Effect of Carouseling on Angular Rate Sensor Error Processes

Collin, Jussi; Kirkko-Jaakkola, Martti; Takala, Jarmo

doi:10.1109/tim.2014.2335921

Cited by 16 publications

(10 citation statements)

References 28 publications

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“…The RMS (Root Mean Square) of azimuth misalignment

σ_{ϕ_{D b}}

σ_{ϕ_{D a}}

σ_{ϕ_{D r}}

and

σ_{ϕ_{D m}}

due to

ε_{b E}

w_{a E}

ε_{r E}

and

ε_{m E}

can be expressed as [15,16]:

σ_{ϕ_{D b}} = \frac{σ_{b E}}{normalΩ \cos L}

σ_{ϕ_{D a}} = \frac{σ_{a E}}{\sqrt{t_{n}} normalΩ \cos L}

σ_{ϕ_{D r}} = \frac{σ_{r E} \sqrt{t_{n}}}{\sqrt{3} normalΩ \cos L}

σ_{ϕ_{D m}} = \frac{\sqrt{\frac{1}{2} τ^{2} σ_{m E}^{2} false(2 t - τ e^{- \frac{2 t}{τ}} + 4 τ e^{- \frac{t}{τ}} - 3 τ false) + P_{ε_{m E}} false(0 false) τ false(1 - 2 e^{- \frac{1}{τ} t} + e^{- \frac{2}{τ} t} false)}}{t_{n} normalΩ \cos L}

where

t_{n}

is the alignment time.

…”

Section: Error Model For a Coriolis Vibration Gyroscopementioning

confidence: 99%

“…Proof of Equation (9) (Propagation of the ARW in a North-Finding System) [15,16]The equivalent east gyroscope integration error

δ θ_{a E}

caused by the ARW can be expressed as follows:

δ {\overset{θ}{true}}_{a E} = w_{a E}, w_{a E} \in N (0, σ_{a E}^{2})

P_{a E}

is the variance of

δ θ_{a E}

which can be expressed as follows:

\begin{array}{l} {\dot{P}}_{a E} = q_{a E} = σ_{a E}^{2} \\ P_{a E} false(t false) = σ_{a E}^{2} t \end{array}

where

q_{a E}

is the variance of

w_{a E}

t

is the integration time.…”

Section: Appendix A1 Proof Of Equation (9) (Propagation Of the Arw mentioning

confidence: 99%

“…Theoretical Proof of the Effects of the Continuous Rotation on the ARW [15]When the turntable is rotating, the equivalent east gyroscope integration error

δ θ_{a E}

caused by the ARW can be expressed as follows:

δ {\dot{θ}}_{a E} = B_{a} [\begin{matrix} w_{a x} \\ w_{a y} \end{matrix}]

in which

B_{a} = [\begin{matrix} \sin ω_{0} t & \cos ω_{0} t \end{matrix}]

w_{a x} \in N false(0, σ_{a E}^{2} false), w_{a y} \in N false(0, σ_{a E}^{2} false)

Suppose:

q_{a} = E false{[\begin{matrix} w_{a x} \\ w_{a y} \end{matrix}] {[\begin{matrix} w_{a x} \\ w_{a y} \end{matrix}]}^{T} false} = [\begin{matrix} σ_{a E}^{2} & 0 \\ 0 & σ_{a E}^{2} \end{matrix}]

The state covariance matrix

P_{a}

can be calculated as follows:

\begin{matrix} {\dot{P}}_{a} = B_{a} q_{a} {boldnormal B}_{a}^{T} = [\begin{matrix} \sin ω_{0} t & \cos ω_{0} t \end{matrix}] boldnormal q [\begin{matrix} \sin ω_{0} t \\ \cos ω_{0} \end{matrix} \end{matrix}

…”

Section: Appendix A1 Proof Of Equation (9) (Propagation Of the Arw mentioning

confidence: 99%

See 2 more Smart Citations

A New Continuous Rotation IMU Alignment Algorithm Based on Stochastic Modeling for Cost Effective North-Finding Applications

Jiang

et al. 2016

Sensors

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Based on stochastic modeling of Coriolis vibration gyros by the Allan variance technique, this paper discusses Angle Random Walk (ARW), Rate Random Walk (RRW) and Markov process gyroscope noises which have significant impacts on the North-finding accuracy. A new continuous rotation alignment algorithm for a Coriolis vibration gyroscope Inertial Measurement Unit (IMU) is proposed in this paper, in which the extended observation equations are used for the Kalman filter to enhance the estimation of gyro drift errors, thus improving the north-finding accuracy. Theoretical and numerical comparisons between the proposed algorithm and the traditional ones are presented. The experimental results show that the new continuous rotation alignment algorithm using the extended observation equations in the Kalman filter is more efficient than the traditional two-position alignment method. Using Coriolis vibration gyros with bias instability of 0.1°/h, a north-finding accuracy of 0.1° (1σ) is achieved by the new continuous rotation alignment algorithm, compared with 0.6° (1σ) north-finding accuracy for the two-position alignment and 1° (1σ) for the fixed-position alignment.

show abstract

“…The RMS (Root Mean Square) of azimuth misalignment

σ_{ϕ_{D b}}

σ_{ϕ_{D a}}

σ_{ϕ_{D r}}

and

σ_{ϕ_{D m}}

due to

ε_{b E}

w_{a E}

ε_{r E}

and

ε_{m E}

can be expressed as [15,16]:

