CN102565813A - Method and device for performing pseudorange observation estimation by carrier smoothing - Google Patents

Abstract

The invention provides a method and a device for performing pseudorange observation estimation by carrier smoothing. The method comprises the following steps: respectively getting a pseudorange and carrier phase observation quantity of each of n frequency points, wherein n is an integer which is not less than 2; simultaneously performing carrier smoothing pseudorange operation on all the frequency points to get the pseudoranges after smoothing; enabling the pseudoranges after smoothing of the multiple frequency points to constitute a measurement equation; and performing value estimation according to the measurement equation and taking the obtained estimated value of r as the estimated value of pseudorange observation quantity. According to the method and the device, on the basis of greatly reducing multi-path and measuring noise, the influence of an ionized layer is eliminated, and the pseudorange estimation precision is further significantly improved.

Description

A kind ofly carry out pseudo range observed quantity estimation approach and device through carrier smoothing

Technical field

The present invention relates to navigation field, be specifically related to a kind ofly carry out pseudo range observed quantity estimation approach and device through carrier smoothing.

Background technology

The speed that ripple is propagated in a kind of medium depends on the refractive index of this medium.Refractive index n be defined as ripple free space velocity of propagation c with at the ratio of medium medium velocity v.For the electromagnetic wave of GNSS (GlobalNavigation Satellite System, GLONASS) emission, with light velocity propagation, the velocity of propagation in ionosphere and troposphere is not equal to the light velocity in free space.

Refractive index: n=c/v (1)

If the refractive index of ripple in a kind of medium is unfixing, but the function of frequency f, then this medium is chromatic dispersion for this ripple.For the electromagnetic wave of L-band, ionosphere is dispersive medium, and the troposphere is a nondispersive medium.In dispersive medium, velocity of propagation (the phase velocity v of signal carrier phase _p) velocity of propagation (the group velocity v of the signal message that carried with ripple _g) unequal.

n _p＝c/v _p v _g＝c/v _g (2)

Group index n _gWith refractive index n mutually _pRelation (can be referring to Hofmann-Wellenhof, B., H.Lichtenegger, and J.Collins, GPS Theory and Practice, New York:Springer-Verlag, 1993) as follows:

$n_g=n_p+f\frac{{\mathrm{dn}}_p}{\mathrm{df}}---\left(3\right)$

The expression formula of ionosphere phase refractive index is:

$n_p=1+\frac{c_2}{f^2}+\frac{c_3}{f^3}+\frac{c_4}{f^4}...---\left(4\right)$

Can know that by relational expression 3 group index is:

$n_g=1-\frac{c_2}{f^2}-\frac{2c_3}{f^3}-\frac{3c_4}{f^4}...---\left(5\right)$

Obtain after ignoring higher order term:

$n_p=1+\frac{c_2}{f^2}$ $n_g=1-\frac{c_2}{f^2}$ c ₂＝-40.3n _e (6)

n _eBe the ionospheric refraction rate.

Be respectively apart from l and measured value (pseudorange) S thereof between satellite SV and receiver user User:

$l={\∫}_{\mathrm{SV}}^{\mathrm{User}}\mathrm{ds}$ $S={\∫}_{\mathrm{SV}}^{\mathrm{User}}\mathrm{nds}---\left(7\right)$

Anaclastic measuring error is:

$\mathrm{\Δ}{S}_{\mathrm{ion}}={\∫}_{\mathrm{SV}}^{\mathrm{User}}\mathrm{nds}-{\∫}_{\mathrm{SV}}^{\mathrm{User}}\mathrm{ds}---\left(8\right)$

Therefore, reflecting the error of on carrier phase and pseudo range observed quantity, introducing is respectively:

$\mathrm{\Δ}{S}_{\mathrm{ion},p}=-\frac{40.3}{f^2}{\∫}_{\mathrm{SV}}^{\mathrm{User}}{n}_e\mathrm{ds}$ $\mathrm{\Δ}{S}_{\mathrm{ion},g}=\frac{40.3}{f^2}{\∫}_{\mathrm{SV}}^{\mathrm{User}}{n}_e\mathrm{ds}---\left(9\right)$

Electron density along the electromagnetic wave propagation path is called total electron content, is defined as:

$\mathrm{TEC}={\∫}_{\mathrm{SV}}^{\mathrm{User}}{n}_e\mathrm{ds}---\left(10\right)$

Formula 9 can be rewritten as:

$\mathrm{\Δ}{S}_{\mathrm{ion},p}=-\frac{40.3}{f^2}\mathrm{TEC}$ $\mathrm{\Δ}{S}_{\mathrm{ion},g}=\frac{40.3}{f^2}\mathrm{TEC}---\left(11\right)$

Can draw to draw a conclusion based on above quantitative test: the error that ionospheric refraction is introduced carrier phase measurement is leading, then is to lag behind to pseudorange, but its absolute value equates, with square being inversely proportional to of frequency, is directly proportional with TEC.Theoretically, the scattering effect of utilizing frequency to cause possibly estimate TEC, utilizes TEC and frequency can obtain the range error at each frequency again.

