CN104457745B - X-ray pulsar phase estimation method based on loop tracks - Google Patents

Abstract

Based on the X-ray pulsar phase estimation method of loop tracks, step is：(1) observation pulsar, its pulse period P under record quiescent conditions are determined₀With nominal contour s (n)；(2) in observation time section, record the time of advent of all observation pulsar photons；(3) for first τ_sThe photon sequence time of advent in duration, according to quiescent conditions lower pulse period P₀Folded, generated measurement pulse profile c (n)；(4) ask for the phase difference estimation value of s (n) and c (n)；(5) combined from single order and third-order filter, phase difference estimation value is filtered, obtain frequency and phase feedback update information Δ f, Δ φ；(6) the pulse period P under quiescent conditions is corrected using Δ f₀, the revised pulse period is obtained, and obtains next τ_sMeasurement pulse profile new in duration；(7) using Δ φ amendments calibration pulse profile s (n), obtain revised calibration pulse profile；(8) according to obtain new phase difference estimation value.

Description

X-ray pulsar phase estimation method based on loop tracks

Technical field

The invention belongs to Spacecraft Autonomous Navigation field, is related to a kind of the dynamic of X-ray pulsar navigation signal processing State effect modification method, it is adaptable to LEO, deep space and interplanetary flight spacecraft, and without dense atmosphere celestial body lander And its high-precision independent navigation and control of surface stroller.

Background technology

X-ray pulsar is a kind of natural beacon, the X-ray pulse signal of energy stable radiation.Led using X-ray pulsar Boat is a kind of new astronomical navigation method, is independent navigation truly.Observed by the timing of pulse signals, can High-precision ranging information and temporal information are obtained, by being imaged to pulsar, it is also possible to obtain attitude information.Pulsar navigation Whole solar autonomous navigation technology is applied to, for the adaptability that task different phase only needs to carry out navigation algorithm is adjusted Whole, navigation accuracy will not be reduced with the increase of flying distance, and the technology will realize that survey of deep space and space flight are appointed future Seamless navigation and the accurate maximally efficient approach for controlling in business.

The ultimate principle of X-ray pulsar navigation is the impulse phase and datum mark by measuring synchronization spacecraft Impulse phase difference at (solar system barycenter) position, by certain navigation algorithm, obtains observation moment spacecraft with respect to base Position on schedule.As can be seen here, pulsar phase estimation method is one of key link of X-ray pulsar navigation, is only entered The accurate impulse phase measurement of row, can just carry out follow-up spacecraft navigator fix.The measuring method of impulse phase is using sight The information for measuring is compared with the calibration pulse profile of prior record, to obtain the phase contrast of the two.As pulsar is led Boat X-ray detector record is the photon time of advent rather than direct pulse information, it is therefore desirable to carry out corresponding pulsar Navigation signal processing links, with the conversion for realizing being estimated from the photon time of advent to impulse phase.But for spacecraft, Due to Doppler effect and relativistic effect caused by its own motion, when pulsar navigation signal processing is carried out, pulse Cycle constantly changes so that when carrying out phase estimation using calibration pulse profile, it may appear that the situation that estimated accuracy declines.

The content of the invention

Present invention solves the technical problem that being：Existing pulsar navigation signal processing link is overcome using fixed standard arteries and veins Rush profile and realize that impulse phase estimates that caused estimated accuracy is degenerated, there is provided it is all that one kind obtains pulse profile using feedback control loop Phase change update information realizes the method that dynamic spacecraft impulse phase is accurately estimated.

The present invention technical solution be：It is based on the X-ray pulsar phase estimation method of loop tracks including as follows Step：

(1) determine observation pulsar, record the pulse period P that pulsar is observed under quiescent conditions₀With calibration pulse profile s (n)；Wherein calibration pulse profile is the mathematic expectaion of pulsar photon arriving amt in a cycle in n-th sampled point The sampled value at place, N is total number of sample points, n=1,2 ..., N；

(2) in observation time section τ₀To τ₀+τ_obsIt is interior, record the time of advent of all observation pulsar photons, wherein τ₀For Observation time starting point, τ_obsTo observe total duration；

(3) for first τ_sThe observation pulsar photon sequence τ time of advent in duration_k∈[τ₀,τ₀+τ_s], according to static Under the conditions of pulse period P₀Folded, generated measurement pulse profile c (n),

C (n)=α s (n+ φ × N)+β+ω (n)

Wherein α is scale factor, and β is shift factor, and ω (n) is measurement noise, and φ is measurement pulse profile and standard arteries and veins The phase contrast rushed between profile；