σ_{ϕ_{D b}} = \frac{σ_{b E}}{normalΩ \cos L}

σ_{ϕ_{D a}} = \frac{σ_{a E}}{\sqrt{t_{n}} normalΩ \cos L}

σ_{ϕ_{D r}} = \frac{σ_{r E} \sqrt{t_{n}}}{\sqrt{3} normalΩ \cos L}

σ_{ϕ_{D m}} = \frac{\sqrt{\frac{1}{2} τ^{2} σ_{m E}^{2} false(2 t - τ e^{- \frac{2 t}{τ}} + 4 τ e^{- \frac{t}{τ}} - 3 τ false) + P_{ε_{m E}} false(0 false) τ false(1 - 2 e^{- \frac{1}{τ} t} + e^{- \frac{2}{τ} t} false)}}{t_{n} normalΩ \cos L}

where

t_{n}

is the alignment time.

…”

Section: Error Model For a Coriolis Vibration Gyroscopementioning

confidence: 99%

“…Proof of Equation (9) (Propagation of the ARW in a North-Finding System) [15,16]The equivalent east gyroscope integration error

δ θ_{a E}

caused by the ARW can be expressed as follows:

δ {\overset{θ}{true}}_{a E} = w_{a E}, w_{a E} \in N (0, σ_{a E}^{2})

P_{a E}

is the variance of

δ θ_{a E}

which can be expressed as follows:

\begin{array}{l} {\dot{P}}_{a E} = q_{a E} = σ_{a E}^{2} \\ P_{a E} false(t false) = σ_{a E}^{2} t \end{array}

where

q_{a E}

is the variance of

w_{a E}

t

is the integration time.…”

Section: Appendix A1 Proof Of Equation (9) (Propagation Of the Arw mentioning

confidence: 99%

“…Theoretical Proof of the Effects of the Continuous Rotation on the ARW [15]When the turntable is rotating, the equivalent east gyroscope integration error

δ θ_{a E}

caused by the ARW can be expressed as follows:

δ {\dot{θ}}_{a E} = B_{a} [\begin{matrix} w_{a x} \\ w_{a y} \end{matrix}]

in which

B_{a} = [\begin{matrix} \sin ω_{0} t & \cos ω_{0} t \end{matrix}]

w_{a x} \in N false(0, σ_{a E}^{2} false), w_{a y} \in N false(0, σ_{a E}^{2} false)

Suppose:

q_{a} = E false{[\begin{matrix} w_{a x} \\ w_{a y} \end{matrix}] {[\begin{matrix} w_{a x} \\ w_{a y} \end{matrix}]}^{T} false} = [\begin{matrix} σ_{a E}^{2} & 0 \\ 0 & σ_{a E}^{2} \end{matrix}]

The state covariance matrix

P_{a}

can be calculated as follows:

\begin{matrix} {\dot{P}}_{a} = B_{a} q_{a} {boldnormal B}_{a}^{T} = [\begin{matrix} \sin ω_{0} t & \cos ω_{0} t \end{matrix}] boldnormal q [\begin{matrix} \sin ω_{0} t \\ \cos ω_{0} \end{matrix} \end{matrix}

…”

Section: Appendix A1 Proof Of Equation (9) (Propagation Of the Arw mentioning

confidence: 99%

See 1 more Smart Citation

A New Continuous Rotation IMU Alignment Algorithm Based on Stochastic Modeling for Cost Effective North-Finding Applications

Jiang

et al. 2016

Sensors

View full text Add to dashboard Cite

show abstract

“…Rotation modulation is often used to improve the inertial navigation system precision [14,15,16]. It refers to rotating the IMUs around one axis, or multiple axes continuously or discretely.…”

Section: Introductionmentioning

confidence: 99%

“…It refers to rotating the IMUs around one axis, or multiple axes continuously or discretely. The inertial sensors’ bias drift and other slowly changing errors can be modulated to zero-mean periodical values [14,16]. This makes the MEMS gyro north finder an intriguing possibility and a development trend [15].…”

Section: Introductionmentioning

confidence: 99%

A Novel MEMS Gyro North Finder Design Based on the Rotation Modulation Technique

Zhang

Zhou

Song

et al. 2017

Sensors

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Gyro north finders have been widely used in maneuvering weapon orientation, oil drilling and other areas. This paper proposes a novel Micro-Electro-Mechanical System (MEMS) gyroscope north finder based on the rotation modulation (RM) technique. Two rotation modulation modes (static and dynamic modulation) are applied. Compared to the traditional gyro north finders, only one single MEMS gyroscope and one MEMS accelerometer are needed, reducing the total cost since high-precision gyroscopes and accelerometers are the most expensive components in gyro north finders. To reduce the volume and enhance the reliability, wireless power and wireless data transmission technique are introduced into the rotation modulation system for the first time. To enhance the system robustness, the robust least square method (RLSM) and robust Kalman filter (RKF) are applied in the static and dynamic north finding methods, respectively. Experimental characterization resulted in a static accuracy of 0.66° and a dynamic repeatability accuracy of 1°, respectively, confirming the excellent potential of the novel north finding system. The proposed single gyro and single accelerometer north finding scheme is universal, and can be an important reference to both scientific research and industrial applications.

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