CN104050389A - Method for evaluating accuracy and completeness of navigation system in real time and on line - Google Patents

Abstract

The invention discloses a method for evaluating the accuracy and completeness of a navigation system in real time and on line. According to the characteristic of information fusion of the navigation system, based on the multi-dimensional Gaussian probability distribution characteristic of a covariance matrix and a Rayleigh probability distribution characteristic of an inclusion radius threshold, real-time on-line evaluation of the actual navigation accuracy and completeness of the navigation system can be achieved. The method for evaluating the accuracy and completeness of the navigation system in real time and on line is easy and convenient to operate, makes full use of filtering information of integrated navigation, largely improves the calculation speed, meets the requirement for real-time performance of monitoring the performance of the navigation system, and guarantees an enough confidence coefficient. The method can be realized in an engineering mode easily, meets the requirements for the navigation performance of each leg, and has great actual application significance.

Description

A kind of method of real-time online assessment navigation system accuracy and integrity

Technical field

The present invention relates to navigational system Performance Evaluation and surveillance technology field.

Background technology

Flight management system is the nucleus equipment of large aircraft avionics system, it is by providing integrated navigation function, performance management function, flight plan management function and the flight guidance function based on multisensor, comprehensive other system, such as navigational system, display system, robot pilot and autothrottle system, in whole flight process, auxiliary unit is realized the robotization of aerial mission and is controlled, and guarantees that aircraft flies automatically along the plan of expection, and meets the flying quality of Operational requirements.

Navigation feature is the basic function of flight management system, and it provides the optimum estimate of aircraft current state for aircraft.FMS uses sensor accuracy data, sensor raw data and current conditional information, select the best of breed of alignment sensor to reduce position fixing error, the best solution of estimating aircraft position and speed is provided, finally meets the required navigation performance of area navigation.

In order to ensure navigational system performance, meet desired properties requirement, have two keys, the one, in the budget of the required navigation performance index of design phase, another is the assessment of real-time actual navigation performance.For new navigation system, actual navigation performance is calculated in real time by navigational system, and it comprises the assessment that flies to manage degree of accuracy and the relevant integrity of calculating location to current.

Thales of the Honeywell Inc. of the U.S., HarperCollins, GE company and France has monopolized the avionics produce market of branch line, main line and commercial aircraft, grasp core technology and the development thereof of flight management system, on the types such as Air Passenger, Boeing, realizing already real-time calculating, supervision and the alarm of navigation performance.Our gap of internal and overseas is larger, although go back at present the goods shelf products that neither one is shaped, the paces of foreign technology development are catching up with always in domestic Ge great colleges and universities, institutes, have carried out a series of method research of guaranteeing navigational system precision and reliability.But the navigation desired properties requirement for how, carries out real-time online assessment to the actual navigation precision of navigational system and relevant integrity thereof, and domestic correlative study is very few.Patent CN103557872 is described the system ensemble error real-time computing technique in a kind of RNP, but only relate to a kind of computing method of navigation accuracy, do not mention the integrity of navigational system, more do not provide real-time online and assess the method whether integrity of navigational system meets the demands.

Summary of the invention

In order to solve, existing navigational system lacks navigation precision and integrity real-time online calculates and the problem of alarm ability, goal of the invention of the present invention is to provide a kind of method of real-time online assessment navigation system accuracy and integrity, by probability conversion, realize the real-time online of navigational system actual accuracy and integrity and assess, for civil aircraft operation meets each leg required navigation performance demand, provide technical guarantee.

Goal of the invention of the present invention is achieved through the following technical solutions:

A method for real-time online assessment navigation system accuracy and integrity, comprises following steps:

One, by inertial navigation system IRS and global position system GPS, gather desired parameters;

Two, according to the parameter of obtaining, set up state equation and the measurement equation of Kalman filter, state equation and measurement equation are carried out discretize operation time renewal and measure upgrading, obtain the covariance matrix P of Kalman filter _k, and obtain the estimation of navigational parameter;

Three, according to the characteristic of polynary Gaussian distribution, the covariance matrix of cutting apart Kalman filter, the Collision risk that obtains IRS/GPS integrated navigation system, the location criteria of asking for IRS/GPS integrated navigation system is poor, realizes the estimation of the actual navigation performance ANP of IRS/GPS navigational system degree of accuracy;

Four, according to the Rayleigh probability density characteristics that contains radius threshold value, 95% the containing radius of take is reference value, according to difference, contains the corresponding different multiplying of probability, carries out probability conversion, ask for the different containing radiuses that contain under probability demands, realize the estimation of the actual navigation of navigational system integrity.

