claims (3)

  1. A kind of 1. martian atmosphere approach section Combinated navigation method of dynamic pressure auxiliary, it is characterised in that：In boat position recursion air navigation aid On the basis of, the plasma density in detector stationary point is estimated by the plasma model of foundation in real time, according to estimating in real time online Count obtained plasma density and independently switch air navigation aid；When plasma density is less than communication critical electron density, nothing Line telecommunication is normal, the Combinated navigation method exported using radio and inertia measurement, by measuring detector and aerogram Relative distance information between mark is modified to the state estimation deviation of detector；When plasma density is more than radio communication During critical electron density, radio communication " black barrier ", the air navigation aid aided in using dynamic pressure, the three of Inertial Measurement Unit output Axle acceleration and Mars enter the dynamic pressure value that air data system measurement obtains and are considered as externally measured, and combine nonlinear filtering side Method is estimated the state of detector, and then improves the reliability and precision of state estimation of star air approach section air navigation aid；
    Concrete methods of realizing comprises the following steps,
    Step 1：Plasma density model is established, estimates the plasma density in detector stationary point in real time；
    Enter hypersonic section in martian atmosphere, detector can cause detector with Aerodynamic Heating caused by martian atmosphere severe friction The air ionization of surrounding produces plasma, faces when the density of plasma exceedes corresponding to the radio-communication frequencies of detector During boundary's electron density, radio communication can be caused to interrupt, produce communication " black barrier "；Therefore, estimate in real time around detector Plasma density is the precondition that dynamic pressure auxiliary navigation method independently switches；Plasma density around detector is main Determined by the relatively areographic speed of detector and martian atmosphere density, detector stationary point plasma is obtained by formula (1) The estimate of density：
    ne=c ρaVb (1)
    Wherein, a, b, c are model coefficient, V be detector relative to areographic speed, unit km/s, ρ are martian atmosphere Density, it is assumed that martian atmosphere density p exponentially formal distribution, be calculated by formula (2)：
    <mrow> <mi>&amp;rho;</mi> <mo>=</mo> <msub> <mi>&amp;rho;</mi> <mn>0</mn> </msub> <msup> <mi>e</mi> <mfrac> <mrow> <mo>(</mo> <msub> <mi>r</mi> <mn>0</mn> </msub> <mo>-</mo> <mi>r</mi> <mo>)</mo> </mrow> <msub> <mi>h</mi> <mi>s</mi> </msub> </mfrac> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>
    Wherein, ρ0=2e-4kg/m3Represent martian atmosphere reference density, r0=3,437,200m represent reference altitude, hs=7500m Martian atmosphere absolute altitude；
    Step 2：The plasma that plasma density model according to step 1 can estimate around detector in real time is close Degree；When plasma density is less than critical electron density corresponding to detector radio-communication frequencies, radio communication is normal, is The Combinated navigation method that system is exported using radio and inertia measurement, when plasma density is more than the critical electronics of radio communication During density, radio communication " black barrier ", detector uses the air navigation aid of dynamic pressure auxiliary；The navigation of described dynamic pressure measurement auxiliary Method refers to the stationary point dynamic pressure value that Mars is obtained into air data system measurement and three axles of Inertial Measurement Unit output accelerate Angle value is considered as externally measured, and the state of detector is estimated by nonlinear filtering algorithm；According to radio navigation method Or dynamic pressure Assisted Combinatorial air navigation aid establishes corresponding Radio Measurement model and dynamic pressure measurement model respectively；
    Step 3：The plasma density model obtained according to step 1, and the Radio Measurement model of step 2 foundation and dynamic pressure are surveyed Model is measured, the state of detector is estimated by nonlinear filtering algorithm, and then improves martian atmosphere approach section navigation shape State estimated accuracy.
  2. A kind of 2. martian atmosphere approach section Combinated navigation method of dynamic pressure auxiliary as claimed in claim 1, it is characterised in that：Institute The non-linear filtering method stated uses EKF or Unscented kalman filtering algorithm.
  3. A kind of 3. martian atmosphere approach section Combinated navigation method of dynamic pressure auxiliary as claimed in claim 1, it is characterised in that：Institute Step 2 concrete methods of realizing stated is,
    When plasma density is less than communication critical electron density, radio communication is normal, by measuring detector and radio Relative distance between beacon is modified to the state deviation of detector；
    Depending on navigation accuracy needs, radio beacon is more for described aerogram target quantity and position, metrical information Abundanter, navigation accuracy is higher；Assuming that detector has three beacons in visible range during entrance：One orbiter, orbital vehicle and Two martian surface beacons；Aerogram target position is before detector enters martian atmosphere by ground Deep Space Network Accurate Determining； The distance between detector and i-th beacon are calculated by formula (3)：
    <mrow> <mtable> <mtr> <mtd> <mrow> <mi>y</mi> <mo>=</mo> <msub> <mi>h</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>R</mi> <mi>i</mi> </msub> <mo>+</mo> <msub> <mi>&amp;epsiv;</mi> <mrow> <mi>R</mi> <mi>i</mi> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <mi>r</mi> <mo>-</mo> <msub> <mi>r</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mi>T</mi> </msup> <mrow> <mo>(</mo> <mi>r</mi> <mo>-</mo> <msub> <mi>r</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> </mrow> </msqrt> <mo>+</mo> <msub> <mi>&amp;epsiv;</mi> <mrow> <mi>R</mi> <mi>i</mi> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>