Can know that by the analysis of preceding text ionosphere time-delay is the function of frequency, theoretically, the GPS-L1 of dual-frequency receiver output and L2 frequency pseudo range observed quantity carried out calculus of differences can eliminate its influence fully.The expression formula of pseudorange P is following:

P＝ρ+dρ+c(dt-dT)+ΔS _ion，g+ΔS _trop，g+ε _P (12)

For the pseudo range observed quantity of L1 and two frequencies of L2, very apart from ρ, satellite orbital error d ρ, satellite clock correction dt, receiver clock correction dT and troposphere time-delay Δ S _{Trop, g}Equate relation below the ionosphere time-delay is satisfied:

f _L1 ²ΔS _ion，g，L1＝f _L2 ²ΔS _ion，g，L2 (13)

Measure noise and multipath ε _PBetween two frequencies, do not have definite relation, therefore be modeled as noise jointly.According to relational expression 13, can obtain ionosphere time-delay estimated value

$\mathrm{\Δ}{\hat{S}}_{\mathrm{ion},g,L1}=\frac{{f_{L2}}^2}{{f_{L2}}^2-{f_{L1}}^2}(P_{L1}-P_{L2})---\left(14\right)$

Can know according to aforementioned analysis

$\mathrm{\Δ}{\hat{S}}_{\mathrm{ion},g,L1}=\frac{{f_{L2}}^2}{{f_{L2}}^2-{f_{L1}}^2}[(\mathrm{\Δ}{S}_{\mathrm{ion},g,L1}-\mathrm{\Δ}{S}_{\mathrm{ion},g,L2})+({\mathrm{\ϵ}}_{P,L1}-{\mathrm{\ϵ}}_{P,L2})]---\left(15\right)$

Finally

$\mathrm{\Δ}{\hat{S}}_{\mathrm{ion},g,L1}=\mathrm{\Δ}{S}_{\mathrm{ion},g,L1}+\frac{{f_{L2}}^2}{{f_{L2}}^2-{f_{L1}}^2}({\mathrm{\ϵ}}_{P,L1}-{\mathrm{\ϵ}}_{P,L2})---\left(16\right)$

Clearly, the accuracy of ionosphere time-delay estimated value depends on and the size of noise under the very big situation of multipath error, can't guarantee the validity of estimated value.In addition, if the too small f that causes of the frequency difference between frequency _L2 ²-f _L1 ²Too small, noise is exaggerated, and also can reduce the accuracy of estimated value.

Strictly speaking, the pseudorange of different frequent points has only receiver clock correction to equate, because ionospheric effect of dispersion, if the electromagnetic wave of two frequencies arrives receiving antenna at synchronization, then together, its travel path also has minute differences to its x time scarcely.For no other reason than that the time-delay maximum that effect of dispersion causes hundreds of rice only; Then between two frequencies x time at interval below the microsecond level; In the so short mistiming; The motion of satellite and receiver user can be ignored, and the change of satellite clock correction is also insignificant, and the correlativity in time and space makes that the difference of two frequency troposphere time-delays and ionized layer TEC is equally very small.

For the higher GNSS user of positioning accuracy request, ionospheric propagation time-delay and multipath effect are pseudo range measurements and based on two main sources of pseudorange positioning error.At the beginning of design, the Service Signal of GPS just provides two frequencies, hopes to utilize the electromagnetic effect of dispersion of L-band, and estimation is also proofreaied and correct the pseudorange delay time error that is caused by ionosphere.Excessive, possibly cause the time-delay of double frequency pseudorange ionosphere to estimate failure but if multipath effect acts on the error that observed quantity causes.Multipath error is closely related with the surrounding environment of receiving antenna, although industry has been developed multiple sign indicating number ring (DLL) multipath inhibition technology, still is difficult to thoroughly solve the pseudorange multipath error problem in the harsh and unforgiving environments such as city, mountain region.Commercial receiver thereby generally adopted carrier smoothing pseudorange technology utilizes carrier wave observed quantity multipath and measures noise much smaller than pseudo range observed quantity, reduces multipath and noise, satisfies the requirement of pseudorange locating accuracy.

Because ionosphere is time-delay to the influence of pseudorange, be leading to the influence of carrier phase, the carrier smoothing pseudorange can be introduced a system deviation (ionosphericdivergence) again on time-delay basis, the original ionosphere of pseudorange.And this system deviation can accumulate with the continuous service of smoothing algorithm, finally to cause the size of level and smooth back pseudorange error to surpass original/and the error of smoothing pseudo range not.Therefore, smoothing algorithm must reset after lasting computing a period of time, restarted level and smooth.The length of duration depends on the estimation to ionosphere systematic error parameter, if ionosphere is active, the ionosphere system deviation can cause level and smooth back pseudorange error bigger, and frequent reset operation makes multipath and measurement Noise Suppression effect descend.

Summary of the invention

The technical matters that the present invention will solve provides a kind ofly carries out pseudo range observed quantity estimation approach and device through carrier smoothing, the multipath that greatly reduces with measure on the effective noise floor, rejected ionospheric influence, thereby significantly improved the estimated accuracy of pseudorange.

