JP2012173190A - Positioning system and positioning method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a positioning method with high precision such that inertia sensor data and GPS positioning data are merged together.SOLUTION: The positioning method of positioning a moving body by merging the inertia sensor data and GPS positioning data together includes the processes: performing time update of an extended Kalman filter using a multiplication type quaternion error model based upon the inertia sensor data; performing observation update of the extended Kalman filter based upon the GPS positioning data, and estimating a position error, a speed error, and an azimuth error, and a gyro bias error and an acceleration bias error; and correcting errors in position, speed, and attitude based upon the estimated position error, speed error, azimuth error, gyro bias error, and acceleration bias error.

Description

  The present invention relates to a positioning system and a positioning method.

In locations such as indoors and tunnels where positioning data is difficult to obtain, high-precision positioning such as the position, speed, and posture of a moving object is performed regardless of whether it is indoors or outdoors by fusing inertial navigation data and positioning data.
As a positioning system or positioning method that combines inertial navigation data and positioning data, there is one that corrects the position, velocity, and attitude errors of a moving object using a state estimation Kalman filter using inertial navigation data and positioning data. is there. In the state estimation Kalman filter, the error of the position, speed, and posture of the moving object is modeled using the minute change unit quaternion specified by the state variable with a small number of elements, and the error is estimated. There has been proposed a positioning system and a positioning method for correcting position, velocity, and attitude data by multiplying error data (see, for example, Patent Document 1).

JP 2007-276507 A

  In Patent Document 1, inertial sensor data and GPS positioning data are merged to correct the position, speed, and posture of a moving body. However, a small, lightweight, and low-cost inertial sensor (for example, a MEMS sensor) has a large bias error and random drift, and has a problem that high-precision positioning of the position, speed, and posture of a moving body cannot be performed.

  SUMMARY An advantage of some aspects of the invention is to solve at least a part of the problems described above, and the invention can be implemented as the following forms or application examples.

[Application Example 1] A positioning system according to this application example includes gyro bias error estimation and acceleration bias error estimation based on inertial sensor data and GPS positioning data, and position error / speed error / azimuth error estimation. An extended Kalman filter calculation unit that performs bias correction of angular velocity data based on the gyro bias error, and a bias correction unit that performs bias correction of acceleration data based on the acceleration bias error, and the bias corrected angular velocity data A posture calculation unit that calculates posture data based on the data, a coordinate conversion unit that outputs acceleration data of the navigation frame based on the bias-corrected acceleration data and the posture data, and a position / speed calculated based on the acceleration data of the navigation frame Position / velocity calculation unit, and the position An error correction unit that corrects the position / velocity calculated by the speed calculation unit and the attitude data based on the estimation error of the position / velocity / direction output from the extended Kalman filter calculation unit, and the extension Based on the position / velocity calculated by the position / velocity calculation unit and the attitude data calculated by the attitude calculation unit, the Kalman filter calculation unit uses the multiplication type quaternion error model, The acceleration bias error and the position error / velocity error / azimuth error are estimated.
The inertial sensor data means angular velocity data and acceleration data detected by a gyro sensor and an acceleration sensor.

  According to the positioning system of this application example, attitude error modeling is performed using a multiplication type quaternion (hereinafter, sometimes referred to as multiplication type quaternion) error model, and the position, velocity, Posture error is estimated, gyro sensor and acceleration sensor bias errors are estimated, and error correction is performed. The attitude multiplying quaternion error model has a higher accuracy of estimation error than the additive quaternion error model. From this, it is possible to reduce the size and cost, but even when using MEMS (Micro Electro Mechanical System) sensors with large fluctuations in bias error and random drift, even in places where GPS positioning data is interrupted, such as in tunnels and indoors. High-precision positioning is possible.

Application Example 2 A positioning method according to this application example is a positioning method in which inertial sensor data and GPS positioning data are fused to perform positioning of a moving body, and based on the inertial sensor data, a multiplication type quaternion error model The time update of the extended Kalman filter using, and the observation update of the extended Kalman filter based on the GPS positioning data to estimate the position error, velocity error, azimuth error, gyro bias error, acceleration bias error And correcting each position / velocity / attitude error based on the estimated position error / velocity error / azimuth angle error and inertial sensor data based on the estimated gyro bias error / acceleration bias error. And determining at least one of the position, speed, and posture of the moving body. It is characterized in.
Note that the time update of the extended Kalman filter is to update the state vector and the error covariance every time, and the observation update is to update the state vector and the error covariance by obtaining correction information from the outside. That is.

