CN104516006A - Carrier phase smoothing pseudorange algorithm based on improved Kalman filtering - Google Patents

Abstract

The invention provides a carrier phase smoothing pseudorange algorithm based on improved Kalman filtering. The carrier phase smoothing pseudorange algorithm includes acquiring correct pseudorange recursion initial values; estimating predictor and variance estimator of carrier phase smoothing pseudorange; using a smoothing time constant to smooth pseudorange, and calculating variance estimator; circulating recursion till reaching smoothing epoch number. The carrier phase smoothing pseudorange algorithm has the advantages of being better in multi-epoch smoothing effect than that of a conventional smoothing algorithm, small in calculation amount and easy to realize in realtime.

Description

A kind of carrier phase smoothing pseudo-range algorithm based on improved Kalman filter

Technical field

The invention belongs to field of satellite navigation, is a kind of algorithm improving pseudo-range positioning accuracy in Satellite navigation users receiver navigation calculation.

Background technology

Satellite navigation users receiver produces pseudorange and carrier phase two fundamental distance measured values to realize locating to every satellite.Pseudorange and carrier phase have obvious difference, and again in complementary characteristic, pseudo-range measurements reflects the distance between satellite and receiver, adopt pseudorange location can avoid solving the problem such as blur level and process cycle slip; But because it comprises the various error such as clock correction, air time delay, observation noise is large, be subject to Multi-Path Effects, adopts pseudo-range positioning accuracy lower.Carrier-phase measurement has the high advantage of distance accuracy, has very important meaning to hi-Fix, but carrier phase measurement can only measure its part less than a wavelength, there is complete cycle uncertain problem.In the base band signal process of high precision satellite navigation receiver, utilize accurate, level and smooth carrier-phase measurement to coarse, the precision higher than pseudo-range measurements can be obtained without the pseudo-range measurements of blur level is smoothing.

Traditional carrier phase smoothing pseudo-range adopts Hatch filtering algorithm, although traditional algorithm is widely used in engineering, it has the following disadvantages:

(1) suppose that the pseudo range observed quantity of each epoch is equally accurate, ignore the impact of Carrier Phase Noise, smoothing time constant is only relevant with level and smooth number of times.In theory smoothed precision along with level and smooth epoch number increase and improve, but in fact because smoothing time constant in traditional algorithm does not consider the impact of carrier phase observation noise, the smoothing time constant selected in level and smooth in many epoch is not optimum.

(2) smoothing pseudo range initial value selective receiver locking carrier phase after first pseudo-range measurements.

If smoothing pseudo range initial value has a larger deviation, smoother then needs one period of long period to eliminate deviation, and therefore the initial value of smoothing pseudo range should be accurate as far as possible.

Summary of the invention

In order to overcome the deficiencies in the prior art, the invention provides a kind of carrier phase smoothing pseudo-range algorithm based on improved Kalman filter, algorithm is by selecting optimal smoothing time constant and selecting pseudorange initial value as far as possible accurately to improve pseudorange smoothing precision.

The technical solution adopted for the present invention to solve the technical problems comprises the following steps:

Step 1: estimate multiple pseudorange value by the pseudorange variable quantity of the difference reflection of pseudo range observed quantity and adjacent carrier phase observed quantity epoch, using the mean value of multiple estimated value as pseudorange recursion initial value,

Pseudorange recursion initial value wherein, M is initial value evaluation times, M>=1; ρ _mfor t _mthe pseudo range observed quantity of epoch; λ is the carrier wavelength of satellite-signal; φ _mfor t _mthe carrier phase observed quantity of epoch; φ ₁for t ₁the carrier phase observed quantity of epoch;

Step 2: estimation t _kepoch carrier phase smoothing pseudo-range premeasuring, rear one epoch carrier phase smoothed pseudorange premeasuring level and smooth by last epoch after pseudorange, former and later two epoch carrier phase the pseudorange variable quantity that reflects of difference obtain;

T _kepoch carrier phase smoothed pseudorange premeasuring ρ ⁱ _-(t _k)=ρ ⁱ ₊(t _k-1)+λ (φ _k-φ _k-1)=ρ ⁱ ₊(t _k-1)+δ _ρ ⁱ(t _k-1, t _k), wherein, ρ ⁱ ₊(t _k-1) be t _k-1pseudorange after epoch is level and smooth, initial value ρ ⁱ ₊(t _k-1)=ρ _{m, 1}; φ _kfor t _kcarrier phase observed quantity epoch; φ _k-1for t _k-1carrier phase observed quantity epoch; δ _ρ ⁱ(t _k-1, t _k) be t _k-1, t _kthe pseudorange variable quantity of the difference reflection of carrier phase observed quantity two epoch;