In order to address the above problem, the invention provides and a kind ofly carry out the pseudo range observed quantity estimation approach through carrier smoothing, comprising:

Obtain the pseudorange and the carrier phase observed quantity of n frequency respectively; N is the integer more than or equal to 2;

Carry out carrier smoothing pseudorange operation simultaneously at each frequency respectively, obtain the pseudorange

after level and smooth;

Pseudorange behind a plurality of frequencies level and smooth is formed measurement equation:

Z＝HX+V；

Wherein:

$Z=\left[\begin{array}{c}{\tilde{P}}_1\\ {\tilde{P}}_2\\ ...\\ {\tilde{P}}_n\end{array}\right]H=\left[\begin{array}{cc}\frac{d_1}{{f_1}^2}& d_2\\ \frac{d_1}{{f_2}^2}& d_2\\ ...& \\ \frac{d_1}{{f_n}^2}& d_2\end{array}\right]$ $X=\left[\begin{array}{c}{\mathrm{TEC}}_{\mathrm{eff}}\\ r\end{array}\right]V=\left[\begin{array}{c}{\mathrm{\δ}}_{{\tilde{P}}_1}\\ {\mathrm{\δ}}_{{\tilde{P}}_2}\\ ...\\ {\mathrm{\δ}}_{{\tilde{P}}_n}\end{array}\right];$

TEC _EffWith r for treating estimator, f _iBe the frequency of frequency i,

For frequency i goes up by the pseudo range measurement noise and the multipath that fully suppress; I is since 1, and the integer till the n comprises 1 and n; d ₁And d ₂Be constant;

According to above-mentioned measurement equation to TEC _EffCarry out valuation with r, with the valuation of resulting r as the pseudo range observed quantity estimated value.

Preferably, ${\mathrm{TEC}}_{\mathrm{Eff}}=\frac{K-1}{K}{e}^{-\frac{t}{\frac{K}{K-1}\mathrm{\τ}}}{\∫}_{0+}^t{e}^{\frac{t^{\′}}{\frac{K}{K-1}\mathrm{\τ}}}(-2\frac{\mathrm{DTEC}}{{\mathrm{Dt}}^{\′}}){\mathrm{Dt}}^{\′}+\mathrm{TEC};$

Wherein, K is the discrete time constant, and t is a time point, and e is the truth of a matter of natural logarithm; τ is the smoothingtime constant, the Δ t of τ=(K-1), and Δ t is the minimum SI of smoothing pseudo range, TEC is a total electron content.

Preferably, d ₁Span be 40.3 ± 10%, d ₂Span be 1 ± 10%.

Preferably, d ₁Be 40.3, d ₂Be 1.

Preferably, said according to measurement equation to TEC _EffCarry out in the step of valuation with r, adopt least-squares estimation, weighted least-squares estimation or Kalman filtering to carry out valuation.

The present invention also provides a kind of and has carried out the device that pseudo range observed quantity is estimated through carrier smoothing, comprising:

Measurement module is used for obtaining respectively the pseudorange and the carrier phase observed quantity of n frequency; N is the integer more than or equal to 2;

Level and smooth module; Be used for respectively carrying out the operation of carrier smoothing pseudorange simultaneously, obtain the pseudorange

after level and smooth at each frequency

Constructing module is used for the pseudorange behind a plurality of frequencies level and smooth is formed measurement equation:

Z＝HX+V；

Wherein:

$Z=\left[\begin{array}{c}{\tilde{P}}_1\\ {\tilde{P}}_2\\ ...\\ {\tilde{P}}_n\end{array}\right]H=\left[\begin{array}{cc}\frac{d_1}{{f_1}^2}& d_2\\ \frac{d_1}{{f_2}^2}& d_2\\ ...& \\ \frac{d_1}{{f_n}^2}& d_2\end{array}\right]$ $X=\left[\begin{array}{c}{\mathrm{TEC}}_{\mathrm{eff}}\\ r\end{array}\right]V=\left[\begin{array}{c}{\mathrm{\δ}}_{{\tilde{P}}_1}\\ {\mathrm{\δ}}_{{\tilde{P}}_2}\\ ...\\ {\mathrm{\δ}}_{{\tilde{P}}_n}\end{array}\right];$

TEC _EffWith r for treating estimator, f _iBe the frequency of frequency i,

For frequency i goes up by the pseudo range measurement noise and the multipath that fully suppress; I is since 1, and the integer till the n comprises 1 and n; d ₁And d ₂Be constant;

Estimator module, according to above-mentioned measurement equation to TEC _EffCarry out valuation with r, with the valuation of resulting r as the pseudo range observed quantity estimated value.

Preferably, ${\mathrm{TEC}}_{\mathrm{Eff}}=\frac{K-1}{K}{e}^{-\frac{t}{\frac{K}{K-1}\mathrm{\τ}}}{\∫}_{0+}^t{e}^{\frac{t^{\′}}{\frac{K}{K-1}\mathrm{\τ}}}(-2\frac{\mathrm{DTEC}}{{\mathrm{Dt}}^{\′}}){\mathrm{Dt}}^{\′}+\mathrm{TEC};$

Wherein, K is the discrete time constant, and t is a time point, and e is the truth of a matter of natural logarithm; τ is the smoothingtime constant, the Δ t of τ=(K-1), and Δ t is the minimum SI of smoothing pseudo range, TEC is a total electron content.

Preferably, d ₁Span be 40.3 ± 10%, d ₂Span be 1 ± 10%.

Preferably, d ₁Be 40.3, d ₂Be 1.

Preferably, said estimator module adopts least-squares estimation, weighted least-squares estimation or Kalman filtering to carry out valuation.

Technical scheme of the present invention can significantly reduce the multipath effect influence, significantly reduces and measures noise intensity, effectively rejects the influence of ionosphere to pseudo-range measurements; Owing to can carry out whole valuation correction to the ionosphere system deviation that ionospheric error itself is introduced when level and smooth, so the selection of time constant need not be considered ionospheric situation again, duration that also need not limit algorithm.

Description of drawings

Fig. 1 is the schematic block diagram of the pseudo range observed quantity estimation unit of embodiment two.

Embodiment

To combine accompanying drawing and embodiment that technical scheme of the present invention is explained in more detail below.

