# US 9,753,144 B1 · Bias and misalignment compensation for 6-DOF IMU using GNSS/INS data

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- Number: US 9,753,144 B1
- Document ID: US9753144B1
- Status: Granted
- Kind: B1
- Application number: 15/042,758
- Filed: 2016-02-12
- Published: 2017-08-17
- Granted: 2017-09-05
- Earliest claimed: 2016-02-12
- Assignees: GM Global Technology Operations LLC
- Applicants: GM Global Technology Operations LLC
- Inventors: Rouhollah Jafari; Shuqing Zeng
- Web page: https://patentgrep.com/patent/US9753144B1

## CPC

- G01S 19/47: the supplementary measurement being an inertial measurement, e.g. tightly coupled inertial
- G01C 21/12: executed aboard the object being navigated; Dead reckoning
- G01C 21/165: {combined with non-inertial navigation instruments}
- G01C 21/183: {Compensation of inertial measurements, e.g. for temperature effects}
- G01S 19/53: Determining attitude
- 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
- G01C: MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY (measuring liquid level G01F; radio navigation, determining distance or velocity by use of propagation effects, e.g. Doppler effects, propagation time, of radio waves, analogous arrangements using other waves G01S)

## Abstract

A system and method for correcting bias and angle misalignment errors in the angle rate and acceleration outputs from a 6-DOF IMU mounted to a vehicle. The method includes providing velocity and estimation attitude data in an inertial frame from, for example, a GNSS/INS, and determining an ideal acceleration estimation and an ideal rate estimation in a vehicle frame using the velocity and attitude data. The method then determines the IMU bias error and misalignment error using the ideal acceleration and rate estimations and the angle rate and acceleration outputs in an IMU body frame from the IMU.

## Claims

### Claim 1

A method for correcting bias and angle misalignment errors in angle rate and acceleration outputs from a six-degree of freedom (DOF) inertial measurement unit (IMU), said IMU being mounted on a platform, said method comprising:
obtaining velocity and estimation attitude data in an inertial frame;
determining an acceleration estimation and a rate estimation in a platform frame using the velocity and attitude data; and
determining an IMU bias error and a misalignment error using the acceleration and rate estimations and the angle rate and acceleration outputs from the IMU.

### Claim 2 (depends on 1)

The method according to claim 1 wherein obtaining velocity and attitude data includes obtaining velocity and attitude data from a global navigation satellite system (GNSS) and/or an inertial navigation system (INS).

### Claim 3 (depends on 1)

The method according to claim 1 wherein determining an acceleration estimation and a rate estimation includes transforming velocity, roll angle, pitch angle and yaw angle of the platform in the inertial frame to the platform frame.

### Claim 4 (depends on 3)

The method according to claim 3 wherein transforming velocity and roll, pitch and yaw includes using the equations:
{dot over (V)}v=−ΩvVv+Rnvgn+fv
{dot over (R)}nv=−ΩvRnv
where {dot over (V)}v is a time derivate of the velocity in the platform frame, gn=[0,0, −9.80665]t is a vector of gravitation acceleration in the inertial frame, f″ is an acceleration vector in the platform frame, and Rnv is a transformation matrix from the inertial frame to the platform frame corresponding to angle rotations of roll φ, pitch θ and yaw ψ, where:
R
n
v
=
[
⁢
cos
⁢
⁢
θcos
⁢
⁢
ψ
cos
⁢
⁢
θ
⁢
⁢
sin
⁢
⁢
ψ
-
sin
⁢
⁢
θ
cos
⁢
⁢
ψsin
⁢
⁢
ϕ
⁢
⁢
sin
⁢
⁢
θ
-
cos
⁢
⁢
ϕ
⁢
⁢
sin
⁢
⁢
ψ
sin
⁢
⁢
ϕ
⁢
⁢
sin
⁢
⁢
θ
⁢
⁢
sin
⁢
⁢
ψ
+
cos
⁢
⁢
ϕ
⁢
⁢
cos
⁢
⁢
ψ
cos
⁢
⁢
θ
⁢
⁢
sin
⁢
⁢
ϕ
cos
⁢
⁢
ψ
⁢
⁢
cos
⁢
⁢
ϕcosθ
+
sin
⁢
⁢
ϕ
⁢
⁢
sin
⁢
⁢
ψ
cos
⁢
⁢
ϕsinθ
⁢
⁢
sin
⁢
⁢
ψ
-
sin
⁢
⁢
θ
⁢
⁢
cos
⁢
⁢
ψ
cos
⁢
⁢
θ
⁢
⁢
cos
⁢
⁢
ϕ
⁢
]
⁢
and where Ωv=[ωvx] is a skew-symmetric matrix of the IMU angular rate outputs as:
Ω
v
=
[
0
-
ω
ψ
ω
θ
ω
ψ
0
-
ω
ϕ
-
ω
θ
ω
ϕ
0
]
.
Ωb=−{dot over (R)}nv(Rnv)T
fv={dot over (V)}v+ΩvVv−Rnvgn
where Ω is the angular rate, {dot over (V)}v is obtained using numerical derivatives of the velocity data, and {dot over (R)}nv is obtained as:
R
.
n
v
=
∂
R
n
v
ϕ
⁢
ϕ
.
+
∂
R
n
v
θ
⁢
θ
.
+
∂
R
n
v
ψ
⁢
ψ
.
where {dot over (φ)}, {dot over (θ)} and {dot over (ψ)} are calculated numerically.