    Wherein, r, riDetector and the i-th position vector of (i=1,2, the 3) beacon under Mars inertial system, ε are represented respectivelyRiTable Show Radio Measurement noise, Gaussian distributed；
    When plasma density is more than radio communication critical electron density, that is, communicate " black barrier " when, detector passes through inertia Measure the 3-axis acceleration value of output and Mars enters air data system and obtains dynamic pressure value in detector stationary point in flight course, lead to Cross the state of non-linear estimation algorithm estimation detector；The measurement model of the air navigation aid of described dynamic pressure measurement auxiliary is established such as Formula (4)：
    <mrow> <mi>y</mi> <mo>=</mo> <msub> <mi>h</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mi>a</mi> </mtd> </mtr> <mtr> <mtd> <msub> <mi>q</mi> <mi>&amp;infin;</mi> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>+</mo> <msub> <mi>&amp;epsiv;</mi> <mrow> <mi>D</mi> <mi>A</mi> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
    Wherein, εDARepresent measurement noise, Gaussian distributed；A represents detector 3-axis acceleration value, is determined by formula (5)：
    <mrow> <mi>a</mi> <mo>=</mo> <mo>-</mo> <msubsup> <mi>De</mi> <mi>x</mi> <mi>w</mi> </msubsup> <mo>+</mo> <mi>L</mi> <mo>&amp;lsqb;</mo> <mo>-</mo> <msubsup> <mi>e</mi> <mi>y</mi> <mi>w</mi> </msubsup> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mi>&amp;sigma;</mi> <mo>+</mo> <msubsup> <mi>e</mi> <mi>z</mi> <mi>w</mi> </msubsup> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;sigma;</mi> <mo>&amp;rsqb;</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>
    q∞Detector stationary point dynamic pressure value is represented, is determined by formula (6)：
    <mrow> <msub> <mi>q</mi> <mi>&amp;infin;</mi> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mi>&amp;rho;</mi> <mo>|</mo> <mo>|</mo> <msub> <mi>v</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>l</mi> </mrow> </msub> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>
    Wherein,Represent expression of the velocity coordinate system unit vector under Mars inertial system；σ represents angle of heel, For system control variables, it is assumed that angle of heel σ is constant value；D, L represents resistance acceleration and lift acceleration, is determined by formula (7)：
    <mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>F</mi> <mi>T</mi> </msub> <mo>=</mo> <mn>0.5</mn> <mfrac> <mrow> <msub> <mi>C</mi> <mi>D</mi> </msub> <msup> <mi>&amp;rho;V</mi> <mn>2</mn> </msup> <mi>S</mi> </mrow> <mi>m</mi> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>F</mi> <mi>N</mi> </msub> <mo>=</mo> <mn>0.5</mn> <mfrac> <mrow> <msub> <mi>C</mi> <mi>L</mi> </msub> <msup> <mi>&amp;rho;V</mi> <mn>2</mn> </msup> <mi>S</mi> </mrow> <mi>m</mi> </mfrac> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>
    Wherein, CD, CLThe resistance coefficient and lift coefficient of detector are represented, S represents detector area of reference, and m represents detector matter Amount, parameter CD, CL, S, m are considered as constant value；
    The definition of the axle of velocity coordinate system three is determined by formula (8) and formula (9)：
    <mrow> <msubsup> <mi>e</mi> <mi>x</mi> <mi>w</mi> </msubsup> <mo>=</mo> <mfrac> <msub> <mi>v</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>l</mi> </mrow> </msub> <mrow> <mo>|</mo> <mo>|</mo> <msub> <mi>v</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>l</mi> </mrow> </msub> <mo>|</mo> <mo>|</mo> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <msubsup> <mi>e</mi> <mi>y</mi> <mi>w</mi> </msubsup> <mo>=</mo> <mo>-</mo> <mfrac> <mrow> <msubsup> <mi>e</mi> <mi>x</mi> <mi>w</mi> </msubsup> <mo>&amp;times;</mo> <mi>r</mi> </mrow> <mrow> <mo>|</mo> <mo>|</mo> <msubsup> <mi>e</mi> <mi>x</mi> <mi>w</mi> </msubsup> <mo>&amp;times;</mo> <mi>r</mi> <mo>|</mo> <mo>|</mo> </mrow> </mfrac> <mo>,</mo> <msubsup> <mi>e</mi> <mi>z</mi> <mi>w</mi> </msubsup> <mo>=</mo> <msubsup> <mi>e</mi> <mi>x</mi> <mi>w</mi> </msubsup> <mo>&amp;times;</mo> <msubsup> <mi>e</mi> <mi>y</mi> <mi>w</mi> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow>
    Wherein,For the relatively areographic speed of detector, Ω=[0,0,7.095e-5]TRad/s is represented Expression of the Mars spin velocity under Mars inertial system；
    Then the measurement model of whole air navigation aid is as follows：
    When plasma density is less than radio communication critical electron density, that is, when communicating normal：
    <mrow> <mi>y</mi> <mo>=</mo> <msub> <mi>h</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <mi>r</mi> <mo>-</mo> <msub> <mi>r</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mi>T</mi> </msup> <mrow> <mo>(</mo> <mi>r</mi> <mo>-</mo> <msub> <mi>r</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> </mrow> </msqrt> <mo>+</mo> <msub> <mi>&amp;epsiv;</mi> <mrow> <mi>R</mi> <mi>i</mi> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow>
    When plasma density is more than radio communication critical electron density, that is, communicate " black barrier " when：
    <mrow> <mi>y</mi> <mo>=</mo> <msub> <mi>h</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mi>a</mi> </mtd> </mtr> <mtr> <mtd> <msub> <mi>q</mi> <mi>&amp;infin;</mi> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>+</mo> <msub> <mi>&amp;epsiv;</mi> <mrow> <mi>D</mi> <mi>A</mi> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow>
    The plasma density that martian atmosphere approach section navigation system is estimated to obtain online in real time according to system independently switches navigation Method, it is ensured that the metrical information that martian atmosphere approach section navigation system can obtain during entrance maximizes.
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