CN104596544B - A kind of method of aerial navigation performance prediction under ionospheric scintillation - Google Patents

Abstract

The invention discloses a method for predicting aviation navigation performance under ionospheric scintillation. The method is applicable to the aviation flight process under ionospheric scintillation. The navigation performance is described by parameters such as navigation error, navigation integrity and usability. The navigation performance Prediction results are calculated by air navigation terminals. By establishing the mapping relationship between the ionospheric scintillation parameters and the tracking loop of the navigation receiver, the navigation ranging error and the average lock-out time under the scintillation environment are analyzed, and the frequency of the navigation lock-out is calculated. Evaluate navigation accuracy, autonomy integrity, and availability against aviation user trajectories and flight operations requirements. The advantage of this method is that it can provide accurate calculation and prediction results of aviation navigation performance parameters in any scene and setting parameters during ionospheric scintillation, so as to ensure the effectiveness and safety of aviation navigation. This method can also be used to evaluate various The degree to which the aviation navigation terminal is affected by ionospheric scintillation provides a theoretical and empirical basis for the development of high-performance aviation navigation terminals.

Description

A Method for Air Navigation Performance Prediction under Ionospheric Scintillation

technical field

The invention relates to the field of aviation navigation performance evaluation, in particular to a method for predicting aviation navigation performance under ionospheric scintillation.

Background technique

Ionospheric scintillation refers to the fluctuation of radio wave amplitude, phase and time delay caused by the inhomogeneity of the ionospheric plasma structure and the non-stationary time and space when the radio wave signal passes through the ionosphere. Strong ionospheric scintillation can cause large-scale disruption of navigation communications. Historical data show that the ionospheric storms and strong scintillation phenomena that occurred from late October to early November 2003 once caused the United States' Wide Area Augmentation System (WAAS, Wide Area Argumentation System) to be shut down for up to 30 hours, seriously affecting its inland aviation. transportation. In order to solve the above problems, the study of the impact of ionospheric scintillation on the performance of aviation navigation has become a hot and difficult point in related fields in recent years. At present, the research on the impact of ionospheric scintillation on navigation performance mainly relies on experimental methods. Due to the strong suddenness and irregularity of ionospheric scintillation events, it is difficult to obtain experimental data, which makes its research not universal. change. However, the performance requirements of navigation terminals for high-safety operations in dense aviation traffic and complex environments are constantly increasing. Under such circumstances, how to accurately predict the performance of aviation navigation under ionospheric scintillation has become a technical problem that needs to be broken through.

According to the regulations of Performance Based Navigation required by international civil aviation, aviation navigation performance mainly includes accuracy, integrity, continuity and availability. In theory, navigation error is an important parameter to evaluate navigation performance. Traditional navigation performance prediction methods are often based on basic navigation error characteristics to evaluate and predict various navigation performances independently. In fact, the navigation environment and the navigation signal receiving model not only affect the navigation error itself, but also make a strong correlation between various navigation performances. Under ionospheric scintillation, the electromagnetic environment of navigation signal propagation is greatly changed, which makes the traditional navigation signal receiving model have limitations, and also changes some statistical characteristics of navigation errors. In this case, the traditional navigation performance Predictive methods will fail. Although some researchers have obtained statistical empirical parameters of navigation errors under ionospheric scintillation through flight experiments and other methods for specific scenarios, this method is not universally applicable, causing other researchers to still face difficulties in the research process. Many obstacles. Therefore, it is one of the difficult problems that researchers in this field are trying to solve to design and implement a pervasive, autonomous, and flexible method for air navigation performance prediction under ionospheric scintillation.

Contents of the invention

The technical problem to be solved by the present invention is: to overcome the deficiencies of the prior art, to propose a method for predicting aviation navigation performance under ionospheric scintillation, to establish a navigation receiver tracking loop model associated with the navigation environment, and to calculate the navigation measurement error and The average lock-out time of the navigation tracking loop is derived from the average lock-out time to deduce the frequency of ionospheric scintillation that causes the navigation signal to track the lock-out, establish a statistical model of this frequency, and then combine the user's flight trajectory and flight time with the user's aviation navigation performance. Prediction is made to effectively guarantee navigation performance.

