CN105510942A - Kalman filtering-based GPS single-point positioning system - Google Patents
Kalman filtering-based GPS single-point positioning system Download PDFInfo
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- CN105510942A CN105510942A CN201510987332.8A CN201510987332A CN105510942A CN 105510942 A CN105510942 A CN 105510942A CN 201510987332 A CN201510987332 A CN 201510987332A CN 105510942 A CN105510942 A CN 105510942A
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
- G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
- G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
- G01S19/42—Determining position
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
- G01S19/01—Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
- G01S19/13—Receivers
- G01S19/35—Constructional details or hardware or software details of the signal processing chain
- G01S19/37—Hardware or software details of the signal processing chain
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- Engineering & Computer Science (AREA)
- Radar, Positioning & Navigation (AREA)
- Remote Sensing (AREA)
- Signal Processing (AREA)
- Computer Networks & Wireless Communication (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Position Fixing By Use Of Radio Waves (AREA)
Abstract
The invention relates to a Kalman filtering-based GPS single-point positioning system. A Kalman filtering model and equations for GPS positioning are established, and Kalman filtering recursive calculation is carried out; in each positioning epoch process, a Kalman filter predicts the current position and speed of a receiver, and the clock difference of the GPS receiver through using an state equation; the Kalman filter can predict the pseudo-range and Doppler frequency shift of the GPS receiver relative to each satellite according to a state priori estimated value and the positions and velocities of the satellites provided by satellite ephemeris, and the differences of the measured predicted values and the actual measured values of the receiver can form measurement residuals; and the Kalman filter can obtain the correction quantity of a system state estimated value and an optimal estimated value after correction through processing the measurement residuals. According to the Kalman filtering-based GPS single-point positioning system of the invention, a GPS single-point positioning method and Kalman filtering technologies are mainly researched, and therefore, the estimation accuracy of positioning can be effectively improved.
Description
Technical field
What the present invention relates to is a kind of satellite positioning method, particularly be a kind of GPS single-point locating system based on Kalman filtering.
Background technology
GPS (being called for short GPS) is the satellite navigation and location system that U.S. Department of Defense started in 1973 to set up.The fundamental purpose that this system was set up originally is to provide Navigation and localization service to aeroamphibious delivery vehicle.Through the development of 20 years, consume tens billion of dollar, on March 10th, 1994,24 satellites are all disposed complete.Military, the civil navigation location of more than 10 year facts have proved, gps satellite navigation positioning system can provide round-the-clock, high-precision navigator fix service to multiple user in the scope in the whole world more than 98% simultaneously.
In daily life, most GPS position application is all adopt relative positioning.Because relative positioning have ignored complicated error component, so positioning equation resolves than faster, in the daily life that positioning accuracy request is not very high, namely this locator meams has saved the time undoubtedly, in turn ensure that positioning precision.But when adopting relative positioning mode to position, must be placed on receiver on known point as reference receiver using one, this adds the cost of location undoubtedly, but also the complexity that operation is become.Owing to affecting, these errors such as the error (as tropospheric delay error) of positioning precision can becoming gradually be uncorrelated along with the increase of the distance of receiver and satellite in addition, so the precision of location must be made to reach the precision of expection by the observation time postponing receiver.These shortcomings greatly limit the usable range of GPS relative positioning.For this problem, 1997 U.S. jet propulsion laboratory (JPL) the people such as zumbeger propose a kind of effective solution, i.e. non-poor accurate one-point positioning method.
The correction of the pseudorange value that traditional GPS One-Point Location needs known receiver to observe, co-ordinates of satellite that the satellite orbit parameter utilizing navigation message to provide calculates and satellite clock, just can position.The advantage of traditional GPS One-Point Location is that acquisition and processing data are fairly simple, and user only just need can obtain its three-dimensional coordinate in WGS--84 coordinate system by a GPS.But due to the impact of the precision being subject to the pseudorange that receiver observes, the precision of satellite position utilizing satellite navigation message to try to achieve and the precision of satellite clock, traditional GPS Point-positioning Precision is not very high, so traditional GPS One-Point Location can only be used in the field of some low precision.
Summary of the invention
The present invention is to obtain for the purpose of the optimum estimate of locating, and the method for main research GPS One-Point Location and Kalman Filter Technology, effectively to improve the estimated accuracy of location.
The object of the present invention is achieved like this:
First set up Kalman filter model and the equation of GPS location, carry out Kalman filtering recurrence calculation afterwards.In each location epoch process, Kalman filter first utilization state equation is predicted the current position of receiver, speed, GPS clock difference; Then, the satellite position provided according to this state priori estimates and satellite ephemeris and speed, Kalman filter just can predict that GPS is to the pseudorange of each satellite and values of Doppler frequency shift, and these differences measuring the actual measured value of predicted value and receiver define again measures remnants; Finally, Kalman filter just can obtain the correcting value of system state estimation value by carrying out process to measurement remnants and correct later optimal estimation value.