According to above-mentioned feature, described parameter comprises:

(1.1) with cycle Δ T, read three attitude angle, three positions, three velocity informations, three angular velocity informations and three linear acceleration information of inertial navigation system IRS output, three attitude angle information are respectively pitching angle theta, roll angle φ, crab angle ψ; Three positional informations are respectively longitude L, latitude λ, height h; Three velocity informations are respectively the east orientation speed v under geographic coordinate system _e, north orientation speed v _n, day to speed v _u, three angular velocity informations component under body system that is body axis system with respect to the angular velocity of inertial space three linear acceleration information are the lower specific force information f of body system ^b, wherein the sensing of the x-axis, y-axis and z-axis of body axis system is respectively to the right, forward, downwards;

(1.2) with cycle Δ T, read the pseudorange ρ of global position system GPS output _ginformation.

According to above-mentioned feature, described step 2 specifically comprises following steps:

(2.1) with inertial navigation system IRS, take boat system as the leading factor, take global position system GPS as secondary navigation system, attitude error, velocity error, site error, inertia type instrument error and the global position system GPS clocking error of choosing inertial navigation system IRS are quantity of state, set up the state equation of Kalman filter:

${\stackrel{\·}{x}}_{\mathrm{KF}}=F_{\mathrm{KF}}{x}_{\mathrm{KF}}+w_{\mathrm{KF}},$

In formula $F_{\mathrm{KF}}=\left[\begin{array}{ccccccc}-\left({\mathrm{\ω}}_{\mathrm{in}}^n\right)\×& F_{v2\mathrm{\φ}}& 0_{3\×3}& -C_b^n& 0_{3\×3}& 0& 0\\ \left(C_b^n{f}^b\right)\×& F_{v2v}& 0_{3\×3}& 0_{3\×3}& C_b^n& 0& 0\\ 0_{3\×3}& F_{v2p}& F_{p2p}& 0_{3\×3}& 0_{3\×3}& 0& 0\\ 0_{3\×3}& 0_{3\×3}& 0_{3\×3}& 0_{3\×3}& 0_{3\×3}& 0& 0\\ 0_{3\×3}& 0_{3\×3}& 0_{3\×3}& 0_{3\×3}& 0_{3\×3}& 0& 0\\ 0_{1\×3}& 0_{1\×3}& 0_{1\×3}& 0_{1\×3}& 0_{1\×3}& 0& 1\\ 0_{1\×3}& 0_{1\×3}& 0_{1\×3}& 0_{1\×3}& 0_{1\×3}& 0& -{\mathrm{\β}}_{\mathrm{tru}}\end{array}\right],$ W _kFfor system white noise, wherein $F_{v2\mathrm{\φ}}=\left[\begin{array}{ccc}0& -1/(R_M+h)& 0\\ 1/(R_N+h)& 0& 0\\ \tan L/(R_N+h)& 0& 0\end{array}\right],$ $F_{v2v}=(v^n\×)F_{v2\mathrm{\φ}}-({2\mathrm{\ω}}_{\mathrm{ie}}^n+{\mathrm{\ω}}_{\mathrm{en}}^n)\×,$

$F_{v2p}=\left[\begin{array}{ccc}0& \frac{1}{R_M+h}& 0\\ \frac{1}{(R_N+h)\cos L}& 0& 0\\ 0& 0& 1\end{array}\right],$ $F_{p2p}=\left[\begin{array}{ccc}0& 0& -\frac{v_N}{{(R_N+h)}^2}\\ \frac{v_E\sin L}{(R_N+h){\cos }^{2}L}& 0& -\frac{v_E}{{(R_N+h)}^2\cos L}\\ 0& 0& 0\end{array}\right],$

for body is tied to the attitude matrix of Department of Geography, f ^bfor specific force, for instruction angular speed, for the component of rotational-angular velocity of the earth under Department of Geography, for Department of Geography is the projection of angular velocity under Department of Geography with respect to the earth, with all can be according to attitude matrix, positional information and ask for v ⁿfor velocity under geographic coordinate system, R _mand R _nbe respectively radius of curvature of meridian and radius of curvature in prime vertical, the computing of * expression multiplication cross;

(2.2) choose global position system GPS pseudorange information and the difference of the pseudorange that calculates according to inertial navigation system IRS information as measurement amount, set up the measurement equation of Kalman filter:

z _KF＝H _KFx _KF+v _KF，

H wherein _kFfor measuring battle array, v _kFmeasurement noise for pseudorange information;