(4) according to calibration pulse profile s (n) and measurement pulse profile c (n), obtain the estimated value of the phase difference of the two

(5) combined from single order and third-order filter, be directed at the phase place of pulse profile s (n) and measurement pulse profile c (n) Difference estimated valueIt is filtered, obtains frequency feedback update information Δ f and phase feedback update information Δ φ；Wherein wave filter group Conjunction is expressed as：

Δ φ=∫ Δ f

Wherein, Δ φ, Δ f are respectively the feedback modifiers information of phase place and frequency, a₃₁、a₃₂、a₃₃Represent that three ranks filter respectively The each integral element amplification coefficient of device, a₁₁Represent firstorder filter amplification coefficient；Integral operation in described filter combination is adopted Realized with square wave digital integrator；

(6) the pulse period P under quiescent conditions is corrected using frequency feedback update information Δ f₀, obtain revised pulse CycleAnd utilizeTo next τ_sIn duration, the observation pulsar photon sequence time of advent is rolled over It is folded, and obtain next τ_sIn duration, the observation pulsar photon sequence time of advent, thus obtains new measurement pulse profile

(7) using phase feedback update information Δ φ amendments calibration pulse profile s (n), obtain revised calibration pulse Profile

(8) basisWithObtain new phase difference estimation value

(9) for observation time section τ₀To τ₀+τ_obsEach interior processes step-length τ_s, repeat step (3)～step (8), Until all the observation pulsar photon series processing time of advent is finished, final phase difference estimation value is obtained.

Present invention advantage compared with prior art is：

(1) the inventive method can realize the stable observation under spacecraft current intelligence to pulsar.Due to spacecraft certainly The motion of body, the pulse signal for receiving be introduced into Doppler frequency change so that the pulse period that actual observation is obtained with it is quiet The pulse period for obtaining is observed under the conditions of only inconsistent.The inventive method utilizes loop filtering feedback compensation structure, can enter Before the wide folding of road wheel, corrected impulse periodic quantity, it is ensured that profile folds the correctness of result.

(2) present invention can improve the precision of impulse phase measurement.When impulse phase measurement is carried out, as photon is reached The uncertainty of time, causes impulse phase measurement result to there is randomness.The inventive method utilizes phase feedback track loop Filter effect can be produced, the random error to including in impulse phase measurement result is filtered, and improves impulse phase Certainty of measurement.

Description of the drawings

FB(flow block)s of the Fig. 1 for the inventive method；

Fig. 2 is the Laplace transformation schematic diagram of corresponding wave filter in step 4 of the present invention；

Fig. 3 shows for the change for adopting phase measurement error after phase-tracking method amendment of the invention in the embodiment of the present invention It is intended to.

Specific embodiment

As shown in figure 1, for the flow chart of the inventive method, key step is as follows：

Step one：It is determined that observing pulsar and recording its pulse period P under quiescent conditions₀With nominal contour s (n), wherein Nominal contour is the mathematic expectaion of pulsar photon arriving amt in a cycle in n-th sampled pointThe sampled value at place, N For total number of sample points, n=1,2 ..., N.

It is assumed that observation time starting point is τ₀, process step-length τ_s, observe total duration τ_obs.(the τ in the observation time section₀To τ₀+ τ_obs), record all pulsar photon times of advent.For k-th photon, its time of advent is recorded for τ_k。

Step 2：To first group of photon sequence τ time of advent_k∈[τ₀,τ₀+τ_s], according to quiescent conditions lower pulse period P₀, Access time sequence midpoint τ₀+τ_s/ 2 used as reference point is folded, and selection total number of sample points is N, generates measurement pulse profile c (n), Pulse profile folding is carried out.Due to spacecraft and the alternate position spike of navigational coordinate system origin, between measurement profile and nominal contour There is phase shift.Simultaneously as the presence of observation noise, measures the ratio contracting that also there is amplitude between profile and nominal contour Put and displacement and measurement noise.Therefore the relation of measurement profile is represented by：

C (n)=α s (n+ φ × N)+β+ω (n)

Wherein, α is scale factor, and β is shift factor, and ω (n) is measurement noise, embodies observation noise to measuring profile Impact；φ is to measure the phase contrast between profile and nominal contour, and for pulsar navigation, other resolve link and use.

Step 3：According to nominal contour s (n) and measurement profile c (n), the estimated value of phase difference is obtained。

Step 4：Using wave filter to phase difference estimation valueIt is filtered.