Carrying out utilizing Kalman filtering testing the speed, needing when locating to set up rationally, motion model accurately, inaccurate carrier movement model will cause filtering to produce Divergent Phenomenon in computation process.Constant speed model and constant accelerator model are two kinds of motion models that Kalman filtering is commonly used, and wherein constant speed model is the most idealized, the simplest a kind of motion model.Adopt constant speed model in the present invention, according to error observation equation, the basic model independently deriving Kalman filtering is as follows:
Kalman filter model may be summarized to be:
State equation:
=
+
(1)
Observation equation:
=HX+
(2)
In formula:
(0,
),
(0,
) be system noise and observation noise
=
(3)
=
(4)
State-transition matrix in state equation
for
=
(5)
Interference matrix
for
=
(6)
T is data sampling interval;
Matrix of coefficients
for
=
(7)
In above formula:
=
，
=
,
=
；
=
。
Accompanying drawing explanation
Fig. 1 is the Kalman filtering algorithm flow process of GPS location.
Embodiment
Below in conjunction with accompanying drawing citing, the present invention is described in more detail:
Composition graphs 1, Fig. 1 is the Kalman filtering algorithm flow process of GPS location.First set up Kalman filter model and the equation of GPS location, carry out Kalman filtering recurrence calculation afterwards.In each location epoch process, Kalman filter first utilization state equation is predicted the current position of receiver, speed, GPS clock difference; Then, the satellite position provided according to this state priori estimates and satellite ephemeris and speed, Kalman filter just can predict that GPS is to the pseudorange of each satellite and values of Doppler frequency shift, and these differences measuring the actual measured value of predicted value and receiver define again measures remnants; Finally, Kalman filter just can obtain the correcting value of system state estimation value by carrying out process to measurement remnants and correct later optimal estimation value.
The Kalman filter model of One-Point Location is generally constant speed model, can obtain higher positioning precision when carrying out filtering process by adopting above-mentioned model.The three-dimensional position of user and speed are certain state variables.Because gps system utilizes user clock to measure electric wave time of arrival, and user clock is generally crystal clock, and precision and stability is not high, and thus the clock correction of user clock and frequency difference also will as state variables.Ignore phase ambiguity, by the speed of receiver antenna, three-dimensional coordinate, receiver clock-offsets
with drift frequently
as state vector.The state vector of Kalman filtering is:
=
（8）
Observation model and the state equation of standard Kalman filtering requirements system are linear, and the observation equation in GPS One-Point Location is nonlinear, so will carry out linearizing process to observation equation.Conventional linearizing method is using the one-step prediction value of filtering as approximate value, and carry out Taylor expansion to observation equation at one-step prediction value place, carry out linearization process to observation equation, this method is called extended BHF approach.
Observational error equation is
=
－
+c
(9)
K point rough coordinates (
,
,
) (reading by observation file), will
=
+
,
=
+
,
=
+
bring in above formula, carry out Taylor expansion, ignore the high-order term of more than second order, the linear equation that pseudorange is located can be drawn
=
+
+
+
+c
(10)
In formula:
=
，
=
,
=
；
(
,
,
) for receiver k is to the observation vector of satellite j
direction cosine;
=
；
for receiver k is to the distance of satellite j
approximate value.
Error equation after linearization is write as matrix form
=HX+
。
Claims (2)
1. based on a GPS single-point locating system for Kalman filtering, it is characterized in that: Kalman filter model and the equation of first setting up GPS location, carry out Kalman filtering recurrence calculation afterwards; In each location epoch process, Kalman filter first utilization state equation is predicted the current position of receiver, speed, GPS clock difference; Then, the satellite position provided according to this state priori estimates and satellite ephemeris and speed, Kalman filter just can predict that GPS is to the pseudorange of each satellite and values of Doppler frequency shift, and these differences measuring the actual measured value of predicted value and receiver define again measures remnants; Finally, Kalman filter just can obtain the correcting value of system state estimation value by carrying out process to measurement remnants and correct later optimal estimation value.