(2.3) by state equation with measurement equation z _kF=H _kFx _kF+ v _kFcarry out discretize, obtain following form: $\left\{\begin{array}{c}{x}_k={\mathrm{\Φ}}_{k,k-1}{x}_{k-1}+w_{k-1}\\ z_k=H_k{x}_k+v_k\end{array}\right.,$

X wherein _kfor t _kstate value constantly, Φ _{k, k-1}for t _k-1to t _kmatrix of shifting of a step, w _k-1for system noise acoustic matrix, z _kfor t _kmeasuring value constantly, H _kfor measuring battle array, v _kfor measurement noise;

(2.4) carry out IRS/GPS filtering renewal, be specially:

Time upgrades:

${\hat{x}}_{k|k-1}={\mathrm{\Φ}}_{k,k-1}{\hat{x}}_{k-1}$

$P_{k|k-1}={\mathrm{\Φ}}_{k,k-1}{P}_{k-1}{\mathrm{\Φ}}_{k,k-1}^T+Q_{k-1}$

Measure and upgrade:

$K_k=P_{k|k-1}{H}_k^T{[H_k{P}_{k|k-1}{H}_k^T+R_k]}^{-1}$

${\hat{x}}_k={\hat{x}}_{k|k-1}+K_k[z_k-H_k{\hat{x}}_{k|k-1}]$

P _k＝[I-K _kH _k]P _k|k-1

Wherein, t _kfor the current filtering moment, for t _k-1state optimization filter value constantly, for t _kthe one-step prediction value of moment quantity of state, P _k|k-1for t _kthe variance battle array of state one-step prediction constantly, K _kfor t _kfilter gain matrix constantly, for t _kstate optimization filter value constantly, its filtering error variance battle array is P _k, Q _k-1and R _kbe respectively system noise w _k-1with measurement noise v _kvariance battle array;

(2.5), according to the IRS information of obtaining in step 1 and the GPS information of obtaining, by the time of filtering equations, upgrade and measure and upgrade, and then obtain taking as the leading factor with IRS the optimal estimation of the quantity of state of boat system ? ${\hat{x}}_{\mathrm{KF}}=[{\hat{x}}_{\mathrm{NAV}};{\hat{x}}_{\mathrm{IMU}};{\hat{x}}_{\mathrm{GPS}}].$

According to above-mentioned feature, the concrete steps of described step 3 are:

(3.1), according to the characteristic of polynary Gaussian distribution, cut apart the covariance matrix P of Kalman filter _k, obtain the component of position estimation error in surface level, i.e. longitude error δ λ and latitude error δ φ;

(3.2) longitude and latitude error is converted into the straight line error (x, y) in surface level, $\left\{\begin{array}{c}x=\mathrm{\δ\λ}\·R\cos \mathrm{\φ}\\ y=\mathrm{\δ\φ}\·R\end{array}\right.,$ Wherein R is earth radius, and φ is aircraft place latitude;

(3.3) site error E in note surface level _pos=[x y], the Collision risk P of structure IRS/GPS integrated navigation system _pos, P _pos=Cov[E _pos];

(3.4) ask for Collision risk P _pos2 eigenvalue λ _1,2, λ wherein _1,2be respectively the major semi-axis σ of 1 σ error ellipse _majorwith minor semi-axis σ _minor;

(3.5) according to the major semi-axis σ of 1 σ error ellipse _major, ask for actual navigation performance ANP precision: ANP=2.45 * σ _major;

(3.6) when actual navigation performance ANP precision surpasses required navigation performance RNP precision, airborne navigational system sends warning information, and prompting navigation accuracy does not meet the demands.

According to above-mentioned feature, the concrete steps of described step 4 are:

(4.1) the containing radius r of estimation 95% _acc=2.45 * (0.5 * (σ _major+ σ _minor));

(4.2) according to the corresponding relation between multiplying power factor x and containing Probability p, ask for the different containing radiuses that contain under probability demands: r _cs=xr _acc;

(4.3) when containing radius r _csbe greater than while containing limit value (2 * RNP), airborne navigational system sends alarm, and prompting navigation integrity does not meet the demands.

Advantage of the present invention and remarkable result: the feature that the present invention is directed to inertia/GPS information fusion, designed more new architecture of a kind of inertia/GPS based on Kalman filtering, the Rayleigh probability density characteristics of the multidimensional gaussian probability distribution character based on covariance matrix and containing radius threshold value, by probability, change, can realize the real-time online of the actual navigation precision of navigational system and integrity is estimated.The inventive method is easy, makes full use of the filtering information of inertia/GPS combination, has greatly promoted arithmetic speed, meets the real-time demand of navigational system performance monitoring, and guarantees enough degree of confidence.This inventive method is a kind of method that is easy to Project Realization, for large aircraft, at civil area, flies, and the required navigation performance that meets each leg requires to have important real world applications meaning.