Wave filter is made up of multiple integral.The present invention selects single order and third-order filter to combine, and its formula can be written as：

Δ φ=∫ Δ f

Wherein, Δ φ, Δ f are respectively the feedback modifiers information of phase place and frequency.a₃₁、a₃₂、a₃₃Represent that three ranks filter respectively The each integral element amplification coefficient of device, a₁₁Represent firstorder filter amplification coefficient.With Single order and three ranks filtering computation structure are represented respectively, complete filter function is constituted by feedback control loop, suppresses feedback modifiers letter High fdrequency components in breath, reduce the noise of feedback modifiers information.According to feedback control loop mathematical feature, a can be obtained₁₁、a₃₁、a₃₂ And a₃₃Optimal value, as shown in Figure 2.

It is that calculating is integrated under discrete conditions, square wave digital integrator can be adopted, i.e., by carrying out y (t)=y (t- Δ t)+Δ t × x (t) recursive operations, simulation y (t)=∫ x (t).

Step 5：Using the pulse period P0 under the frequency information Δ f amendment quiescent conditions of feedback.According to cycle and frequency Relation, can obtainI.e.

Operate by more than, according to upper one group of photon sequence time of advent observation information, by the feedback compensation to the cycle, Reduce the revised pulse periodWith the difference in true pulse cycle.Using the pulse period after renewalTo next group of photon The time of advent, sequence was folded, and obtained next group of measurement pulse profile c (n), at the same improve the photon sequence time of advent with The similarity of true pulse profile.

Step 6：Nominal contour s (n) is corrected using the phase information Δ φ of feedback, i.e.,：

The purpose of the amendment is to translating between primary standard profile s (n) so as to which phase value approaches next group of measurement Pulse profile c (n), so that the phase difference estimation value of outputThe state for tending to 0 is maintained, amendment nominal contour is realizedTracking to c (n).Now phase feedback update information can be reflected as the phase contrast of s (n) and c (n), i.e. phase measurement As a result.

As nominal contour s (n) characterizes the change that photon in a cycle reaches probability, variable n excursions are 1, 2,…,N.When carrying out phase information amendment, need to consider cyclic shift to be realized by MOD function mod (), describe phase shift Move to the impact in whole cycle.

Step 7：According to the nominal contour after renewalThe current sequence photon time of advent obtained with step 5 is generated Measurement profile c (n), obtain new phase difference estimation value

Step 8：Repeat step four to seven, until the whole photon sequences time of advent are calculated and finished.Namely with τ_sTo process Step-length, processes total duration τ_obs。

Embodiment

Step one：It is determined that observing pulsar and recording its pulse period P under quiescent conditions₀With nominal contour s (n).This reality It is PSR B0531+21 that example chooses the pulsar of observation, and the pulse period under its quiescent conditions is P₀=33.085ms.Observe Point is τ₀=55746.0MJD, processes step-length τ_s=1s, observation interval τ_obs=2s.Whole light are collected in observation time section The sub- time of advent, it is designated as τ_k(k=1,2,3 ...).Total number of sample points N=1024.

Step 2：To first group of photon sequence τ time of advent_k∈ [0s, 1s], enters according to quiescent conditions lower pulse period P0 Row is folded, and is folded reference point and is taken as 0.5s.Definition measurement pulse profile c (n)=0 first, (n=1,2 ..., 1024), if kth The individual photon time of advent meets：

Wherein { } means and rounds up, then it is assumed that photon time of advent corresponding to layout when n-th of folding cycle, Corresponding measurement pulse profile function c (n)=c (n)+1, is processed to this group of photon sequence data time of advent, directly successively Finish to the whole data processings photon time of advent.

Step 3：According to nominal contour s (n) and measurement profile c (n), the two phase contrast is calculated using cross correlation algorithm I.e.：

Wherein s_kN () represents carries out k positions ring shift right to 1024 n dimensional vector ns, i.e.,

s_k(n)=s (mod (n+k, k))

Function cov () represents cross-correlation calculation, can be realized by vector dot product mode.Auto-correlation cross correlation value maximum The corresponding time location of ring shift right amount is the phase contrast between nominal contour and measurement profile.

Step 4：Using wave filter to phase difference estimation valueIt is filtered.

According to the Laplace transformation of track loop, the one group of feasible solution that must filter each parameter in computing formula can be pushed away, i.e.,：

For the simplicity that subsequent integration is calculated, intermediate variable x is defined₁、x₂.Due to current time for integration initial value, frequency with The calculating of the feedback modifiers information of phase place can be written as

Δ φ=Δ f × τ_s

Δ φ is also simultaneously current slot this algorithm output, the impulse phase estimated value after smoothing.