2. a kind of GPS single-point locating system based on Kalman filtering according to claim 1, it is characterized in that: carry out utilizing Kalman filtering testing the speed, when locating needs set up rationally, motion model accurately, inaccurate carrier movement model will cause filtering to produce Divergent Phenomenon in computation process; Constant speed model and constant accelerator model are two kinds of motion models that Kalman filtering is commonly used, and wherein constant speed model is the most idealized, the simplest a kind of motion model; Adopt constant speed model in the present system, according to error observation equation, the basic model independently deriving Kalman filtering is as follows:
Kalman filter model may be summarized to be:
State equation:
=
+
(1)
Observation equation:
=HX+
(2)
In formula:
(0,
),
(0,
) be system noise and observation noise
=
(3)
=
(4)
State-transition matrix in state equation
for
=
(5)
Interference matrix
for
=
(6)
T is data sampling interval;
Matrix of coefficients
for
=
(7)
In above formula:
=
，
=
,
=
；
=
。
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| CN201510987332.8A CN105510942A (en) | 2015-12-27 | 2015-12-27 | Kalman filtering-based GPS single-point positioning system |
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| CN201510987332.8A CN105510942A (en) | 2015-12-27 | 2015-12-27 | Kalman filtering-based GPS single-point positioning system |
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Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2017215026A1 (en) * | 2016-06-16 | 2017-12-21 | 东南大学 | Extended kalman filter positioning method based on height constraint |
| CN108241161A (en) * | 2016-12-23 | 2018-07-03 | 瑞士优北罗股份有限公司 | For the distributed Kalman filter framework of reference carrier wave fuzziness estimation |
| CN108872790A (en) * | 2018-07-10 | 2018-11-23 | 武汉科技大学 | A kind of MMC method for diagnosing faults based on Kalman filtering and support vector machines |
| CN109696698A (en) * | 2019-03-05 | 2019-04-30 | 湖南国科微电子股份有限公司 | Navigator fix prediction technique, device, electronic equipment and storage medium |
| CN112526564A (en) * | 2020-12-01 | 2021-03-19 | 湘潭大学 | Precise single-point positioning re-convergence method |
| CN113109848A (en) * | 2021-04-14 | 2021-07-13 | 长沙学院 | Navigation positioning method under low-speed rotation condition of carrier and application system thereof |
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| JPH07198821A (en) * | 1994-01-06 | 1995-08-01 | Japan Radio Co Ltd | Gps receivr and its positoning method |
| CN101581774A (en) * | 2009-06-26 | 2009-11-18 | 山东正元地理信息工程有限责任公司 | High-precision point positioning method and system for global navigation satellite system (GNSS) |
| CN102540220A (en) * | 2011-12-30 | 2012-07-04 | 合众思壮北斗导航有限公司 | Satellite positioning method and equipment |
| CN105738931A (en) * | 2014-12-09 | 2016-07-06 | 哈尔滨米米米业科技有限公司 | GPS point positioning system based on Kalman filtering |
-
2015
- 2015-12-27 CN CN201510987332.8A patent/CN105510942A/en active Pending
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPH07198821A (en) * | 1994-01-06 | 1995-08-01 | Japan Radio Co Ltd | Gps receivr and its positoning method |
| CN101581774A (en) * | 2009-06-26 | 2009-11-18 | 山东正元地理信息工程有限责任公司 | High-precision point positioning method and system for global navigation satellite system (GNSS) |
| CN102540220A (en) * | 2011-12-30 | 2012-07-04 | 合众思壮北斗导航有限公司 | Satellite positioning method and equipment |
| CN105738931A (en) * | 2014-12-09 | 2016-07-06 | 哈尔滨米米米业科技有限公司 | GPS point positioning system based on Kalman filtering |
Cited By (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2017215026A1 (en) * | 2016-06-16 | 2017-12-21 | 东南大学 | Extended kalman filter positioning method based on height constraint |
| US10422883B2 (en) | 2016-06-16 | 2019-09-24 | Southeast University | Positioning method using height-constraint-based extended Kalman filter |
| CN108241161A (en) * | 2016-12-23 | 2018-07-03 | 瑞士优北罗股份有限公司 | For the distributed Kalman filter framework of reference carrier wave fuzziness estimation |
| CN108241161B (en) * | 2016-12-23 | 2023-03-10 | 瑞士优北罗股份有限公司 | Distributed Kalman filter architecture for carrier range ambiguity estimation |
| CN108872790A (en) * | 2018-07-10 | 2018-11-23 | 武汉科技大学 | A kind of MMC method for diagnosing faults based on Kalman filtering and support vector machines |
| CN109696698A (en) * | 2019-03-05 | 2019-04-30 | 湖南国科微电子股份有限公司 | Navigator fix prediction technique, device, electronic equipment and storage medium |
| CN112526564A (en) * | 2020-12-01 | 2021-03-19 | 湘潭大学 | Precise single-point positioning re-convergence method |
| CN113109848A (en) * | 2021-04-14 | 2021-07-13 | 长沙学院 | Navigation positioning method under low-speed rotation condition of carrier and application system thereof |
| CN113109848B (en) * | 2021-04-14 | 2023-03-14 | 长沙学院 | Navigation positioning method under low-speed rotation condition of carrier |
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Application publication date: 20160420 |