Accompanying drawing explanation

Fig. 1 is the workflow schematic diagram of the inventive method;

Fig. 2 is ANP degree of accuracy estimation flow in the inventive method;

Fig. 3 is ANP integrity estimation flow in the inventive method.

Embodiment

Below in conjunction with accompanying drawing, technical scheme of the present invention is elaborated:

The present invention is directed to the feature of inertia/GPS information fusion, designed more new architecture of a kind of inertia/GPS based on Kalman filtering, the Rayleigh probability density characteristics of the multidimensional gaussian probability distribution character based on covariance matrix and containing radius threshold value, by probability, change, can realize the real-time online of the actual navigation precision of navigational system and integrity is estimated.Specifically comprise the following steps:

One, by inertial navigation system IRS and global position system GPS, gather desired parameters

(1.1) with cycle Δ T, read three attitude angle, three positions, three velocity informations, three angular velocity informations and three linear acceleration information of inertial navigation system IRS output, three attitude angle information are respectively pitching angle theta, roll angle φ, crab angle ψ; Three positional informations are respectively longitude L, latitude λ, height h; Three velocity informations are respectively the east orientation speed v under geographic coordinate system _e, north orientation speed v _n, day to speed v _u, three angular velocity informations component under body system that is body axis system with respect to the angular velocity of inertial space three linear acceleration information are the lower specific force information f of body system ^b, wherein the sensing of the x-axis, y-axis and z-axis of body axis system is respectively to the right, forward, downwards.

(1.2) with cycle Δ T, read the pseudorange ρ of global position system GPS output _ginformation.

Two, utilize Kalman filter to realize the optimal estimation step of IRS/GPS integrated navigation parameter:

With IRS, take boat system as the leading factor, take GPS as secondary navigation system, attitude error, velocity error, site error, inertia type instrument error and the gps clock error of choosing IRS are quantity of state, set up the state equation of Kalman filtering, the difference of the pseudorange of choosing GPS measurement pseudorange and calculating according to IRS information is as measurement amount, set up the measurement variance of Kalman filter, thereby build the combined Kalman filter KF of IRS/GPS; According to the IRS information of obtaining in step 1 and the GPS information of obtaining, obtain the optimal estimation of navigational parameter

The Kalman filtering implement body of described step 2 comprises the following steps:

(2.1) foundation of IRS/GPS filter state equation

The 17 dimension quantity of state x of structure Kalman filter KF _kF=[x _nAV; x _iMU; x _gPS], it is comprised of three parts, comprises IRS navigational parameter error $x_{\mathrm{NAV}}={\left[\begin{array}{ccccc}{\left({\mathrm{\φ}}^n\right)}^T& {\left({\mathrm{\δv}}^n\right)}^T& \mathrm{\δL}& \mathrm{\δ\λ}& \mathrm{\δh}\end{array}\right]}^T,$ Inertia type instrument error and gps clock error x _gPS=[δ t _uδ t _ru] ^t, wherein, φ ⁿthree attitude errors, δ v for IRS ⁿfor the velocity error of lower three directions of Department of Geography of IRS, latitude error that δ L is IRS, latitude error that δ λ is IRS, height error that δ h is IRS, for the gyro of IRS under body system three axial constant value drifts, accelerometer three axial normal value biased error, δ t under body system for IRS _uequivalent clocking error, δ t for GPS _ruequivalent clock frequency error for GPS;

And then set up the state equation of KF:

${\stackrel{\·}{x}}_{\mathrm{KF}}=F_{\mathrm{KF}}{x}_{\mathrm{KF}}+w_{\mathrm{KF}}$