  According to the positioning method of this application example, the attitude error is modeled using the multiplication type quaternion error model, the time update and observation update of the extended Kalman filter are performed, the gyro bias error / acceleration bias error estimation and error correction, By combining error estimation and error correction of GPS positioning data (position, speed, direction), it is possible to perform highly accurate positioning of a moving body in a tunnel or indoor.

  Application Example 3 In the positioning method according to the application example described above, it is preferable that at least one of the azimuth angle error and the position error is error-modeled using a multiplication quaternion.

  As described above, by performing position error modeling in addition to posture error modeling, positioning of a moving body with higher accuracy can be performed.

[Application Example 4] The positioning method according to the application example described above uses distance information and relative velocity information observed from the outside as observation information, and an error of the position / velocity / azimuth angle of the moving body by a multiplication quaternion error model. It is preferable to estimate the gyro bias error / acceleration bias error and correct the position / velocity / posture of the moving body.
Here, the distance information and the relative velocity information (sometimes referred to as “Measurement”) observed from the outside include relative velocity information using pseudorange and Doppler effect.

  As described above, it is also possible to perform highly accurate positioning of the moving body by correcting the error of the measurement data using the multiplication type quaternion error model.

  Application Example 5 In the positioning method according to this application example, when the moving body is moving, positioning is performed using the positioning method according to any one of claims 2 to 4, When the moving body is stopped, the speed is set to 0, the yaw angle is not changed, and the roll angle and the pitch angle are calculated from the detected values of the acceleration sensor to obtain the observed values. It is preferable to perform correction and correction of the gyro bias error and the acceleration bias error.

  When the moving body is stopped, the accuracy of the GPS positioning data is lowered. Therefore, using the multiplying quaternion error model with the roll angle and pitch angle calculated from the detected value of the acceleration sensor as the speed 0, the yaw angle invariant (δψ = 0), the posture correction, the gyro bias error, and By correcting the acceleration bias error, it is possible to detect the position and orientation of the moving body when stopped.

1 is a configuration block diagram showing an overview of a positioning system according to Embodiment 1. FIG. FIG. 2 is a configuration block diagram illustrating an outline of an arithmetic control unit according to the first embodiment. 5 is a flowchart illustrating an example of a positioning method according to the first embodiment. The graph showing an example of the movement locus | trajectory of the moving body by simulation. The graph showing an example of the speed of the moving body by simulation. Results of performance evaluation by simulation in the Z-axis direction. Results of performance evaluation by simulation related to attitude error. Results of performance evaluation by simulation related to attitude error. Results of performance evaluation by simulation related to gyro bias error. Results of performance evaluation by simulation related to acceleration bias error.

Hereinafter, embodiments of the present invention will be described with reference to the drawings.
(Embodiment 1)

  FIG. 1 is a configuration block diagram illustrating an overview of the positioning system according to the first embodiment. The positioning system 1 performs arithmetic processing on data input from the gyro sensor 20, the acceleration sensor 30, the GPS (Global Positioning System) signal receiving unit 40, the gyro sensor 20, the acceleration sensor 30, and the GPS signal receiving unit 40. The calculation control unit 10 and the storage unit 50 are included. The arithmetic control unit 10 is connected to a driving device 62 that controls the position, speed, and posture of the moving body, or a display unit 61 for displaying in the form of necessary data.

  The gyro sensor 20 is disposed on a moving body, and uses, for example, a quartz vibration sensor or a MEMS sensor, and detects a rotational angular velocity based on a Coriolis force that the micro diaphragm receives by rotation. In the present embodiment, a plurality of gyro sensors 20 are provided so as to detect the rotational angular velocities around each axis of the body frame (b-frame), and output data representing the rotational angular velocities around the axes.

  The acceleration sensor 30 is disposed on the moving body, and measures and outputs the acceleration of the moving body in at least one direction. In the present embodiment, the acceleration sensor 30 is a quartz vibration sensor or a MEMS sensor, and measures and outputs the movement acceleration of the moving body in each axial direction of the body frame.

  The GPS signal receiving unit 40 receives a signal from a GPS satellite and outputs data representing the position (latitude, longitude, altitude) of the moving body. Since the GPS signal receiver 40 used in the present embodiment is widely used, a detailed description thereof is omitted here.