Step 3: solve t _kthe variance evaluation amount p of carrier phase smoothing pseudo-range premeasuring epoch ⁱ _-(t _k)=p ⁱ ₊(t _k-1)+2 σ ² _c, wherein, p ⁱ _-(t _k) be ρ ⁱ _-(t _k) variance evaluation amount; p ⁱ ₊(t _k-1) be ρ ⁱ ₊(t _k-1) variance evaluation amount, initial value p ⁱ ₊(t ₁)=0; 2 σ ² _cfor δ _ρ ⁱ(t _k-1, t _k) variance evaluation amount, σ ² _cfor the variance of carrier phase observational error;

Step 4: represent smoothing time constant by the variance evaluation amount of pseudorange and the variance of pseudo range observed quantity; t _ksmoothing time constant k (t selected by epoch _k)=p ⁱ _-(t _k) (p ⁱ _-(t _k)+σ ² _p) ^-1, wherein, σ ² _pfor the variance of pseudo range observed quantity;

Step 5:t _kpseudorange t after epoch is level and smooth _kcarrier phase smoothing pseudo-range premeasuring epoch, smoothing time constant and t _kepoch, pseudo range observed quantity represented; t _kpseudorange after epoch is level and smooth wherein, ρ (t _k) be t _kepoch pseudo range observed quantity;

Step 6:t _kthe variance evaluation amount of pseudorange after epoch is level and smooth as in step 3 in next recursive process

Step 7: when level and smooth epoch, number k was less than level and smooth number K epoch of setting, algorithm returns step 2 and carries out recursion, until k=K, algorithm recursion terminates.

The invention has the beneficial effects as follows: improved Kalman filter algorithm chooses optimal smoothing time constant under the minimum prerequisite of smoothing pseudo range square error, and the smooth effect of many epoch is better than traditional smoothing algorithm; In addition, because algorithm adopts scalar form computing, calculated amount is little, is easy to real-time implementation, therefore in high-precision satellite navigation receiver base band signal process, has important practical significance.

Accompanying drawing explanation

Fig. 1 is method flow diagram of the present invention;

Fig. 2 is without level and smooth pseudo range observed quantity schematic diagram;

Fig. 3 is the pseudorange schematic diagram after traditional algorithm is level and smooth;

Fig. 4 is the pseudorange schematic diagram after improved Kalman filter algorithm is level and smooth.

Embodiment

Below in conjunction with drawings and Examples, the present invention is further described, the present invention includes but be not limited only to following embodiment.

In theory, number K level and smooth epoch is larger for Hatch filtering algorithm, and smoothed precision is higher, increasing in fact along with level and smooth number epoch, and when level and smooth epoch, number was greater than 500, carrier phase observational error is can not be uncared-for relative to total smoothed precision.Know by analysis, pseudorange observation error, carrier phase observational error and level and smooth after these 3 parameters of pseudorange observation error jointly determine the selection of smoothing time constant.Improved Kalman filter algorithm is by the thought of Kalman filtering, rear one epoch carrier phase smoothed pseudorange premeasuring level and smooth by last epoch after pseudorange, pseudorange variable quantity that former and later two epoch, carrier phase reflected obtain, consider the impact of pseudorange observation error, carrier phase observational error and the pseudorange observation error after smoothly in filtering.Algorithm, under the prerequisite of the variance of the variance and carrier phase observational error that correctly estimate pseudorange observation error, selects optimum smoothing time constant under the condition that smoothing pseudo range error mean square value is minimum.Improved Kalman filter carrier phase smoothing pseudo-range algorithm flow as shown in Figure 1.

Step 1: first algorithm needs to obtain more correct pseudorange recursion initial value, multiple pseudorange value is estimated, using the mean value of multiple estimated value as pseudorange recursion initial value as shown in Equation 1 by the pseudorange variable quantity of the difference reflection of pseudo range observed quantity and adjacent carrier phase observed quantity epoch.

${\mathrm{\ρ}}_{m,1}=\frac{1}{M}\underset{m=1}{\overset{M}{\mathrm{\Σ}}}[{\mathrm{\ρ}}_m-\mathrm{\λ}({\mathrm{\φ}}_m-{\mathrm{\φ}}_1)---\left(1\right)$

Wherein: ρ _{m, 1}: the pseudorange initial value estimated; M: initial value evaluation times, M>=1; ρ _m: t _mthe pseudo range observed quantity of epoch; λ: the carrier wavelength of satellite-signal; φ _m: t _mthe carrier phase observed quantity of epoch; φ ₁: t ₁the carrier phase observed quantity of epoch.

