1. An apparatus for estimating a roll angle of a projectile, comprising:
a measurement unit disposed within the projectile, the measurement unit outputting roll rate, yaw rate, and pitch rate signals indicative of rotation rates about substantially orthogonal roll, yaw, and pitch axes, the roll axis substantially aligned with a longitudinal axis of the projectile; and
a controller disposed within the projectile, the controller for estimating the roll angle by:
sampling the roll rate, yaw rate, and pitch rate signals to obtain time sequential roll rate, yaw rate, and pitch rate samples,
calculating time sequential cumulative roll estimates by summing the roll rate samples,
calculating time sequential gravity vector estimates from the corresponding yaw rate and pitch rate samples,
de-rolling each gravity vector estimate based on the corresponding cumulative roll estimate,
filtering the de-rolled gravity vector estimates to determine a filtered initial roll estimate, and
adding the filtered initial roll estimate to a current cumulative roll estimate to provide a current roll angle estimate.
2. The apparatus for estimating a roll angle of a projectile of claim 1, wherein filtering the de-rolled gravity vector estimates comprises integrating the de-rolled gravity vector estimates.
3. The apparatus for estimating a roll angle of a projectile of claim 1, wherein filtering the de-rolled gravity vector estimates comprises:
determining a primary coning frequency
processing the de-rolled gravity vector estimates to reject the primary coning frequency.
4. The apparatus for estimating a roll angle of a projectile of claim 3, wherein determining a primary coning frequency comprises a windowed Fourier transform.
5. The apparatus for estimating a roll angle of a projectile of claim 3, wherein processing the de-rolled gravity vector estimates comprises forming a moving average of the integral of the de-rolled gravity vector estimates with an averaging time period equal to the period of the primary coning frequency.
6. The apparatus for estimating a roll angle of a projectile of claim 1, wherein filtering the de-rolled gravity vector estimates comprises:
integrating the de-rolled gravity vector estimates;
processing the de-rolled gravity vector estimates to reject a primary coning frequency; and
selecting either the integrated de-rolled gravity vector estimates or the processed de-rolled gravity vector estimates as the initial roll orientation.
7. The apparatus for estimating a roll angle of a projectile of claim 6, wherein the selecting is based on a coning amplitude.
8. A method for estimating a roll angle of a projectile, comprising:
sampling roll rate, yaw rate, and pitch rate signals provided by a measurement unit to obtain time sequential roll rate, yaw rate, and pitch rate samples,
calculating time sequential cumulative roll estimates by summing the roll rate samples,
calculating time sequential gravity vector estimates from the corresponding yaw rate and pitch rate samples,
de-rolling each gravity vector estimate based on the corresponding cumulative roll estimate,
filtering the de-rolled gravity vector estimates to determine a filtered initial roll estimate, and
adding the filtered initial roll estimate to a current cumulative roll estimate to provide a current roll angle estimate.
9. The method for estimating a roll angle of a projectile of claim 8, wherein filtering the de-rolled gravity vector estimates comprises integrating the de-rolled gravity vector estimates.
10. The method for estimating a roll angle of a projectile of claim 8, wherein filtering the de-rolled gravity vector estimates is performed with an adaptive filter.
11. The method for estimating a roll angle of a projectile of claim 8, wherein filtering the de-rolled gravity vector estimates comprises:
determining a primary coning frequency
processing the de-rolled gravity vector estimates to reject the primary coning frequency.
12. The method for estimating a roll angle of a projectile of claim 11, wherein determining a primary coning frequency comprises a windowed Fourier transform.
13. The method for estimating a roll angle of a projectile of claim 11, wherein processing the de-rolled gravity vector estimates comprises forming a moving average of the integral of the de-rolled gravity vector estimates with an averaging time period equal to the period of the primary coning frequency.
14. The method for estimating a roll angle of a projectile of claim 8, wherein filtering the de-rolled gravity vector estimates comprises:
filtering the de-rolled gravity vector estimates using a plurality of filters to provide a corresponding plurality of filter results;
selecting one of the plurality of filter results as the filtered initial roll estimate.
15. The method for estimating a roll angle of a projectile of claim 14, wherein the plurality of filters comprises:
a first filter that integrates the de-rolled gravity vector estimates; and
a second filter that processes the de-rolled gravity vector estimates to reject a primary coning frequency.
16. The method for estimating a roll angle of a projectile of claim 15, wherein either the integrated de-rolled gravity vector estimates or the processed de-rolled gravity vector estimates is selected as the filtered initial roll estimate based on a coning amplitude.
The claims below are in addition to those above.
All refrences to claim(s) which appear below refer to the numbering after this setence.
What is claimed is:
1. A scanning optical system comprising:
an object side lens unit for condensing light from an object:
a mirror for performing a main scan to read the image of the object by deflecting the light transmitted through the object side lens; and
an image side lens unit for forming an image on the image sensing surface using both the extra-axial light and axial light in a subscan direction deflected by the mirror; and
wherein the following condition is satisfied:
0.1<(fpfm)Lf<20.0
where fp represents the sum of the Abbe numbers of the positive optical power lenses within the object side lens unit. fm represents the sum of the Abbe numbers of the negative optical power lenses within the object side lens unit, and Lf represents the number of lenses in the object side lens unit.
2. The scanning optical system according to claim 1, wherein the following condition is satisfied:
10.0<(rprm)Lr<50.0
where rp represents the sum of the Abbe numbers of the positive optical power lenses within the image side lens unit, rm represents the sum of the Abbe numbers of the negative optical power lenses within the image side lens unit, and Lr represents the number of lenses in the image side lens unit.
3. The scanning optical system according to claim 1, wherein the object side lens unit has a cemented lens comprising a negative lens element and a positive lens element on the outermost object side.
4. The scanning optical system according to claim 3, wherein the cemented lens satisfies the following condition:
f1f<1.0
where f1 represents the optical power of the cemented lens on the outermost object side within the object side lens unit, and f represents the optical power of the object side lens unit.
5. The scanning optical system according to claim 1, wherein the object side lens unit comprises sequentially from the object side an object side front lens unit and an object side back lens unit arranged with a relatively large spacing there between.
6. The scanning optical system according to claim 5, wherein the outermost image side lens element within the object side front lens unit and the outermost object side lens element within the object side back lens unit satisfy the condition below:
0.4<Rf1rRf2f<5.0
where Rf1r represents the radius of curvature of the image side surface of the outermost image side lens element within the object side front lens unit, and Rf2f represents the radius of curvature of the object side surface of the outermost object side lens element within the object side back lens unit.
7. The scanning optical system according to claim 5, wherein the object side front lens unit satisfies the following condition:
0.05<Tf12f<0.4
where Tf12 represents the distance between the object side front lens unit and the object side back lens unit, and f represents the optical power of the object side lens unit.