In formula $F_{\mathrm{KF}}=\left[\begin{array}{ccccccc}-\left({\mathrm{\ω}}_{\mathrm{in}}^n\right)\×& F_{v2\mathrm{\φ}}& 0_{3\×3}& -C_b^n& 0_{3\×3}& 0& 0\\ \left(C_b^n{f}^b\right)\×& F_{v2v}& 0_{3\×3}& 0_{3\×3}& C_b^n& 0& 0\\ 0_{3\×3}& F_{v2p}& F_{p2p}& 0_{3\×3}& 0_{3\×3}& 0& 0\\ 0_{3\×3}& 0_{3\×3}& 0_{3\×3}& 0_{3\×3}& 0_{3\×3}& 0& 0\\ 0_{3\×3}& 0_{3\×3}& 0_{3\×3}& 0_{3\×3}& 0_{3\×3}& 0& 0\\ 0_{1\×3}& 0_{1\×3}& 0_{1\×3}& 0_{1\×3}& 0_{1\×3}& 0& 1\\ 0_{1\×3}& 0_{1\×3}& 0_{1\×3}& 0_{1\×3}& 0_{1\×3}& 0& -{\mathrm{\β}}_{\mathrm{tru}}\end{array}\right],$ W _kFfor system white noise, wherein $F_{v2\mathrm{\φ}}=\left[\begin{array}{ccc}0& -1/(R_M+h)& 0\\ 1/(R_N+h)& 0& 0\\ \tan L/(R_N+h)& 0& 0\end{array}\right],$ $F_{v2v}=(v^n\×)F_{v2\mathrm{\φ}}-({2\mathrm{\ω}}_{\mathrm{ie}}^n+{\mathrm{\ω}}_{\mathrm{en}}^n)\×,$

$F_{v2p}=\left[\begin{array}{ccc}0& \frac{1}{R_M+h}& 0\\ \frac{1}{(R_N+h)\cos L}& 0& 0\\ 0& 0& 1\end{array}\right],$ $F_{p2p}=\left[\begin{array}{ccc}0& 0& -\frac{v_N}{{(R_N+h)}^2}\\ \frac{v_E\sin L}{(R_N+h){\cos }^{2}L}& 0& -\frac{v_E}{{(R_N+h)}^2\cos L}\\ 0& 0& 0\end{array}\right],$

for body is tied to the attitude matrix of Department of Geography, f ^bfor specific force, for instruction angular speed, for the component of rotational-angular velocity of the earth under Department of Geography, for Department of Geography is the projection of angular velocity under Department of Geography with respect to the earth, with all can be according to attitude matrix, positional information and ask for v ⁿfor velocity under geographic coordinate system, R _mand R _nbe respectively radius of curvature of meridian and radius of curvature in prime vertical, the computing of * expression multiplication cross;

(2.2) foundation of IRS/GPS filtering measurement equation

GPS is measured to pseudorange information ρ _gwith the pseudorange information ρ that utilizes IRS information to calculate _idifference as measurement, measure z _kF=ρ _g-ρ _i, and then set up the state quantity measurement equation z of Kalman filter KF _kF=H _kFx _kF+ v _kF, H wherein _kFfor measuring battle array, v _kFmeasurement noise for pseudorange information.

(2.3) IRS/GPS filtering equations discretize

By state equation with measurement equation z _kF=H _kFx _kF+ v _kFcarry out discretize, obtain following form: $\left\{\begin{array}{c}{x}_k={\mathrm{\Φ}}_{k,k-1}{x}_{k-1}+w_{k-1}\\ z_k=H_k{x}_k+v_k\end{array}\right.$

X wherein _kfor t _kstate value constantly, Φ _{k, k-1}for t _k-1to t _kmatrix of shifting of a step, w _k-1for system noise acoustic matrix, z _kfor t _kmeasuring value constantly, H _kfor measuring battle array, v _kfor measurement noise.

(2.4) IRS/GPS filtering is upgraded

Time upgrades

${\hat{x}}_{k|k-1}={\mathrm{\Φ}}_{k,k-1}{\hat{x}}_{k-1}$

$P_{k|k-1}={\mathrm{\Φ}}_{k,k-1}{P}_{k-1}{\mathrm{\Φ}}_{k,k-1}^T+Q_{k-1}$

Measure and upgrade

$K_k=P_{k|k-1}{H}_k^T{[H_k{P}_{k|k-1}{H}_k^T+R_k]}^{-1}$

${\hat{x}}_k={\hat{x}}_{k|k-1}+K_k[z_k-H_k{\hat{x}}_{k|k-1}]$

P _k＝[I-K _kH _k]P _k|k-1

Wherein, t _kfor the current filtering moment, for t _k-1state optimization filter value constantly, for t _kthe one-step prediction value of moment quantity of state, P _k|k-1for t _kthe variance battle array of state one-step prediction constantly, K _kfor t _kfilter gain matrix constantly, for t _kstate optimization filter value constantly, its filtering error variance battle array is P _k, Q _k-1and R _kbe respectively system noise w _k-1with measurement noise v _kvariance battle array.