The purpose of the present invention is achieved through the following technical solutions: a method for predicting aviation navigation performance under ionospheric scintillation, the method is applicable to under ionospheric scintillation, during aviation flight, navigation performance is determined by navigation error, navigation integrity and usability The navigation performance prediction result is calculated by the aviation navigation terminal, which is characterized in that it can provide accurate aviation navigation performance parameter calculation and prediction results under any scene and setting parameters when the ionosphere scintillates, so as to ensure the effectiveness of aviation navigation. This method can also be used to evaluate the impact of ionospheric scintillation on various aviation navigation terminals, and provide theoretical and empirical basis for the development of high-performance aviation navigation terminals. The method comprises the steps of:

Step A, setting the amplitude scintillation and phase scintillation parameters of ionospheric scintillation, setting the type of navigation signal;

Step B, establish the tracking loop model of the navigation receiver, and calculate the tracking code pseudo-range measurement error and carrier phase measurement error;

Step C, performing post-filtering on the measured error to obtain the output measurement error of the navigation receiver;

Step D, calculate the average lock-out time of the tracking loop according to the set ionospheric scintillation parameters and the established navigation receiver tracking loop model;

Step E, establishing the correlation expression of the average out-of-lock time with respect to the interruption frequency of the navigation signal under ionospheric scintillation, and calculating the out-of-lock frequency of the navigation signal;

Step F, calculate the position of the navigation satellite according to the user's flight trajectory and flight time, and obtain the geometric parameters of the satellite;

Step G, according to the specific flight operation requirements, calculate the autonomous integrity monitoring availability prediction of the navigation terminal;

Step H, calculate the navigation protection level during the flight, compare it with the navigation warning limit specified in the operation requirements, and judge whether it is available;

Step I. According to the calculation result of the navigation performance parameters in the set time period, predict the navigation usability in the time period.

Wherein, in the step A: the amplitude scintillation parameter of the ionospheric scintillation is S ₄ , and its value range is [0.1,2], the phase scintillation parameter is τ, and its value range is [0.1,1], and the navigation signal refers to GNSS intermediate frequency digital signals, including GPS, GALILEO, GLONASS and Beidou navigation signals.

Wherein, in the step B: the navigation receiver tracking loop model is composed of a first-order, second-order or third-order tracking loop, and its tracking code pseudo-range is calculated by the following formula:

The code tracking error is expressed as: Wherein B _nd is the tracking bandwidth of the code tracking loop, T _s is the pre-detection integration time of the tracking loop, C/N ₀ is the carrier-to-noise ratio of the navigation signal, and d is the correlation distance of the code tracking loop;

The carrier tracking error is expressed as:

and Among them, B _np is the tracking bandwidth of the carrier tracking loop, k is the order of the tracking loop, p is the spectral coefficient of the phase power spectral density, f _n is the free oscillation frequency of the carrier tracking loop.

Wherein, in the step C: the post-filtering of code pseudo-range and carrier tracking quantity measurement adopts the Kalman filter method, and its state equation is:

in are the estimated pseudorange values at time k and k-1 respectively, φ _k and φ _k-1 are the carrier phase measurements at time k and k-1 respectively, and their measurement errors follow the Gaussian [0,σ _φ ] distributed.

Its observation equation can be expressed as:

Among them, ρ _k is the measurement of pseudo-range, and its measurement error w _k obeys the Gaussian distribution of [0,σ _τ ].

Wherein, in the step D: assuming that the probability density function of the output value ε of each tracking loop is p _k (ε), and the error limit of the tracking loop is ±θ _b , the number of times the tracking loop can track stably can be Expressed as: The average lockout time can be calculated as Where T is the update time of the loop, which is generally equal to the pre-detection integration time T _s .