Step 5：Using the pulse period P under the frequency information Δ f amendment quiescent conditions of feedback₀, i.e.,

Using the pulse period P after renewal to the next group of photon sequence τ time of advent_k∈ [1s, 2s] is folded, its side Similar to step 3, difference is that the pulse period P under quiescent conditions is substituted with the pulse period P after renewal to method₀Participate in calculating, And obtain this group of photon sequence c time of advent (n).

Step 6：Nominal contour s (n) is corrected using the phase information Δ φ of feedback, i.e.,：

Step 7：According to the nominal contour after renewalObtain with step 5, by the current sequence photon time of advent Row τ_kMeasurement profile c (n) that ∈ [1s, 2s] is generated, carries out cross-correlation calculation, to obtain this section of photon sequence phase time of advent Difference.Its method is similar to step 3.

Step 8：Repeat step four to seven, as photon observation information is using finishing, now only needs to carry out step 4 Operation：

Δ φ=Δ φ (t-1)+Δ f × τ_s

Δ φ is also simultaneously current slot this algorithm output, the impulse phase estimated value after smoothing.

By observation time τ_obs7200s is extended to, the pulsar x-ray photon observed on geo-synchronous orbit satellite is simulated The time of advent, while carrying out this method and being provided without this method, only pass through cross-correlation phase estimation method, obtain two methods Shown in phase estimation error curve such as Fig. 3 (a) and Fig. 3 (b).Only with the phase error root-mean-square that cross-correlation method is estimated to obtain For 5.8631e-004 (rad)；The phase error root-mean-square that this method is obtained is adopted for 4.0603e-004 (rad), precision improvement 30%.It can be seen that the inventive method can effectively improve pulsar navigation impulse phase certainty of measurement.

The content not being described in detail in description of the invention belongs to the known technology of those skilled in the art.

Claims (2)

1. the X-ray pulsar phase estimation method based on loop tracks, it is characterised in that comprise the steps：

(1) determine observation pulsar, record the pulse period P that pulsar is observed under quiescent conditions₀With calibration pulse profile s (n)； Wherein calibration pulse profile is the mathematic expectaion of pulsar photon arriving amt in a cycle in n-th sampled pointPlace Sampled value, N is total number of sample points, n=1,2 ..., N；

(2) in observation time section τ₀To τ₀+τ_obsIt is interior, record the time of advent of all observation pulsar photons, wherein τ₀For observation Start time, τ_obsTo observe total duration；

(3) for first τ_sThe observation pulsar photon sequence τ time of advent in duration_k∈[τ₀,τ₀+τ_s], according to quiescent conditions Lower pulse period P₀Folded, generated measurement pulse profile c (n), footmark k is represented k-th photon,

C (n)=α s (n+ φ × N)+β+ω (n)

Wherein α is scale factor, and β is shift factor, and ω (n) is measurement noise, and φ is measurement pulse profile and calibration pulse wheel Phase contrast between exterior feature；

(4) according to calibration pulse profile s (n) and measurement pulse profile c (n), obtain the estimated value of the phase difference of the two

(5) combined from single order and third-order filter, to calibration pulse profile s (n) and the phase contrast for measuring pulse profile c (n) Estimated valueIt is filtered, obtains frequency feedback update information Δ f and phase feedback update information Δ φ；Wherein filter combination It is expressed as：

$\mathrm{\Δ}f=\left(\right(a_{31}\widetilde{\mathrm{\φ}}+\∫\left(a_{32}\widetilde{\mathrm{\φ}}+\∫a_{33}\widetilde{\mathrm{\φ}}\right))+a_{11}\widetilde{\mathrm{\φ}})/2$

Δ φ=∫ Δ f

Wherein, Δ φ, Δ f are respectively the feedback modifiers information of phase place and frequency, a₃₁、a₃₂、a₃₃Represent that third-order filter is each respectively Integral element amplification coefficient, a₁₁Represent firstorder filter amplification coefficient；

(6) the pulse period P under quiescent conditions is corrected using frequency feedback update information Δ f₀, obtain the revised pulse periodAnd utilizeTo next τ_sIn duration, the observation pulsar photon sequence time of advent is folded, and Obtain next one τ_sIn duration, the observation pulsar photon sequence time of advent, thus obtains new measurement pulse profile

(7) using phase feedback update information Δ φ amendments calibration pulse profile s (n), obtain revised calibration pulse profile

(8) basisWithObtain new phase difference estimation value

(9) for observation time section τ₀To τ₀+τ_obsEach interior processes step-length τ_s, repeat step (5)～step (8), until All the observation pulsar photon series processing time of advent is finished, and obtains final phase difference estimation value.

2. the X-ray pulsar phase estimation method based on loop tracks according to claim 1, it is characterised in that：Institute Integral operation in the filter combination stated is realized using square wave digital integrator.