Need to prove that if do not conflict, each characteristic among the embodiment of the invention and the embodiment can mutually combine, all within protection scope of the present invention.In addition; Can in computer system, carry out in the step shown in the process flow diagram of accompanying drawing such as a set of computer-executable instructions, and, though logical order has been shown in process flow diagram; But in some cases, can carry out step shown or that describe with the order that is different from here.

At first, the inventor is following to the analysis of carrier smoothing pseudorange algorithm:

Multipath in the pseudorange disturbs and measures noise and is significantly higher than the carrier phase observed quantity, but the latter has comprised a fixing integral circumference ambiguity.Bearing accuracy based on the raw pseudo range observed quantity is lower, though carrier phase difference location can provide the precision of centimetre-sized, finding the solution integral circumference ambiguity with the observed quantity that provides by means of the difference base station is prerequisite.Utilize accurate relatively carrier phase observed quantity smoothing pseudo range can under the condition that need not find the solution integral circumference ambiguity, improve the receiver-autonomous bearing accuracy of GNSS.The expression formula of carrier phase:

Φ＝ρ+dρ+c(dt-dT)+ΔS _ion，p+ΔS _trop，p+N _Φ+M _Φ+n _Φ (17)

Comparison expression (12) and (17), carrier phase are very apart from ρ, satellite orbital error d ρ, satellite clock correction dt, receiver clock correction dT and troposphere time-delay Δ S _{Trop, p}Identical with in the expression formula of pseudorange, visible from formula (11), ionosphere time-delay equal and opposite in direction, opposite in sign.N _ΦThe expression integral circumference ambiguity, the size of carrier phase multipath error and measurement noise is much smaller than pseudo range observed quantity.Carrier smoothing pseudorange algorithm comes down to a regressive filter, progressively increases the weight of carrier phase and reduces the weight of pseudorange and keep up to resetting.

${\tilde{P}}_m=W_{P,m}{P}_m+W_{\mathrm{\Φ},m}[{\tilde{P}}_{m-1}+({\mathrm{\Φ}}_m-{\mathrm{\Φ}}_{m-1})]---\left(18\right)$

Wherein:

Be pseudo range observed quantity, m is a positive integer, P _mBe pseudorange;

$W_{P,m}=W_{P,m-1}-\frac{1}{K}$ $W_{\mathrm{\Φ},m}=W_{\mathrm{\Φ},m-1}+\frac{1}{K}---\left(19\right)$

K is the discrete time constant.Under the original state:

${\tilde{P}}_1=P_1$ W _P，1＝1 W _Φ，1＝0 (20)

When the m increase and above K, weight no longer changes:

$W_{P,m}=\frac{1}{K}$ $W_{\mathrm{\Φ},m}=1-\frac{1}{K}$ m≥K (21)

Therefore, thereafter algorithm mathematics model can be described by constant coefficient recursion equation:

${\tilde{P}}_i=\frac{P_i+(K-1)[{\tilde{P}}_{i-1}+({\mathrm{\Φ}}_i-{\mathrm{\Φ}}_{i-1})]}{K}---\left(22\right)$

Error analysis to carrier smoothing pseudorange algorithm is following:

Because carrier phase is very apart from ρ, satellite orbital error d ρ, satellite clock correction dt, receiver clock correction dT and troposphere time-delay Δ S _{Trop, p}Identical with in the expression formula of pseudorange, and also equal basically between different frequencies, can rewrite the expression formula of pseudorange and carrier phase:

P _i＝r _i+I _i+M _{P_i}+n _{P_i} (23)

Φ _i＝r _i-I _i+N _Φ+M _{Φ_i}+n _{Φ_i}

Wherein

r _i＝ρ _i+dρ _i+c(dt _i-dT _i)+ΔS _{trop_i} (24)

I _i＝ΔS _{ion，g_i} ΔS _{trop_i}＝ΔS _{trop，g_i}＝ΔS _{trop，p_i}

Definition is dispersed the error that (ionospheric divergence), multipath and measurement noise cause by ionosphere sign indicating number-carrier wave:

${\mathrm{\ϵ}}_i={\tilde{P}}_i-r_i-I_i---\left(25\right)$

The Δ t of definition smoothingtime constant τ=(K-1), Δ t is the minimum SI of smoothing pseudo range.Ignore carrier wave multipath and carrier wave and measure noise, under Δ t → 0 condition, can represent the Algorithm Error of following formula definition by following integral equation:

$\mathrm{\ϵ}={\mathrm{\ϵ}}_{0+}{e}^{-\frac{t}{\frac{K}{K-1}\mathrm{\τ}}}+\frac{K-1}{K}{e}^{-\frac{t}{\frac{K}{K-1}\mathrm{\τ}}}{\∫}_{0+}^t{e}^{\frac{t^{\′}}{\frac{K}{K-1}\mathrm{\τ}}}(-2\frac{\mathrm{dI}}{{\mathrm{dt}}^{\′}}+\frac{M_P}{\mathrm{\τ}}+\frac{n_P}{\mathrm{\τ}}){\mathrm{dt}}^{\′}---\left(26\right)$

Multipath error depends on the geometry site between reflecting body and antenna fully; Its Changing Pattern is similar to sine function; Cycle is greatly about a minute level (can be referring to M.Elizabeth Cannon, Lecture Notes ofENGO 561 Satellite Positioning, Winter 2005):

M _P＝A _Pcos(ω _Pt+α _P) (27)

Multipath signal strength is A _P, the cycle is ω _PThe inverse of/2 π.Pseudorange multipath effect steady-state error behind carrier smoothing is:

${\mathrm{\ϵ}}_{M_P}=\frac{A_P}{\sqrt{1+{\left(\frac{K}{K-1}\mathrm{\τ}{\mathrm{\ω}}_P\right)}^2}}\sin ({\mathrm{\ω}}_{P}t+{\mathrm{\α}}_P+{\mathrm{\α}}^{\′})---\left(28\right)$

The level and smooth back multipath error cycle that is all sine function is constant, and intensity weakens.Clearly, the smoothingtime constant is big more, and effect is good more.