Wherein, in the step E: respectively calculate the average loss of lock time T ₁ under normal conditions and the average loss of lock time T ₂ in the case of ionospheric scintillation, then the relationship between the frequency of ionospheric scintillation and the average loss of lock time is: Among them, m is a fixed coefficient, and its value is related to the degree of ionospheric scintillation.

Wherein, in the step E: the frequency of the navigation signal losing lock is statistically subject to the Poisson distribution, and the calculation method of the distribution parameter is:

λ ₀ =ρλ ^Nscin T _span , where N _scin is the number of satellites that are simultaneously out of lock due to ionospheric scintillation, ρ is the correlation coefficient, which characterizes the correlation degree of the signal channels of N _scin satellites, and T _span is the flight time. Assuming that the reacquisition time of the navigation terminal's signal out of lock is T _reacq , then the out of lock time of N _scin satellite signals within the flight time is T _unlock =λ ₀ T _reacq .

Wherein, in the step F: the geometric parameters of the satellite can be described by the matrix H, and

[a _i1 a _i2 a _i3 ] are the unit vectors of the user and the i-th satellite in the northeast direction, and n is the total number of visible satellites.

Wherein, in the step G: the calculation method of the autonomous integrity monitoring availability prediction of the navigation terminal is:

First calculate _Hw = (H'PH) ^-1 H'P, where calculate

Compare the HPL _slope and VPL _slope with the horizontal warning limit and the vertical warning limit respectively, if they are greater than the warning limit, the autonomous integrity of the navigation terminal is unavailable.

Wherein, in the step H: the calculation method of the navigation protection level is: calculating △x=H _w △z, where △z is the pseudorange residual, which satisfies the Gaussian distribution [0, σ]. make

h ₁₁ =[a ₁₁ a ₂₁ ... a _n1 ], h ₁₂ =[a ₁₂ a ₂₂ ... a _n2 ] h ₁₃ =[a ₁₃ a ₂₃ ... a _n3 ].

γ=[σ ₁ σ ₂ ... σ _n ]

but

The horizontal protection levels are:

The vertical protection level is: VPL=|△x ₃ |+α ₂ ·du.

Wherein, in the step I: the navigation availability judgment method is: within a certain period of time, the navigation protection level calculated with the unit time step is compared with the navigation warning limit in the operation demand, if the protection level is greater than the warning limit, then Navigation is unavailable at this moment; in this time period, set the total number of comparisons as N ₁ , and the number of times the protection level is greater than the warning limit as N ₂ , then the availability calculation method is:

The beneficial effects of the present invention are mainly reflected in:

(1) Compared with the traditional method, the advantage of the present invention (as shown in FIG. 1 ) is that it considers the impact of the ionospheric scintillation environment on the transmission of navigation errors, so as to improve the estimation accuracy of navigation errors, as shown in FIG. 3 .

(2) Compared with the traditional method, the present invention (as shown in FIG. 1 ) calculates the impact of the ionospheric scintillation environment on the average lock-out time of the navigation tracking loop, and its effect is shown in FIG. 4 .

(3) By setting the correlation coefficient of different navigation signal receiving channels and the reacquisition time of the navigation receiver, the present invention can effectively predict the availability of aviation navigation under ionospheric scintillation, as shown in FIG. 5 .

Description of drawings

Fig. 1 is a flow chart of the present invention;

Fig. 2 is a schematic diagram of a navigation tracking loop in the present invention;

Fig. 3 is a schematic diagram of the navigation error transfer process in the present invention;

Fig. 4 is a schematic diagram of the relationship between the average out-of-lock time and ionospheric scintillation parameters in the present invention;

Fig. 5 is a schematic diagram of the relationship among correlation coefficient, reacquisition time and navigation availability in the present invention.

detailed description

The specific implementation of the present invention will be described in detail below in conjunction with the accompanying drawings, and the description takes the navigation performance evaluation and prediction of GPS satellites under ionospheric scintillation as an example.