According to the IRS information of obtaining in step 1 and the GPS information of obtaining, by the time of filtering equations, upgrade and measure and upgrade, and then obtain taking as the leading factor with IRS the optimal estimation of the quantity of state of boat system ? ${\hat{x}}_{\mathrm{KF}}=[{\hat{x}}_{\mathrm{NAV}};{\hat{x}}_{\mathrm{IMU}};{\hat{x}}_{\mathrm{GPS}}].$

Three, based on polynary Gaussian distribution characteristic, realize the step that actual navigation performance ANP degree of accuracy is estimated:

According to the characteristic of polynary Gaussian distribution, cut apart the covariance matrix P of Kalman filter _k, the Collision risk P of acquisition IRS/GPS integrated navigation system _pos, ask for the poor λ of location criteria of IRS/GPS integrated navigation system _1,2thereby, realize the estimation of the actual navigation precision ANP of IRS/GPS navigational system, according to the requirement of required navigation performance RNP, whether assessment degree of accuracy meets the demands.

The ANP degree of accuracy of described step 3 is estimated specifically to comprise the following steps:

(3.1) cut apart IRS/GPS filtering covariance matrix

The covariance matrix P of cutting apart Kalman filter _k, obtain the component of position estimation error in surface level, i.e. longitude error δ λ and latitude error δ φ;

(3.2) conversion longitude and latitude error

Longitude and latitude error is converted into the straight line error (x, y) in surface level, $\left\{\begin{array}{c}x=\mathrm{\δ\λ}\·R\cos \mathrm{\φ}\\ y=\mathrm{\δ\φ}\·R\end{array}\right.,$ Wherein R is earth radius, and φ is aircraft place latitude;

(3.3) build Collision risk

Site error E in note surface level _pos=[x y], the Collision risk P of structure IRS/GPS integrated navigation system _pos, P _pos=Cov[E _pos];

(3.4) ask for the eigenwert of error matrix

Ask for Collision risk P _pos2 eigenvalue λ _1,2, λ wherein _1,2be respectively the major semi-axis σ of 1 σ error ellipse _majorwith minor semi-axis σ _minor;

(3.5) ask for ANP degree of accuracy

According to the major semi-axis σ of 1 σ error ellipse _major, ask for ANP, ANP=2.45 * σ _major;

(3.6) navigation system accuracy alarm

When ANP surpasses RNP, airborne navigational system sends warning information, and prompting navigation accuracy does not meet the demands.

Four, the Rayleigh probability density characteristics based on containing radius threshold value is realized the step that ANP integrity is estimated:

According to the Rayleigh probability density characteristics that contains radius threshold value, 95% the containing radius of take is reference value, according to difference, contains the corresponding r of probability _accdifferent multiplying, carries out probability conversion, asks for the different containing radiuses that contain under probability demands, realizes the estimation of the actual navigation of navigational system integrity, and according to containing limit value requirement, whether assessment integrity meets the demands.

The ANP integrity of described step 4 is estimated specifically to comprise the following steps:

(4.1) ask for 95% containing radius

Estimate 95% containing radius r _acc=2.45 * (0.5 * (σ _major+ σ _minor));

(4.2) ask for the different containing radiuses that contain under probability demands

According to the mapping table 1 between multiplying power factor x and containing Probability p, ask for the different containing radiuses that contain under probability demands: r _cs=xr _acc;

Multiplying power x	Probability p
		2.4	0.999999968
2.32	0.9999999
		2.15	0.999999
2.00	0.99999375
		1.96	0.99999
1.75	0.9999
		1.52	0.999
1.24	0.99
		1.00	0.95
0.88	0.9

Table 1

(4.3) navigational system integrity alarm

When containing radius r _csbe greater than while containing limit value (2 * RNP), airborne navigational system sends alarm, and prompting navigation integrity does not meet the demands.

Claims (5)

1. real-time online is assessed a method for navigation system accuracy and integrity, comprises following steps:

One, by inertial navigation system IRS and global position system GPS, gather desired parameters;

Two, according to the parameter of obtaining, set up state equation and the measurement equation of Kalman filter, state equation and measurement equation are carried out discretize operation time renewal and measure upgrading, obtain the covariance matrix P of Kalman filter KF _k, and obtain the estimation of navigational parameter;

Three, according to the characteristic of polynary Gaussian distribution, the covariance matrix of cutting apart Kalman filter KF, obtain the Collision risk of IRS/GPS integrated navigation system, the location criteria of asking for IRS/GPS integrated navigation system is poor, realizes the estimation of the actual navigation performance ANP of IRS/GPS navigational system degree of accuracy;

Four, according to the Rayleigh probability density characteristics that contains radius threshold value, 95% the containing radius of take is reference value, according to difference, contains the corresponding different multiplying of probability, carries out probability conversion, ask for the different containing radiuses that contain under probability demands, realize the estimation of the actual navigation of navigational system integrity.