Suppose that the pseudo range measurement noise is a white noise, time correlation function is:

$R_{n_P}={{\mathrm{\σ}}_P}^2\mathrm{\δ}\left(t\right)---\left(29\right)$

Wherein δ (t) is impulse function/Dirac function, σ _P ²It is the pseudorange noise power.After level and smooth, noise power is:

σ _SP ²＝σ _P ²/2τ (30)

Thus it is clear that,, also hope to adopt bigger time constant from suppressing the angle of noise.

Suppose that ionosphere time-delay Changing Pattern is as follows:

I＝a+bt+ct ² (31)

Since pseudorange and carrier phase ionosphere time-delay opposite in sign, the steady-state system deviation that smoothing algorithm is introduced:

ε _I＝4cτt (32)

The once existence of a 4c τ t about the algorithm duration means the constantly accumulation of ionosphere system deviation, and the speed of accumulating rate is directly proportional with time constant.In order to reduce the ionosphere system deviation; The algorithm time constant is dwindled in requirement; And the algorithm continuous working period can not be long, otherwise the benefit that complete cancellation algorithms inhibition multipath of system deviation meeting and measurement noise bring, even the pseudorange total error after causing smoothly is greater than raw pseudo range.The selection of time constant and duration is all depended on (can be referring to Euiho Kim to the estimation of ionosphere and multipath effect parameter; Todd Walter; And J.D.Powell, " Adaptive CarrierSmoothing Using Code and Carrier Divergence ", ION NTM 2007; San Diego, CA).

Embodiment one, a kind ofly carries out the pseudo range observed quantity estimation approach through carrier smoothing, comprising:

Obtain the pseudorange and the carrier phase observed quantity of n frequency respectively; N is the integer more than or equal to 2;

Carry out carrier smoothing pseudorange operation simultaneously at each frequency respectively, obtain the pseudorange

after level and smooth;

Pseudorange behind a plurality of frequencies level and smooth is formed measurement equation:

Z＝HX+V；(33)

Wherein:

$Z=\left[\begin{array}{c}{\tilde{P}}_1\\ {\tilde{P}}_2\\ ...\\ {\tilde{P}}_n\end{array}\right]H=\left[\begin{array}{cc}\frac{d_1}{{f_1}^2}& d_2\\ \frac{d_1}{{f_2}^2}& d_2\\ ...& \\ \frac{d_1}{{f_n}^2}& d_2\end{array}\right]$ $X=\left[\begin{array}{c}{\mathrm{TEC}}_{\mathrm{eff}}\\ r\end{array}\right]V=\left[\begin{array}{c}{\mathrm{\δ}}_{{\tilde{P}}_1}\\ {\mathrm{\δ}}_{{\tilde{P}}_2}\\ ...\\ {\mathrm{\δ}}_{{\tilde{P}}_n}\end{array}\right];---\left(34\right)$

TEC _EffWith r for treating estimator, f _iBe the frequency of frequency i,

For frequency i goes up by the pseudo range measurement noise and the multipath that fully suppress; I is 1,2 ..., n, just be since 1, the integer till the n comprises 1 and n; d ₁And d ₂Be constant;

According to above-mentioned measurement equation to TEC _EffCarry out valuation with r, with the valuation of resulting r as the pseudo range observed quantity estimated value.

In the present embodiment, the smoothing pseudo range equation structure measurement equation through a plurality of frequencies obtains the pseudo range observed quantity estimated value with the mode of valuation, can reject the influence that bring in ionosphere, improves result's precision.

Wherein, d ₁And d ₂Can confirm according to derivation or simulation result.

In the present embodiment, d ₂Span can but be not limited to 1 ± 10%, optimum is 1.

Obviously, the Z in the formula (33) is the measurement of state X, and V is an error in measurement.Treat estimator TEC for two _EffAnd r, can adopt multiple optimum estimation theory, criterion and method to estimate.

Further analyze from the principle angle below.

Select the reasonable time constant can effectively suppress to measure noise and multipath; Under the negative exponential function effect, initial deviation item ε ₀₊Be tending towards 0 gradually with the algorithm accumulated time, thereby can in steady-state analysis, ignore.Be illustrated in the smoothing process by the pseudo range measurement noise and the multipath that fully suppress with

; And the noise like item of the measurement noise of carrier phase and multipath interference composition; Then according to formula (25), the pseudorange after level and smooth can be expressed as:

$\tilde{P}=\mathrm{\ϵ}+r+I=\frac{K-1}{K}{e}^{-\frac{t}{\frac{K}{K-1}\mathrm{\τ}}}{\∫}_{0+}^t{e}^{\frac{t^{\′}}{\frac{K}{K-1}\mathrm{\τ}}}(-2\frac{\mathrm{dI}}{{\mathrm{dt}}^{\′}}){\mathrm{dt}}^{\′}+{\mathrm{\δ}}_{\tilde{P}}+r+I---\left(35\right)$