1. Set the amplitude scintillation and phase scintillation parameters of the ionospheric scintillation, wherein the amplitude scintillation parameter S ₄ is set to 0.6, and the phase scintillation parameter τ is set to 0.5.

2. Establish the tracking loop model of the navigation receiver, where the code tracking loop is set as a second-order loop, and the carrier tracking loop is set as a second-order loop, and the tracking code pseudo-range measurement error and carrier phase measurement error are calculated;

3. Perform post-Kalman filtering on the measured error to obtain the output measurement error of the navigation receiver;

4. Calculate the average lock-out time of the code tracking loop and carrier tracking loop according to the set ionospheric scintillation parameters and the established navigation receiver tracking loop model;

5. Calculate the frequency of navigation signal loss of lock according to the correlation expression of the average loss of lock time with respect to the frequency of interruption of navigation signals under ionospheric scintillation;

6. Set the user's flight trajectory to cruise mode, and the flight time to 7200s, calculate the navigation satellite position according to the GPS almanac parameters, and obtain the geometric parameters of the satellite combined with the current position of the user's flight;

7. According to the flight operation requirements of LPV200, the false alarm probability of integrity risk is 10 ^-5 , the missed detection probability is 10 ^-3 , the horizontal alarm limit is 40 meters, and the vertical alarm limit is 35 meters. On this basis, the autonomous integrity monitoring availability prediction of the navigation terminal is calculated;

8. Calculate the navigation protection level during the flight, compare it with the navigation warning limit specified by LPV200, and judge whether it is available;

9. Set the time period as 7200s, and calculate the navigation protection level every 1s, compare it with the warning limit, and record the number of times the navigation protection level is greater than the warning limit, so as to predict the navigation availability in this time period.

The above method is further explained below.

The model of the navigation tracking loop described in step 2, for the GPS L1 frequency band BPSK modulation signal, the intermediate frequency satellite signal and the local time code correlation, after pre-detection integration, can be decomposed into the same direction branch signal and the orthogonal branch signal , denoted as I _k and Q _{k respectively} ; the intermediate frequency satellite signal is correlated with the local early code (0.5 chip ahead) and the local late code (0.5 chip behind), and the correlation results I _Ek , I _Lk and Q _Ek , Q _Lk are obtained . Then the output of the code discriminator is: The phase discriminator output is

The amplitude of the navigation signal under ionospheric scintillation satisfies the nakagami-m distribution, and the phase satisfies the uniform distribution. From this, it can be deduced that the code phase and carrier tracking error are expressed as:

Code tracking error: where B _nd is the tracking bandwidth of the code tracking loop, T _s is the pre-detection integration time of the tracking loop, C/N ₀ is the carrier-to-noise ratio of the navigation signal, and d is the correlation distance of the code tracking loop;

Carrier Tracking Error:

and Among them, B _np is the tracking bandwidth of the carrier tracking loop, k is the order of the tracking loop, p is the spectral coefficient of the phase power spectral density, f _n is the free oscillation frequency of the carrier tracking loop.

In step 3, since the code pseudo-range measurement error is usually large, the carrier smoothing code pseudo-range equation is established, and the Kalman filter method is used for post-filtering, and the filtering input is the code pseudo-range measurement error sequence and the carrier quantity measurement Error sequence, the output is a smoothed code pseudorange error sequence, which satisfies the Gaussian distribution of [0,σ _o ]. Usually, the code pseudo-range error after post-filtering can be reduced to 10% of that before filtering.

In step 4, the calculation method of the average lock-out time is: assuming that the probability density function of the output value ε of each tracking loop is p _k (ε), and the error limit of the tracking loop is ±θ _b , then the tracking loop can The number of stable tracking can be expressed as: The average lockout time can be calculated as Where T is the update time of the loop, which is generally equal to the pre-detection integration time T _s . In actual calculation, an upper limit of accumulation times is often taken, such as 10 ⁶ , the average lock-out time can actually be calculated by the following formula: The loop update time is selected as 20ms.