The arithmetic control unit 10 is configured using a program control device such as a CPU (Central Processing Unit) and operates according to a program stored in the storage unit 50. In the present embodiment, the arithmetic control unit 10 determines the position, speed, posture, gyro sensor bias, and acceleration of the moving body based on each data output from the gyro sensor 20, the acceleration sensor 30, and the GPS signal receiving unit 40. Each error of the sensor bias is estimated and error correction is performed and output to an output unit such as the display unit 61 or the driving device 62 of the moving body to control the moving body.
The specific configuration and operation of the arithmetic control unit 10 will be described in detail later.

  The storage unit 50 is a storage element such as a RAM (Random Access Memory) and holds a program executed by the arithmetic control unit 10. The storage unit 50 also operates as a work memory for the arithmetic control unit 10. The storage unit 50 may be built in the calculation control unit 10.

In the following description, in order to identify which coordinate system each position, velocity, and orientation data is, the data is indexed to clarify which coordinate system it is. .
(1) A right-handed orthogonal coordinate system with the center of the earth as the origin and the Z-axis so as to be parallel to the rotation axis of the earth is referred to as an “i-frame”.
(2) A right-handed orthogonal coordinate system in which the center of the earth is the origin, the latitude 0 degree, longitude 0 degree direction is the X axis, and the Z axis is defined to be parallel to the rotation axis of the earth is referred to as an “e frame”.
(3) A right-handed orthogonal coordinate system with the moving body as the origin, the north direction as the X axis, and the direction of gravity by the earth as the Z axis is defined as “g frame”.
(4) A right-handed orthogonal coordinate system with the moving body as the origin and the gravity direction of the earth as the Z axis, and the coordinate system when the g frame is rotated by α (rad) about the Z axis in the g frame Is “n-frame”.
(5) A right-handed orthogonal coordinate system in which the moving body is the origin, the traveling direction of the moving body is the X axis, and the lift direction is the Z axis is “b-frame”.

  Note that the rotation around the X axis in the b frame is “roll (roll angle φ)”, the rotation around the Y axis is “pitch (pitch angle θ)”, and the rotation around the Z axis is “yaw (yaw angle ψ)”. Called.

Next, the configuration and operation of the arithmetic control unit 10 will be described with reference to the drawings and mathematical expressions.
FIG. 2 is a configuration block diagram illustrating an outline of the arithmetic control unit according to the first embodiment. The calculation control unit 10 includes a bias correction unit 11, an attitude calculation unit 12, a coordinate conversion unit 13, a position / velocity calculation unit 14, an error correction unit 15 (described as an error correction unit 15), and an extended Kalman filter calculation. The part 16 is configured as a main component.

  The bias correction unit 11 uses the estimated values of the gyro bias error and the acceleration bias error calculated by the extended Kalman filter calculation unit 16 to calculate the angular velocity data and the correction value of the acceleration data using Equation 1, and the acceleration data (B-frame) is output to the coordinate conversion unit 13, and the angular velocity data is output to the posture calculation unit 12.

  The posture calculation unit 12 obtains a posture by using an equation of motion related to the posture of the moving body (Formula 2), and inputs the posture to the coordinate conversion unit 13, the error correction unit 15, and the extended Kalman filter calculation unit 16.

  Based on the b-frame acceleration data output from the acceleration sensor 30 and the attitude data output from the attitude calculation unit 12, the coordinate conversion unit 13 converts the position data into n-frame acceleration data using Equation 3 based on the position data. / Output to speed calculation unit 14

  The position / velocity calculation unit 14 calculates the position and velocity using the equation of motion (Formula 4) related to the position and velocity, and outputs them to the error correction unit 15 and the extended Kalman filter calculation unit 16.

  The extended Kalman filter calculation unit 16 uses the posture data output from the posture calculation unit 12, the position data and velocity data output from the position / speed calculation unit 14, and the GPS positioning data (position, velocity, direction). Then, the Kalman filter estimates the position, velocity, and direction errors, calculates the gyro bias error and the acceleration bias error, and inputs them to the bias correction unit 11. In this embodiment, since the motion equations of speed and posture are nonlinear, an error model in which the Kalman filter is extended is applied. The error model can be expressed by Equation 5.