Step 2: estimation t _kepoch carrier phase smoothing pseudo-range premeasuring, by the thought of Kalman filtering, rear one epoch carrier phase smoothed pseudorange premeasuring level and smooth by last epoch after pseudorange, former and later two epoch carrier phase the pseudorange variable quantity that reflects of difference obtain.By t _k-1epoch is to t _kepoch carrier phase smoothed pseudorange premeasuring as shown in Equation 2.

ρ ⁱ _-(t _k)＝ρ ⁱ ₊(t _k-1)+λ(φ _k-φ _k-1)＝ρ ⁱ ₊(t _k-1)+δ _ρ ⁱ(t _k-1，t _k) (2)

Wherein: ρ ⁱ _-(t _k): t _kepoch carrier phase smoothing pseudo-range premeasuring; ρ ⁱ ₊(t _k-1): t _k-1pseudorange after epoch is level and smooth, initial value ρ ⁱ ₊(t _k-1)=ρ _{m, 1}; φ _k: t _kcarrier phase observed quantity epoch; φ _k-1: t _k-1carrier phase observed quantity epoch; δ _ρ ⁱ(t _k-1, t _k): t _k-1, t _kthe pseudorange variable quantity of the difference reflection of carrier phase observed quantity two epoch.

Step 3: improved Kalman filter algorithm considers the impact of pseudorange observation error, carrier phase observational error and the pseudorange observation error after level and smooth, solves t _kthe variance evaluation amount of carrier phase smoothing pseudo-range premeasuring epoch as shown in Equation 3.

p ⁱ _-(t _k)＝p ⁱ ₊(t _k-1)+2σ ² _c(3)

Wherein: p ⁱ _-(t _k): ρ ⁱ _-(t _k) variance evaluation amount; p ⁱ ₊(t _k-1): ρ ⁱ ₊(t _k-1) variance evaluation amount, initial value p ⁱ ₊(t ₁)=0; 2 σ ² _c: δ _ρ ⁱ(t _k-1, t _k) variance evaluation amount, σ ² _cthe variance of carrier phase observational error.

Step 4: in traditional smoothing algorithm, smoothing time constant is only relevant with number epoch smoothly chosen, when epoch, number was larger, carrier phase observational error is can not be uncared-for relative to total smoothed precision.In improved Kalman filter algorithm, the smoothing time constant variance evaluation amount of pseudorange and the variance of pseudo range observed quantity represents.T _ksmoothing time constant selected by epoch as shown in Equation 4.

k(t _k)＝p ⁱ _-(t _k)(p ⁱ _-(t _k)+σ ² _p) ^-1(4)

Wherein: k (t _k): smoothing time constant, σ ² _p: the variance of pseudo range observed quantity.

Step 5:t _kpseudorange t after epoch is level and smooth _kcarrier phase smoothing pseudo-range premeasuring epoch, smoothing time constant and t _kepoch, pseudo range observed quantity represented.Pseudorange after level and smooth as shown in Equation 5.

${\mathrm{\ρ}}_{+}^i\left(t_k\right)={{\mathrm{\ρ}}^i}_{-}\left(t_k\right)+k\left(t_k\right)(\mathrm{\ρ}\left(t_k\right)-{\mathrm{\ρ}}_{-}^i\left(t_k\right))---\left(5\right)$

Wherein: t _kpseudorange after epoch is level and smooth; ρ (t _k): t _kepoch pseudo range observed quantity.

Step 6:t _kafter epoch is level and smooth, the variance evaluation amount of pseudorange as shown in Equation 6.

$p_{+}^i\left(t_k\right)=[1-k\left(t_k\right)]\×p_{-}^i\left(t_k\right)---\left(6\right)$

Wherein: variance evaluation amount, as in step 3 in next recursive process

Step 7: algorithm recursion

When level and smooth epoch, number k was less than level and smooth number K epoch of setting, algorithm returns step 2 and carries out recursion, until k=K, algorithm recursion terminates.

In certain scientific research project, actual Beidou II satellite-signal is received by receiver, obtain pseudorange and carrier phase observed quantity, utilize Matlab to emulate without level and smooth pseudorange (shown in Fig. 2), pseudorange (shown in Fig. 3) after traditional algorithm is level and smooth and the pseudorange after improved Kalman filter algorithm is level and smooth (shown in Fig. 4).In emulation, level and smooth epoch is spaced apart 1s, and epoch, number was 2000.Pseudo range difference amount can embody the smooth effect of pseudorange intuitively, and adjacent epoch, pseudo range difference amount changing value was less, and pseudorange smoothing effect is better.