2. a kind of real-time online according to claim 1 is assessed the method for navigation system accuracy and integrity, it is characterized in that described parameter comprises:

(1.1) with cycle Δ T, read three attitude angle, three positions, three velocity informations, three angular velocity informations and three linear acceleration information of inertial navigation system IRS output, three attitude angle information are respectively pitching angle theta, roll angle φ, crab angle ψ; Three positional informations are respectively longitude L, latitude λ, height h; Three velocity informations are respectively the east orientation speed v under geographic coordinate system _e, north orientation speed v _n, day to speed v _u, three angular velocity informations component under body system that is body axis system with respect to the angular velocity of inertial space three linear acceleration information are the lower specific force information f of body system ^b, wherein the sensing of the x-axis, y-axis and z-axis of body axis system is respectively to the right, forward, downwards;

(1.2) with cycle Δ T, read the pseudorange ρ of global position system GPS output _ginformation.

3. a kind of real-time online according to claim 1 is assessed the method for navigation system accuracy and integrity, it is characterized in that described step 2 specifically comprises following steps:

(2.1) with inertial navigation system IRS, take boat system as the leading factor, take global position system GPS as secondary navigation system, attitude error, velocity error, site error, inertia type instrument error and the global position system GPS clocking error of choosing inertial navigation system IRS are quantity of state, set up the state equation of Kalman filter:

${\stackrel{\·}{x}}_{\mathrm{KF}}=F_{\mathrm{KF}}{x}_{\mathrm{KF}}+w_{\mathrm{KF}},$

In formula $F_{\mathrm{KF}}=\left[\begin{array}{ccccccc}-\left({\mathrm{\ω}}_{\mathrm{in}}^n\right)\×& F_{v2\mathrm{\φ}}& 0_{3\×3}& -C_b^n& 0_{3\×3}& 0& 0\\ \left(C_b^n{f}^b\right)\×& F_{v2v}& 0_{3\×3}& 0_{3\×3}& C_b^n& 0& 0\\ 0_{3\×3}& F_{v2p}& F_{p2p}& 0_{3\×3}& 0_{3\×3}& 0& 0\\ 0_{3\×3}& 0_{3\×3}& 0_{3\×3}& 0_{3\×3}& 0_{3\×3}& 0& 0\\ 0_{3\×3}& 0_{3\×3}& 0_{3\×3}& 0_{3\×3}& 0_{3\×3}& 0& 0\\ 0_{1\×3}& 0_{1\×3}& 0_{1\×3}& 0_{1\×3}& 0_{1\×3}& 0& 1\\ 0_{1\×3}& 0_{1\×3}& 0_{1\×3}& 0_{1\×3}& 0_{1\×3}& 0& -{\mathrm{\β}}_{\mathrm{tru}}\end{array}\right],$ W _kFfor system white noise, wherein $F_{v2\mathrm{\φ}}=\left[\begin{array}{ccc}0& -1/(R_M+h)& 0\\ 1/(R_N+h)& 0& 0\\ \tan L/(R_N+h)& 0& 0\end{array}\right],$ $F_{v2v}=(v^n\×)F_{v2\mathrm{\φ}}-({2\mathrm{\ω}}_{\mathrm{ie}}^n+{\mathrm{\ω}}_{\mathrm{en}}^n)\×,$

$F_{v2p}=\left[\begin{array}{ccc}0& \frac{1}{R_M+h}& 0\\ \frac{1}{(R_N+h)\cos L}& 0& 0\\ 0& 0& 1\end{array}\right],$ $F_{p2p}=\left[\begin{array}{ccc}0& 0& -\frac{v_N}{{(R_N+h)}^2}\\ \frac{v_E\sin L}{(R_N+h){\cos }^{2}L}& 0& -\frac{v_E}{{(R_N+h)}^2\cos L}\\ 0& 0& 0\end{array}\right],$

for body is tied to the attitude matrix of Department of Geography, f ^bfor specific force, for instruction angular speed, for the component of rotational-angular velocity of the earth under Department of Geography, for Department of Geography is the projection of angular velocity under Department of Geography with respect to the earth, with all can be according to attitude matrix, positional information and ask for v ⁿfor velocity under geographic coordinate system, R _mand R _nbe respectively radius of curvature of meridian and radius of curvature in prime vertical, the computing of * expression multiplication cross;