  Here, the attitude error model is not an addition of Quaternion, but introduces a small change unit quaternion having a smaller number of elements, and models the error using a multiplying Quaternion. Note that an addition-type Quaternion error model using a minute error is expressed by the following equation.

  The norm of the addition type Quaternion is expressed by the following equation.

  As represented by Expression 7, the norm of the addition-type Quaternion using the minute change unit quaternion cannot satisfy the constraint norm = 1.

  On the other hand, in the multiplication type Quaternion using minute error vector elements, the attitude error can be expressed by the following equation.

  The norm of the multiplication type Quaternion can be expressed by the following equation.

  As can be seen from Equation 9, the norm of the multiplication type quaternion is guaranteed to be 1 even in a state including an error by using the multiplication type quaternion error model, and the number of elements of the posture error vector is 4 The number of state vectors to be estimated can be reduced.

  Here, the error vector to be estimated can be expressed by Equation 10.

  Further, using GPS positioning data (position, velocity, direction) as observation data, an observation equation such as Equation 11 and an error covariance such as Equations 12 to 14 can be calculated.

  The estimated error covariance P is expressed by the following equation.

  The system error covariance Q is expressed by the following equation.

  The observation error covariance R is expressed by the following equation.

   From Equations 12 and 13, the time update of the Kalman filter can be expressed by the following equation.

  Further, the observation update of the Kalman filter can be expressed by Expressions 16 and 17.

  Using the estimated values of the position, velocity, azimuth angle, and gyro bias error and acceleration bias error estimated by the extended Kalman filter calculation unit 16, the gyro bias error and acceleration are corrected together with the correction of the position, velocity, and posture of the moving object. The bias error is corrected by an error correction unit (Error correction unit) 15 and output to the output unit 60 (display unit 61, drive device 62) to control the moving body.

Next, the positioning method will be described with reference to a flowchart.
FIG. 3 is a flowchart showing an example of the positioning method according to the present embodiment. Reference is also made to FIGS. First, angular velocity data is detected by the gyro sensor 20, and acceleration data is detected by the acceleration sensor 30 (ST1). Based on the detected angular velocity data and acceleration data, a bias correction unit 11 performs bias correction based on the gyro bias error and acceleration bias error estimated in step (ST7) described later (ST2).

  Subsequently, the posture of the moving body is calculated by the posture calculation unit 12 based on the bias-corrected angular velocity data (ST3). The bias-corrected acceleration data (b-frame) is converted into n-frame data by the coordinate converter 13 and input to the position / velocity calculator 14. The position / speed calculation unit 14 calculates the current position and speed of the moving body (ST4).

  Next, the time update of the extended Kalman filter using the multiplication-type Quaternion error model is performed (ST5). The extended Kalman filter is composed of two steps of time update and observation update. Here, the time update is to update the state vector and the error covariance for each time by using the state equation. If there is no correction information from the outside, errors are accumulated more and more. The observation update is to obtain correction information from the outside, correct the accumulated error, and update the state vector and the error covariance.

  Next, it is determined whether or not a GPS observation signal (GPS positioning data) is detected (ST6). When the GPS observation signal is not detected (No), the steps ST1 to ST5 are repeated. When a GPS observation signal is detected (Yes), the extended Kalman filter calculation unit 16 updates the observation of the extended Kalman filter using the multiplication-type Quaternion error model, and each error of position / velocity / attitude, and gyro bias / acceleration bias Is estimated (ST7).

Next, the gyro bias value and acceleration bias value are updated and position / velocity / posture error correction is performed (ST8), and the position / velocity / posture data with the corrected error is output to the output unit 60 of the moving body (ST9). ). In ST8, the updated gyro bias value and acceleration bias value are input to the bias correction unit 11, the updated attitude is input to the attitude calculation unit 12, and the updated position / velocity information is the position / speed calculation. Input to the unit 14 and repeated in a loop as shown.
(Example)

Next, a specific example of the present embodiment will be described with reference to the drawings for comparison results of error estimation of each error model of the multiplication type quaternion and the addition type quaternion. First, the movement trajectory and speed of a moving body that is a comparison basis will be described.
4 and 5 are graphs showing an example of the movement trajectory and speed by simulation of the moving body. 4A shows the movement trajectory of the moving body (horizontal axis is longitude, vertical axis is latitude), FIG. 4B shows altitude movement (horizontal axis is time [time: sec], and vertical axis is Altitude [m]). FIG. 5A shows the movement in the north-south direction, and FIG. 5B shows the movement in the east-west direction. In both cases, the horizontal axis represents time (time [sec]), and the vertical axis represents speed [m / s]. FIG. 5C shows the velocity [m / s] in the direction perpendicular to the horizontal plane (Z-axis direction). That is, this simulation is a case where the moving body is moving in the horizontal direction.