Bringing formula (11) into following formula can get:

$\tilde{P}=\mathrm{\ϵ}+r+I=\frac{40.3}{f^2}[\frac{K-1}{K}{e}^{-\frac{t}{\frac{K}{K-1}\mathrm{\τ}}}{\∫}_{0+}^t{e}^{\frac{t^{\′}}{\frac{K}{K-1}\mathrm{\τ}}}(-2\frac{\mathrm{dTEC}}{{\mathrm{dt}}^{\′}}){\mathrm{dt}}^{\′}+\mathrm{TEC}]+r+{\mathrm{\δ}}_{\tilde{P}}---\left(36\right)$

Wherein, K is the discrete time constant, and t is a time point, and e is the truth of a matter of natural logarithm; τ is the smoothingtime constant, the Δ t of τ=(K-1), and Δ t is the minimum SI of smoothing pseudo range, TEC is a total electron content.

In the present embodiment, can use TEC _EffAs the ionospheric equivalent TEC of carrier smoothing pseudorange:

${{\mathrm{TEC}}_{\mathrm{eff}}}^{\′}=\frac{K-1}{K}{e}^{-\frac{t}{\frac{K}{K-1}\mathrm{\τ}}}{\∫}_{0+}^t{e}^{\frac{t^{\′}}{\frac{K}{K-1}\mathrm{\τ}}}(-2\frac{\mathrm{dTEC}}{{\mathrm{dt}}^{\′}}){\mathrm{dt}}^{\′}+\mathrm{TEC};---\left(37\right)$

Can find out TEC _Eff' be the equivalent TEC that has taken all factors into consideration behind the population effect of the time-delay of raw pseudo range ionosphere and ionosphere system deviation two error terms relevant of carrier smoothing pseudorange algorithm introducing itself with ionosphere; Present embodiment through type (36) can be merged into a unknown quantity to the time-delay of raw pseudo range ionosphere and two unknown quantitys of additional ionospheric error that carrier smoothing pseudorange algorithm is introduced; Add r two unknown quantitys altogether, only need the smoothing pseudo range equation of two frequencies just can carry out valuation; Usually, the GPS receiver can provide three frequencies, and therefore the redundant equation of a frequency will be arranged, and can make that the valuation result is more accurate.

In a kind of embodiment of present embodiment, can be directly with the TEC in the formula (37) _Eff' as the TEC in the formula (34) _Eff, at this moment, d ₁Span can but be not limited to 40.3 ± 10%, optimum is 40.3.

Theoretically, TEC _EffWith r and frequency-independent, if multifrequency receiver carries out the operation of carrier smoothing pseudorange synchronously for each frequency (in time), then aforementioned two variablees of synchronization equate in the value of each frequency.Two unknown quantitys need only plural equation/frequency can be found the solution and obtained about TEC _EffWith the valuation of r, wherein r is carried out PVT resolve and just can accomplish receiver-autonomous location and test the speed.Because present embodiment can carry out whole valuation correction to the ionosphere system deviation that ionospheric error itself and carrier smoothing pseudorange algorithm are introduced, so the selection of time constant need not be considered ionospheric situation again, duration that also need not limit algorithm.

Behind formula (37) substitution (36) substitution following formula, the pseudorange after level and smooth can be expressed as:

$\tilde{P}=\frac{40.3}{f^2}{{\mathrm{TEC}}_{\mathrm{eff}}}^{\′}+r+{\mathrm{\δ}}_{\tilde{P}}---\left(37\right)$

Can find out and since in the valuation of r multipath with measure noise and received effective inhibition of carrier smoothing, ionospheric influence is rejected through above-mentioned Least Squares Estimating again.Therefore, the valuation of r is accurate more than original pseudorange and single-frequency carrier smoothing pseudorange, and the PVT that carries out on this basis resolves and can access higher receiver-autonomous bearing accuracy.

Suppose that receiver generates the pseudorange and the carrier phase observed quantity of n frequency, and carry out the operation of carrier smoothing pseudorange synchronously, then can obtain following system of equations at each frequency:

${\tilde{P}}_1=\frac{40.3}{{f_1}^2}{{\mathrm{TEC}}_{\mathrm{eff}}}^{\′}+r+{\mathrm{\δ}}_{{\tilde{P}}_1}$

${\tilde{P}}_2=\frac{40.3}{{f_2}^2}{{\mathrm{TEC}}_{\mathrm{eff}}}^{\′}+r+{\mathrm{\δ}}_{{\tilde{P}}_2}---\left(39\right)$

...

${\tilde{P}}_n=\frac{40.3}{{f_n}^2}{{\mathrm{TEC}}_{\mathrm{eff}}}^{\′}+r+{\mathrm{\δ}}_{{\tilde{P}}_n}$ n≥2

The matrix form of following formula is formula (33): Z=HX+V; Z, H, X and V see formula (34).

In another embodiment of present embodiment, also can use TEC _Eff"=40.3 * TEC _Eff' as the TEC in the formula (34) _Eff, at this moment,

d ₁Span can but be not limited to 1 ± 10%, optimum is 1.

During practical application, can use d ₃* TEC _Eff' be used as as the TEC in the formula (34) _Eff, d ₃Be constant; At this moment, corresponding adjustment d ₁Just can reach the same valuation effect, optimum is to make d ₁And d ₃Amassing is 40.3; Further, because the TEC in the formula (34) _EffBe to treat estimated value, therefore also can and TEC _EffAs long as ' disproportional relation is adjustment d ₁Get final product.