(2.2) choose global position system GPS pseudorange information and the difference of the pseudorange that calculates according to inertial navigation system IRS information as measurement amount, set up the measurement equation of Kalman filter:

z _KF＝H _KFx _KF+v _KF，

H wherein _kFfor measuring battle array, v _kFmeasurement noise for pseudorange information;

(2.3) by state equation with measurement equation z _kF=H _kFx _kF+ v _kFcarry out discretize, obtain following form: $\left\{\begin{array}{c}{x}_k={\mathrm{\Φ}}_{k,k-1}{x}_{k-1}+w_{k-1}\\ z_k=H_k{x}_k+v_k\end{array}\right.,$

X wherein _kfor t _kstate value constantly, Φ _{k, k-1}for t _k-1to t _kmatrix of shifting of a step, w _k-1for system noise acoustic matrix, z _kfor t _kmeasuring value constantly, H _kfor measuring battle array, v _kfor measurement noise;

(2.4) carry out IRS/GPS filtering renewal, be specially:

Time upgrades:

${\hat{x}}_{k|k-1}={\mathrm{\Φ}}_{k,k-1}{\hat{x}}_{k-1},$

$P_{k|k-1}={\mathrm{\Φ}}_{k,k-1}{P}_{k-1}{\mathrm{\Φ}}_{k,k-1}^T+Q_{k-1};$

Measure and upgrade:

$K_k=P_{k|k-1}{H}_k^T{[H_k{P}_{k|k-1}{H}_k^T+R_k]}^{-1},$

${\hat{x}}_k={\hat{x}}_{k|k-1}+K_k[z_k-H_k{\hat{x}}_{k|k-1}],$

P _k＝[I-K _KH _K]P _k|k-1，

Wherein, t _kfor the current filtering moment, for t _k-1state optimization filter value constantly, for t _kthe one-step prediction value of moment quantity of state, P _k|k-1for t _kthe variance battle array of state one-step prediction constantly, K _kfor t _kfilter gain matrix constantly, for t _kstate optimization filter value constantly, its filtering error variance battle array is P _k, Q _k-1and R _kbe respectively system noise w _k-1with measurement noise v _kvariance battle array;

(2.5), according to the IRS information of obtaining in step 1 and the GPS information of obtaining, by the time of filtering equations, upgrade and measure and upgrade, and then obtain taking as the leading factor with IRS the optimal estimation of the quantity of state of boat system ? ${\hat{x}}_{\mathrm{KF}}=[{\hat{x}}_{\mathrm{NAV}};{\hat{x}}_{\mathrm{IMU}};{\hat{x}}_{\mathrm{GPS}}].$

4. a kind of real-time online according to claim 1 is assessed the method for navigation system accuracy and integrity, it is characterized in that: the concrete steps of described step 3 are:

(3.1), according to the characteristic of polynary Gaussian distribution, cut apart the covariance matrix P of Kalman filter _k, obtain the component of position estimation error in surface level, i.e. longitude error δ λ and latitude error δ φ;

(3.2) longitude and latitude error is converted into the straight line error (x, y) in surface level, $\left\{\begin{array}{c}x=\mathrm{\δ\λ}\·R\cos \mathrm{\φ}\\ y=\mathrm{\δ\φ}\·R\end{array}\right.,$ Wherein R is earth radius, and φ is aircraft place latitude;

(3.3) site error E in note surface level _pos=[x y], the Collision risk P of structure IRS/GPS integrated navigation system _pos, P _pos=Cov[E _pos];

(3.4) ask for Collision risk P _pos2 eigenvalue λ _1,2, λ wherein _1,2be respectively the major semi-axis σ of 1 σ error ellipse _majorwith minor semi-axis σ _minor;

(3.5) according to the major semi-axis σ of 1 σ error ellipse _major, ask for actual navigation performance ANP precision: ANP=2.45 * σ _major;

(3.6) when actual navigation performance ANP precision surpasses required navigation performance RNP precision, airborne navigational system sends warning information, and prompting navigation accuracy does not meet the demands.

5. a kind of real-time online as claimed in claim 1 is assessed the method for navigation system accuracy and integrity, it is characterized in that: the concrete steps of described step 4 are:

(4.1) the containing radius r of estimation 95% _acc=2.45 * (0.5 * (σ _major+ σ _minor));

(4.2) according to the corresponding relation between multiplying power factor x and containing Probability p, ask for the different containing radiuses that contain under probability demands: r _cs=xr _acc;

(4.3) when containing radius r _csbe greater than while containing limit value (2 * RNP), airborne navigational system sends alarm, and prompting navigation integrity does not meet the demands.