The present invention gives a kind of carrier phase smoothing pseudo-range algorithm based on improved Kalman filter, algorithm is selected optimal smoothing time constant by Kalman filtering thought and is averaged by estimation to select pseudorange initial value as far as possible accurately to improve pseudorange smoothing precision.

Step 1: obtain carrier phase observed quantity and pseudo range observed quantity measured data

In certain scientific research project, actual Big Dipper B3 frequency satellite-signal is received by receiver, receiver produces pseudo range observed quantity and carrier phase observed quantity to every satellite, by upper computer software, record is carried out to pseudo range observed quantity and carrier phase observed quantity, wherein adjacent observed quantity epoch is spaced apart 1s, chooses K=2000 epoch.

Step 2: estimation pseudorange initial value

In order to obtain more correct pseudorange initial value, employing formula 1 estimates the pseudorange initial value of smoothing algorithm, i.e. t in algorithm ₁epoch the pseudorange after level and smooth as shown in Equation 7.

ρ ⁱ ₊(t ₁)＝ρ _s,1(7)

Wherein: ρ _{s, 1}: the pseudorange initial value estimated by formula 1, in emulation: the M=10 in formula 1, more pseudorange estimation epoch initial values can be selected when the interval of adjacent epoch is less.

Step 3: calculate t _kepoch carrier phase smoothing pseudo-range premeasuring

The premeasuring of pseudorange and the pseudorange after last epoch is level and smooth, pseudorange variable quantity corresponding to former and later two of carrier phase difference relevant epoch, calculates as shown in Equation 2.

In emulation: ρ ⁱ ₊(t ₁) value be in step 2 estimation pseudorange initial value, ρ ⁱ ₊(t _k) (k>=2) value obtains by step 6; δ _ρ ⁱ(t _k-1, t _k) difference of adjacent carrier phase observations amount for obtaining in step 1.

Step 4: calculate t _kthe variance evaluation amount of carrier phase smoothing pseudo-range premeasuring epoch

T _kthe variance of carrier phase smoothed pseudorange premeasuring epoch as shown in Equation 3.

In emulation: p ⁱ ₊(t ₁)=0, p ⁱ ₊(t _k) (k>=2) obtained by step 7 recursion; σ in recursive process ² _cbe a constant, ask variance to obtain by 2000 carrier phase observed quantities epoch obtained in step 1.

Step 5: calculate t _ksmoothing time constant selected by epoch

Smoothing time constant by pseudorange observation error, carrier phase observational error and level and smooth after these 3 parameters of pseudorange observation error jointly determine, smoothing time constant calculates as shown in Equation 4.

In emulation: t _kthe variance P of carrier phase smoothed pseudorange premeasuring epoch ⁱ _-(t _k) obtained by step 4, σ in recursive process ² _pbe a constant, by obtain in step 1 2000 epoch pseudo range observed quantity ask variance to obtain.

Step 6: revise t _kepoch the pseudorange after smoothing the phase of carrier wave

T _kepoch the pseudorange t after smoothing the phase of carrier wave _kcarrier phase smoothing pseudo-range premeasuring epoch, smoothing time constant and t _kepoch, pseudo range observed quantity represented, its computation of pseudoranges after level and smooth as shown in Equation 5.

In emulation: t _kcarrier phase smoothed pseudorange premeasuring epoch ρ ⁱ _-(t _k) obtained by step 3, t _kepoch smoothing time constant k (t _k) obtained by step 5, t _kepoch pseudo range observed quantity ρ (t _k) obtained by step 1.

Step 7: calculate smoothing pseudo range variance evaluation amount

Pseudorange variance after level and smooth is by t _kepoch smoothing time constant and t _ksmoothing pseudo range premeasuring epoch variance obtains, and calculates as shown in Equation 6.

In emulation: t _kthe variance P of carrier phase smoothed pseudorange premeasuring epoch ⁱ _-(t _k) obtained by step 4, smoothing time constant k (t _k) obtained by step 5.T _kpseudorange variance after epoch is level and smooth as in next recursive process step 4

Step 8: algorithm recursion and simulation comparison

When level and smooth epoch, number k was less than level and smooth number K epoch of setting in step 1, algorithm returns step 3 and carries out recursion, until k=K, algorithm recursion terminates.