  Next, based on the movement trajectory of the moving body shown in FIGS. 4 and 5, the performance comparison result between the multiplication type quaternion error model and the addition type quaternion error model will be described.

  FIG. 6 shows the results of performance evaluation by simulation in the Z-axis direction, FIG. 6A shows the change in altitude, and FIG. 6B shows the change in speed [m / s] in the Z-axis direction. Note that, as shown in FIG. 4B, in the case of horizontal movement at an altitude of 684 m in the Z-axis direction, the multiplication-type Quaternion error model has better accuracy than the addition-type Quaternion error model. I understand.

Next, a simulation result of the posture error will be described.
7 and 8 show the results of performance evaluation by simulation related to the posture error, FIG. 7A shows the roll angle error (φ [deg]), and FIG. 7B shows the pitch angle error (θ [deg]). 8 shows the yaw angle error (ψ [deg]). The horizontal axis represents time (time [sec]), and the vertical axis represents error [deg].
Table 1 shows the dispersion value of each posture calculated from the simulation result.

  As can be seen from FIGS. 7 and 8 and Table 1, the error in the attitude of the moving body, that is, the roll angle error, the pitch angle error, and the yaw angle error is more in the multiplication type Quaternion than in the addition type Quaternion. Becomes smaller.

Next, a simulation result of the bias error will be described.
FIG. 9 shows the results of performance evaluation by simulation related to the bias error, FIG. 9 shows the Z-axis gyro bias error (Gyro Bias [rad / S]), and FIG. 10A shows the X-axis acceleration bias error (Acc). Bias [m / s / s]), FIG. 10B shows the Y-axis acceleration bias error (Acc Bias [m / s / s]). In both cases, the horizontal axis represents time (time [sec]).

  As can be seen from FIGS. 9 and 10, the estimated values of the gyro bias error and the acceleration bias error are smaller in the multiplication type Quaternion than in the addition type Quaternion.

  According to the positioning system and the positioning method of the present embodiment described above, inertial sensor data (acceleration data and angular velocity data) and GPS positioning data are fused, and an extended Kalman filter (extended Kalman filter calculation unit 16) In addition to estimating position, speed, and posture errors, each bias error of the gyro sensor 20 and the acceleration sensor 30 is estimated. Further, since the extended Kalman filter can accurately model the posture error using the multiplication-type Quaternion error model, the error of the position, velocity, posture, and sensor bias can be corrected with high accuracy.

Therefore, the position, velocity, attitude, gyro bias, and acceleration bias errors can be accurately corrected, and the inertial sensor can be reduced in size and cost, but the bias error and random drift fluctuations are large. Even if a sensor is used, highly accurate and highly stable sensor output can be obtained. Therefore, highly accurate positioning is possible even in places where GPS positioning data is interrupted, such as in tunnels and indoors.
(Embodiment 2)

  Next, Embodiment 2 will be described. While the first embodiment described above introduces a small change unit quaternion having a small number of elements and models the posture error using the multiplication-type Quaternion, the second embodiment has only the posture error model. In addition, the position error model is characterized in that the error is modeled using the multiplication type Quaternion. Specifically, error modeling is performed as shown in Equation 18.

In this way, in addition to attitude error modeling, position error modeling is performed to accurately perform error modeling using a multiplying quaternion, and errors in position, velocity, and sensor bias are corrected with higher accuracy. be able to.
(Embodiment 3)

  Subsequently, Embodiment 3 will be described. In the first embodiment described above, the positioning data (position, velocity, azimuth) from the GPS signal receiver 40 is used as observation data, and the position, velocity, orientation error of the moving object and the gyro sensor 20 by the extended Kalman filter, The bias error of the acceleration sensor 30 is estimated. In contrast to the first embodiment, in the third embodiment, at least distance information and relative velocity information (measurement) observed from the outside are used as observation information, and the position / velocity / posture error of the moving object is determined by a multiplication type quaternion error model. And gyro bias error / acceleration bias error are estimated, and the position / velocity / posture of the moving body is corrected.