In step 5, the relationship between the frequency of navigation signal loss of lock and the average time of loss of lock is: Among them, T ₁ is the average lock-out time under normal conditions, T ₂ is the average lock-out time in the case of ionospheric scintillation, m is a fixed coefficient, and its value is related to the degree of ionospheric scintillation, here recorded as The frequency of ionospheric scintillation obeys the Poisson distribution statistically, and the calculation method of its distribution parameters is: λ ₀ =ρλ ^Nscin T _span , where N _scin is the number of satellites that lose tracking due to ionospheric scintillation at the same time, and here it is set to 2 , that is, for users under the GPS constellation, two of all visible satellites lose lock due to ionospheric scintillation at the same time, ρ is the correlation coefficient, and the value here is 0.5, and T _span is the flight time, which is 7200s. Assume that the reacquisition time of the navigation terminal's signal out of lock is T _reacq , where the value is 10s, then the time out of lock of the two satellite signals within the flight time is T _unlock =λ ₀ T _reacq =10λ ₀ .

In step 6, the starting moment and flight time of the flight are known, and the position of the user is set as P _u = [x, y, z], and the position P _s of the i-th satellite at this time can be calculated according to the almanac parameters of the satellite _,i =[ _xi ,y _i , _zi ], and then calculate the geometric parameter matrix H of visible satellites.

In step 7, under the operation requirements of LPV200, the distribution probability of integrity risk is 10 ^-7 /app, and the distribution probability of continuity risk is 10 ^-6 /15s, and the probability of missing detection is obtained by further calculation P _f is the prior probability of failure of a single satellite in a single constellation, here it is set to 10 ^-5 per hour. The false alarm probability is T _sample is the sampling time, that is, the output cycle of the continuity alarm, which is set to 120s here.

First calculate H _w =(H'PH) ^-1 H'P, where P is a weighting matrix, and its diagonal elements are the reciprocal variances of the measurement error residuals of each satellite. For the measurement error residual of the satellite, the model adopted in this method is:

where σ _ure is the satellite ephemeris and star clock error, which is set to 1 meter here, σ _o is calculated by step 3, σ _trop is the tropospheric residual, and σ _mp is the multipath error, expressed as:

Where θ is the elevation angle of the satellite in radians;

Where θ _deg is the elevation angle of the satellite in degrees.

but

Compare the HPL _slope and VPL _slope with the horizontal warning limit and the vertical warning limit respectively, if they are greater than the warning limit, the autonomous integrity of the navigation terminal is unavailable.

In step 8, when calculating the navigation protection level, firstly calculate △x=H _w △z, where △z is the residual error of the pseudo-range, which satisfies the Gaussian distribution [0, σ], and σ is the residual error of the satellite pseudo-range measurement. 7 is calculated. In general, the navigation protection level can be expressed as:

Horizontal Protection Level:

Vertical protection level: VPL＝|△x ₃ |+α ₂ ·du

For the running condition of LPV200, the value of α ₁ is 6, and the value of α ₂ is 5.33.

In step 9, compare the navigation protection level calculated each time with the warning limit, set the total number of comparisons as N ₁ , here is 7200, and the number of times the protection level is greater than the warning limit is N ₂ , then the availability calculation method is:

According to the operation requirements of LPV200, η needs to be greater than 99.999%.

The above are only specific application examples of the present invention, and do not constitute any limitation to the protection scope of the present invention. All technical solutions formed by equivalent transformation or equivalent replacement fall within the protection scope of the present invention.