Step 9: algorithm simulating and comparing

Tradition Hatch filtering adopts typical two gradient control method as shown in Equation 8:

${\mathrm{\ρ}}^i\left(t_k\right)=\frac{1}{k}\mathrm{\ρ}\left(t_k\right)+\frac{k-1}{k}[{\mathrm{\ρ}}^i\left(t_{k-1}\right)+\mathrm{\δ}{\mathrm{\ρ}}^i(t_{k-1},t_k)]---\left(8\right)$

ρ ⁱ(t _k), ρ ⁱ(t _k-1): t _kand t _k-1epoch the pseudorange after level and smooth; 1/k: smoothing time constant, the initial conditions of recursion are ρ ⁱ(t ₁)=ρ (t ₁).

In emulation: obtain 2000 epoch without level and smooth pseudo range observed quantity by step 1; Obtained by step 1 2000 epoch pseudo range observed quantity and carrier phase observed quantity, utilize formula 8 can obtain 2000 pseudoranges after Hatch filtering, mapping is as shown in Figure 3; Can obtain the pseudorange of 2000 epoch after this algorithm is level and smooth by step 6 recursion, mapping as shown in Figure 4.Comparison diagram 2,3 and 4 can draw, the carrier phase smoothing pseudo-range algorithm smoothed precision based on improved Kalman filter is better than convention carrier carrier phase smoothed pseudorange algorithm.

Claims (1)

1., based on a carrier phase smoothing pseudo-range algorithm for improved Kalman filter, it is characterized in that comprising the steps:

Step 1: estimate multiple pseudorange value by the pseudorange variable quantity of the difference reflection of pseudo range observed quantity and adjacent carrier phase observed quantity epoch, using the mean value of multiple estimated value as pseudorange recursion initial value,

Pseudorange recursion initial value wherein, M is initial value evaluation times, M>=1; ρ _mfor t _mthe pseudo range observed quantity of epoch; λ is the carrier wavelength of satellite-signal; φ _mfor t _mthe carrier phase observed quantity of epoch; φ ₁for t ₁the carrier phase observed quantity of epoch;

Step 2: estimation t _kepoch carrier phase smoothing pseudo-range premeasuring, rear one epoch carrier phase smoothed pseudorange premeasuring level and smooth by last epoch after pseudorange, former and later two epoch carrier phase the pseudorange variable quantity that reflects of difference obtain;

T _kepoch carrier phase smoothed pseudorange premeasuring ρ ⁱ _-(t _k)=ρ ⁱ ₊(t _k-1)+λ (φ _k-φ _k-1)=ρ ⁱ ₊(t _k-1)+δ _ρ ⁱ(t _k-1, t _k), wherein, ρ ⁱ+ (t _k-1) be t _k-1pseudorange after epoch is level and smooth, initial value ρ ⁱ ₊(t _k-1)=ρ _{m, 1}; φ _kfor t _kcarrier phase observed quantity epoch; φ _k-1for t _k-1carrier phase observed quantity epoch; δ _ρ ⁱ(t _k-1, t _k) be t _k-1, t _kthe pseudorange variable quantity of the difference reflection of carrier phase observed quantity two epoch;

Step 3: solve t _kthe variance evaluation amount p of carrier phase smoothing pseudo-range premeasuring epoch ⁱ _-(t _k)=p ⁱ ₊(t _k-1)+2 σ ² _c, wherein, p ⁱ-(t _k) be ρ ⁱ-(t _k) variance evaluation amount; p ⁱ+ (t _k-1) be ρ ⁱ+ (t _k-1) variance evaluation amount, initial value p ⁱ+ (t ₁)=0; 2 σ ² _cfor δ _ρ ⁱ(t _k-1, t _k) variance evaluation amount, σ ² _cfor the variance of carrier phase observational error;

Step 4: represent smoothing time constant by the variance evaluation amount of pseudorange and the variance of pseudo range observed quantity; t _ksmoothing time constant k (t selected by epoch _k)=p ⁱ _-(t _k) (p ⁱ _-(t _k)+σ ² _p) ^-1, wherein, σ ² _pfor the variance of pseudo range observed quantity;

Step 5:t _kpseudorange t after epoch is level and smooth _kcarrier phase smoothing pseudo-range premeasuring epoch, smoothing time constant and t _kepoch, pseudo range observed quantity represented; t _kpseudorange after epoch is level and smooth wherein, ρ (t _k) be t _kepoch pseudo range observed quantity;

Step 6:t _kthe variance evaluation amount of pseudorange after epoch is level and smooth as in step 3 in next recursive process

Step 7: when level and smooth epoch, number k was less than level and smooth number K epoch of setting, algorithm returns step 2 and carries out recursion, until k=K, algorithm recursion terminates.