In the present embodiment, said according to above-mentioned measurement equation to TEC _EffCarry out in the step of valuation with r, can adopt estimation methods such as least-squares estimation, weighted least-squares estimation or Kalman filtering to carry out valuation.

The criterion of least-squares estimation is following:

$J\left(\hat{X}\right)={(Z-H\hat{X})}^T(Z-H\hat{X})=\min ---\left(38\right)$

The measurement noise power of considering each frequency is variant, and multipath intensity maybe be also not quite identical, can adopt accurate more weighted least-squares valuation.Its estimation criterion:

$J\left(\hat{X}\right)={(Z-H\hat{X})}^{T}W(Z-H\hat{X})=\min ---\left(40\right)$

W=R in the formula ^-1, R is the variance battle array of error in measurement V.

If hope to utilize temporal correlation to obtain higher estimation accuracy, also can use the bigger Kalman filter of operand.Its expulsion mechanism is described by following state equation:

X _k＝φ _k，k-1X _k-1+Γ _k-1W _k-1 (41)

In the formula: φ _{K, k-1}Be t _K-1A step transfer matrix constantly; Γ _K-1For system noise drives battle array; W _kBe the system incentive noise sequence.

Embodiment two, a kind of device that carries out the pseudo range observed quantity estimation through carrier smoothing, as shown in Figure 1, comprising:

Measurement module is used for obtaining respectively the pseudorange and the carrier phase observed quantity of n frequency; N is the integer more than or equal to 2;

Level and smooth module; Be used for respectively carrying out the operation of carrier smoothing pseudorange simultaneously, obtain the pseudorange

after level and smooth at each frequency;

Constructing module is used for the pseudorange behind a plurality of frequencies level and smooth is formed measurement equation:

Z＝HX+V；(33)

Wherein:

$Z=\left[\begin{array}{c}{\tilde{P}}_1\\ {\tilde{P}}_2\\ ...\\ {\tilde{P}}_n\end{array}\right]H=\left[\begin{array}{cc}\frac{d_1}{{f_1}^2}& d_2\\ \frac{d_1}{{f_2}^2}& d_2\\ ...& \\ \frac{d_1}{{f_n}^2}& d_2\end{array}\right]$ $X=\left[\begin{array}{c}{\mathrm{TEC}}_{\mathrm{eff}}\\ r\end{array}\right]V=\left[\begin{array}{c}{\mathrm{\δ}}_{{\tilde{P}}_1}\\ {\mathrm{\δ}}_{{\tilde{P}}_2}\\ ...\\ {\mathrm{\δ}}_{{\tilde{P}}_n}\end{array}\right];---\left(34\right)$

TEC _EffWith r for treating estimator, f _iBe the frequency of frequency i, For frequency i goes up by the pseudo range measurement noise and the multipath that fully suppress; I is since 1, and the integer till the n comprises 1 and n; d ₁And d ₂Be constant;

Estimator module is used for according to above-mentioned measurement equation TEC _EffCarry out valuation with r, with the valuation of resulting r as the pseudo range observed quantity estimated value.

In the present embodiment, ${\mathrm{TEC}}_{\mathrm{Eff}}=\frac{K-1}{K}{e}^{-\frac{t}{\frac{K}{K-1}\mathrm{\τ}}}{\∫}_{0+}^t{e}^{\frac{t^{\′}}{\frac{K}{K-1}\mathrm{\τ}}}(-2\frac{\mathrm{DTEC}}{{\mathrm{Dt}}^{\′}}){\mathrm{Dt}}^{\′}+\mathrm{TEC};$

Wherein, K is the discrete time constant, and t is a time point, and e is the truth of a matter of natural logarithm; τ is the smoothingtime constant, the Δ t of τ=(K-1), and Δ t is the minimum SI of smoothing pseudo range, TEC is a total electron content.

In the present embodiment, d ₁Span can but be not limited to 40.3 ± 10%, d ₂Span can but be not limited to 1 ± 10%.

In the present embodiment, d ₁Optimum is 40.3, d ₂Optimum is 1.

In the present embodiment, said estimator module can adopt estimation methods such as least-squares estimation, weighted least-squares estimation or Kalman filtering to carry out valuation.

Other variation and realization details can be with embodiment one.

One of ordinary skill in the art will appreciate that all or part of step in the said method can instruct related hardware to accomplish through program, said program can be stored in the computer-readable recording medium, like ROM (read-only memory), disk or CD etc.Alternatively, all or part of step of the foregoing description also can use one or more integrated circuit to realize.Correspondingly, each the module/unit in the foregoing description can adopt the form of hardware to realize, also can adopt the form of software function module to realize.The present invention is not restricted to the combination of the hardware and software of any particular form.

Certainly; The present invention also can have other various embodiments; Under the situation that does not deviate from spirit of the present invention and essence thereof; Those of ordinary skill in the art work as can make various corresponding changes and distortion according to the present invention, but these corresponding changes and distortion all should belong to the protection domain of claim of the present invention.