Claims (7)

1. A method for aviation navigation performance prediction under ionospheric scintillation, characterized in that, the method steps are as follows: Step A, setting the amplitude scintillation and phase scintillation parameters of ionospheric scintillation, setting the type of navigation signal; Step B, establish the tracking loop model of the navigation receiver, and calculate the tracking code pseudo-range measurement error and carrier phase measurement error; Step C, performing post-filtering on the measured error to obtain the output measurement error of the navigation receiver; Step D, calculate the average lock-out time of the tracking loop according to the set ionospheric scintillation parameters and the established navigation receiver tracking loop model; Step E, establishing the correlation expression of the average out-of-lock time with respect to the interruption frequency of the navigation signal under ionospheric scintillation, and calculating the out-of-lock frequency of the navigation signal; Step F, calculate the position of the navigation satellite according to the user's flight trajectory and flight time, and obtain the geometric parameters of the satellite; Step G, according to the specific flight operation requirements, calculate the autonomous integrity monitoring availability prediction of the navigation terminal; Step H, calculate the navigation protection level during the flight, compare it with the navigation warning limit specified in the operation requirements, and judge whether it is available; Step I. According to the calculation result of the navigation performance parameters in the set time period, predict the navigation usability in the time period. 2. The method for predicting aviation navigation performance under ionospheric scintillation according to claim 1, characterized in that: in said step A: the amplitude scintillation parameter of ionospheric scintillation is S ₄ , and its value range is [0.1,2 ], the phase scintillation parameter is τ, and its value range is [0.1,1]. The navigation signal refers to the GNSS intermediate frequency digital signal, and the types include GPS, GALILEO, GLONASS and Beidou navigation signals. 3. the method for aviation navigation performance prediction under ionospheric scintillation according to claim 1, it is characterized in that: in the described step C: the post-filtering of code pseudo-range and carrier tracking quantity measurement adopts Kalman filter method, its state The equation is: in are the estimated pseudorange values at time k and k-1 respectively, φ _k and φ _k-1 are the carrier phase measurements at time k and k-1 respectively, and their measurement errors follow the Gaussian [0,σ _φ ] distributed; Its observation equation can be expressed as: Among them, ρ _k is the measurement of pseudo-range, and its measurement error w _k obeys the Gaussian distribution of [0,σ _τ ]. 4. the method for aviation navigation performance prediction under ionospheric scintillation according to claim 1, is characterized in that: in the described step D: assume that the probability density function of the output value ε of each tracking loop is p _k (ε) , the error limit of the tracking loop is ±θ _b , then the number of times the tracking loop can track stably can be expressed as: The average lockout time can be calculated as Where T is the update time of the loop, which is generally equal to the pre-detection integration time T _s . 5. the method for aviation navigation performance prediction under ionospheric scintillation according to claim 1, is characterized in that: in the described step E: ionospheric scintillation frequency obeys Poisson distribution statistically, and the calculation method of its distribution parameter is: λ ₀ ＝ρλ ^Nscin T _span , where N _scin is the number of satellites that lose track due to ionospheric scintillation at the same time, ρ is the correlation coefficient, which characterizes the correlation degree of the signal channels of N _scin satellites, T _span is the flight time, and the navigation The reacquisition time of the terminal's signal out of lock is T _reacq , and the out of lock time of N _scin satellite signals within the flight time is T _unlock =λ ₀ T _reacq . 6. The method for aviation navigation performance prediction under ionospheric scintillation according to claim 1, characterized in that: in the step F: the geometric parameters of the satellite can be described by matrix H, and [a _i1 a _i2 a _i3 ] are the unit vectors of the user and the i-th satellite in the northeast direction, and n is the total number of visible satellites. 7. the method for aviation navigation performance prediction under ionospheric scintillation according to claim 1, is characterized in that: in the described step 1: navigation usability judging method is: In a certain period of time, the navigation protection level calculated by unit time step is compared with the navigation warning limit in the operation demand. If the protection level is greater than the warning limit, the navigation is unavailable at this moment; The total number of times is N ₁ , and the number of times the protection level is greater than the warning limit is N ₂ , then the availability calculation method is: $\mathrm{<span\; class="notranslate">\; \&eta;</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; 100</span>}\mathrm{<span\; class="notranslate">\; \%</span>}<span\; class="notranslate">\; .</span>$