### Claim 5 (depends on 1)

The method according to claim 1 wherein determining an IMU bias error and a misalignment error includes comparing the acceleration estimation and the ideal rate estimation to the angle rate and acceleration outputs from the IMU.

### Claim 6 (depends on 5)

The method according to claim 5 wherein comparing the acceleration estimation and the rate estimation includes transforming the acceleration and angular rate estimations from the platform frame to an IMU body frame.

### Claim 7 (depends on 6)

The method according to claim 6 wherein determining the IMU bias error and misalignment error includes identifying three misalignment angles using the acceleration estimations at two different sample time.

### Claim 8 (depends on 7)

The method according to claim 7 wherein determining the misalignment angles includes varying a longitudinal acceleration of the platform with a constant lateral and vertical acceleration.

### Claim 9 (depends on 7)

The method according to claim 7 wherein determining the misalignment angles includes varying the longitudinal and vertical accelerations of the platform with a constant lateral acceleration.

### Claim 10 (depends on 7)

The method according to claim 7 wherein determining the IMU bias error and misalignment error includes using equations:
fbias=fb−Rvbfv,
ωbias=ωb−Rvbωv.

### Claim 11 (depends on 1)

The method according to claim 1 further comprising using the IMU bias error and misalignment error to determine platform velocity in the event that providing velocity and estimation attitude data is unavailable.

### Claim 12 (depends on 1)

The method according to claim 1 wherein the platform is a vehicle and the IMU is mounted to a vehicle structure.

### Claim 13

A method for correcting bias and angle misalignment errors in angle rate and acceleration outputs from a six-degree of freedom (DOF) inertial measurement unit (IMU) mounted on a vehicle, said method comprising:
providing velocity and estimation attitude data in an inertial frame from a global navigation satellite system (GNSS) and/or an inertial navigation system (INS);
determining an acceleration estimation and a rate estimation in a vehicle frame using the velocity and attitude data that includes transforming velocity, roll angle, pitch angle and yaw angle of the vehicle in the inertial frame to the vehicle frame; and
determining an IMU bias error and a misalignment error using the acceleration and rate estimations and the angle rate and acceleration outputs from the IMU that includes comparing the acceleration estimation and the rate estimation to the angle rate and acceleration outputs from the IMU and transforming the acceleration and angular rate estimations from the vehicle frame to an IMU body frame.

### Claim 14 (depends on 13)

The method according to claim 13 wherein determining the IMU bias error and misalignment error includes identifying three misalignment angles using the ideal acceleration estimations at two different sample time.

### Claim 15 (depends on 14)

The method according to claim 14 wherein determining the misalignment angles includes varying a longitudinal acceleration of the vehicle with a constant lateral and vertical acceleration.

### Claim 16 (depends on 14)

The method according to claim 14 wherein determining the misalignment angles includes varying the longitudinal and vertical accelerations of the vehicle with a constant lateral acceleration.

### Claim 17 (depends on 14)

The method according to claim 14 wherein determining the IMU bias error and misalignment error includes using equations:
fbias=fb−Rvbfv,
ωbias=ωb−Rvbωv,
where fbias is the misalignment error, fb is acceleration in the body frame, fv is acceleration in the vehicle frame, ωbias is the bias error, ωb is angular rate in the body frame, ωv is angular rate in the vehicle frame, and Rvb is a transformational matrix between the vehicle frame and the body frame.

### Claim 18 (depends on 13)

The method according to claim 13 further comprising using the IMU bias error and misalignment error to determine vehicle velocity in the event that providing velocity and estimation attitude data is unavailable.

### Claim 19

A system for correcting bias and angle misalignment errors in angle rate and acceleration outputs from a six-degree of freedom (DOF) inertial measurement unit (IMU), said IMU being mounted on a platform, said system comprising:
means for providing velocity and estimation attitude data in an inertial frame;
means for determining an ideal acceleration estimation and a rate estimation in a platform frame using the velocity and attitude data; and
means for determining an IMU bias error and a misalignment error using the acceleration and rate estimations and the angle rate and acceleration outputs from the IMU.

### Claim 20 (depends on 19)

The system according to claim 19 wherein the means for providing velocity and attitude data provides the velocity and attitude data from a global navigation satellite system (GNSS) and/or an inertial navigation system (INS).