Claims (10)

1. one kind is carried out the pseudo range observed quantity estimation approach through carrier smoothing, comprising:

Obtain the pseudorange and the carrier phase observed quantity of n frequency respectively; N is the integer more than or equal to 2;

Carry out carrier smoothing pseudorange operation simultaneously at each frequency respectively, obtain the pseudorange

after level and smooth;

Pseudorange behind a plurality of frequencies level and smooth is formed measurement equation:

Z＝HX+V；

Wherein:

$Z=\left[\begin{array}{c}{\tilde{P}}_1\\ {\tilde{P}}_2\\ ...\\ {\tilde{P}}_n\end{array}\right]H=\left[\begin{array}{cc}\frac{d_1}{{f_1}^2}& d_2\\ \frac{d_1}{{f_2}^2}& d_2\\ ...& \\ \frac{d_1}{{f_n}^2}& d_2\end{array}\right]$ $X=\left[\begin{array}{c}{\mathrm{TEC}}_{\mathrm{eff}}\\ r\end{array}\right]V=\left[\begin{array}{c}{\mathrm{\δ}}_{{\tilde{P}}_1}\\ {\mathrm{\δ}}_{{\tilde{P}}_2}\\ ...\\ {\mathrm{\δ}}_{{\tilde{P}}_n}\end{array}\right];$

TEC _EffWith r for treating estimator, f _iBe the frequency of frequency i,

For frequency i goes up by the pseudo range measurement noise and the multipath that fully suppress; I is since 1, and the integer till the n comprises 1 and n; d ₁And d ₂Be constant;

According to above-mentioned measurement equation to TEC _EffCarry out valuation with r, with the valuation of resulting r as the pseudo range observed quantity estimated value.

2. the method for claim 1 is characterized in that:

${\mathrm{TEC}}_{\mathrm{eff}}=\frac{K-1}{K}{e}^{-\frac{t}{\frac{K}{K-1}\mathrm{\τ}}}{\∫}_{0+}^t{e}^{\frac{t^{\′}}{\frac{K}{K-1}\mathrm{\τ}}}(-2\frac{\mathrm{dTEC}}{{\mathrm{dt}}^{\′}}){\mathrm{dt}}^{\′}+\mathrm{TEC};$

Wherein, K is the discrete time constant, and t is a time point, and e is the truth of a matter of natural logarithm; τ is the smoothingtime constant, the Δ t of τ=(K-1), and Δ t is the minimum SI of smoothing pseudo range, TEC is a total electron content.

3. method as claimed in claim 2 is characterized in that:

d ₁Span be 40.3 ± 10%, d ₂Span be 1 ± 10%.

4. like claim 2 or 3 described methods, it is characterized in that:

d ₁Be 40.3, d ₂Be 1.

5. the method for claim 1 is characterized in that:

Said according to measurement equation to TEC _EffCarry out in the step of valuation with r, adopt least-squares estimation, weighted least-squares estimation or Kalman filtering to carry out valuation.

6. a device that carries out the pseudo range observed quantity estimation through carrier smoothing is characterized in that, comprising:

Measurement module is used for obtaining respectively the pseudorange and the carrier phase observed quantity of n frequency; N is the integer more than or equal to 2;

Level and smooth module; Be used for respectively carrying out the operation of carrier smoothing pseudorange simultaneously, obtain the pseudorange

after level and smooth at each frequency

Constructing module is used for the pseudorange behind a plurality of frequencies level and smooth is formed measurement equation:

Z＝HX+V；

Wherein:

$Z=\left[\begin{array}{c}{\tilde{P}}_1\\ {\tilde{P}}_2\\ ...\\ {\tilde{P}}_n\end{array}\right]H=\left[\begin{array}{cc}\frac{d_1}{{f_1}^2}& d_2\\ \frac{d_1}{{f_2}^2}& d_2\\ ...& \\ \frac{d_1}{{f_n}^2}& d_2\end{array}\right]$ $X=\left[\begin{array}{c}{\mathrm{TEC}}_{\mathrm{eff}}\\ r\end{array}\right]V=\left[\begin{array}{c}{\mathrm{\δ}}_{{\tilde{P}}_1}\\ {\mathrm{\δ}}_{{\tilde{P}}_2}\\ ...\\ {\mathrm{\δ}}_{{\tilde{P}}_n}\end{array}\right];$

TEC _EffWith r for treating estimator, f _iBe the frequency of frequency i,

For frequency i goes up by the pseudo range measurement noise and the multipath that fully suppress; I is since 1, and the integer till the n comprises 1 and n; d ₁And d ₂Be constant;

Estimator module, according to above-mentioned measurement equation to TEC _EffCarry out valuation with r, with the valuation of resulting r as the pseudo range observed quantity estimated value.

7. device as claimed in claim 6 is characterized in that:

${\mathrm{TEC}}_{\mathrm{eff}}=\frac{K-1}{K}{e}^{-\frac{t}{\frac{K}{K-1}\mathrm{\τ}}}{\∫}_{0+}^t{e}^{\frac{t^{\′}}{\frac{K}{K-1}\mathrm{\τ}}}(-2\frac{\mathrm{dTEC}}{{\mathrm{dt}}^{\′}}){\mathrm{dt}}^{\′}+\mathrm{TEC};$

Wherein, K is the discrete time constant, and t is a time point, and e is the truth of a matter of natural logarithm; τ is the smoothingtime constant, the Δ t of τ=(K-1), and Δ t is the minimum SI of smoothing pseudo range, TEC is a total electron content.

8. device as claimed in claim 7 is characterized in that:

d ₁Span be 40.3 ± 10%, d ₂Span be 1 ± 10%.

9. like claim 7 or 8 described devices, it is characterized in that:

d ₁Be 40.3, d ₂Be 1.

10. method as claimed in claim 6 is characterized in that:

Said estimator module adopts least-squares estimation, weighted least-squares to estimate or Kalman filtering is carried out valuation.

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