As the measurement, relative velocity information using a pseudorange and a Doppler effect can be used, and even using such a method, it is possible to perform highly accurate positioning of the moving object.
(Embodiment 4)

Next, Embodiment 4 will be described. In the fourth embodiment, while the moving body is moving, the positioning data (position, speed) from the GPS signal receiving unit 40 using the positioning method described in the first, second, and third embodiments described above. , Azimuth), or distance information and relative speed information as observation data, the position, speed, and attitude errors of the moving body and the bias errors of the gyro sensor 20 and acceleration sensor 30 are estimated and corrected.
Here, since the accuracy of the positioning data from the GPS signal receiving unit 40 is not good while the moving body is stationary, in the fourth embodiment, the following observation data is used to detect position, speed, and posture errors. , And estimate the inertial sensor bias error.
(1) The speed is set to zero (V = 0).
(2) The yaw angle is unchanged (Δψ = 0).
(3) Since the moving body is stationary, the roll angle and the pitch angle are obtained from the output of the acceleration sensor 30 using the following mathematical formula.

  In this way, the roll angle and pitch angle calculated by Equation 19 and the zero speed and yaw angle invariant are used as observation values in the extended Kalman filter, and even when the moving body is stopped, Correction and sensor bias can be corrected.

  DESCRIPTION OF SYMBOLS 1 ... Positioning system, 10 ... Calculation control part, 11 ... Bias correction part, 12 ... Attitude calculation part, 13 ... Coordinate conversion part, 14 ... Position / speed calculation part, 15 ... Error (Error) correction part, 16 ... Extended Kalman Filter operation unit, 20 ... gyro sensor, 30 ... acceleration sensor, 40 ... GPS signal receiving unit.

Claims (5)

An extended Kalman filter calculation unit for performing gyro bias error estimation and acceleration bias error estimation, position error / velocity error / azimuth error estimation based on inertial sensor data and GPS positioning data;
A bias correction unit that performs bias correction of angular velocity data based on the gyro bias error, and performs bias correction of acceleration data based on the acceleration bias error;
An attitude calculation unit for calculating attitude data based on the bias-corrected angular velocity data;
A coordinate converter that outputs acceleration data of a navigation frame based on the bias-corrected acceleration data and the attitude data;
A position / velocity calculation unit for calculating a position / velocity based on the acceleration data of the navigation frame;
An error correction unit that corrects the position / velocity and the posture data calculated by the position / velocity calculation unit based on the estimation error of the position / velocity / azimuth output from the extended Kalman filter calculation unit;
Have
The extended Kalman filter calculation unit uses the multiplication quaternion error model based on the position / velocity calculated by the position / velocity calculation unit and the attitude data calculated by the attitude calculation unit. A positioning system that estimates the acceleration bias error and the position error / velocity error / azimuth error. A positioning method in which inertial sensor data and GPS positioning data are fused to perform positioning of a moving object,
Performing a time update of an extended Kalman filter using a multiplying quaternion error model based on the inertial sensor data;
Updating the extended Kalman filter based on the GPS positioning data, estimating a position error, velocity error, azimuth error, and gyro bias error / acceleration bias error;
Correcting each position / velocity / attitude error based on the estimated position error / velocity error / azimuth angle error;
Correcting inertial sensor data based on the estimated gyro bias error / acceleration bias error, and
A positioning method characterized in that at least one of position, speed, and posture of the moving body is obtained. The positioning method according to claim 2,
A positioning method, wherein at least one of the azimuth angle error and the position error is error-modeled using a multiplication quaternion. The positioning method according to claim 2,
Using the distance information and relative velocity information observed from the outside as observation information, the multiplication type quaternion error model is used to estimate the position / velocity / azimuth angle error of the moving body, and the gyro bias error / acceleration bias error. A positioning method, wherein the position, speed, and posture of the moving body are corrected. When the moving body is moving, positioning is performed using the positioning method according to any one of claims 2 to 4,
When the moving body is stopped, the velocity is set to 0, the yaw angle is not changed, the roll angle and the pitch angle are calculated from the detected values of the acceleration sensor to obtain the observed values, and the posture is determined based on the observed values. And a gyro bias error and an acceleration bias error are corrected.

Images