When a missile is engaged in a GPS free tracking loop how is its internal orientation estimated with respect to ground?
I'm assuming this orientation is needed because the force of gravity will be impacting the missiles flight path and this needs to be compensated for, am I wrong? Do they all use IMU? The IMU I have looked at all have bad performance and the cost of extreme precision IMU is greater than the smaller missiles so that can't be the solution.
As per comments, this question is referring to guided weapons such as Stinger (IR guidance).
Guided missiles that acquire their target via signal return, such as infrared, radar or laser designation (Homing Guidance, see section 16.4.2) have absolutely no need to "know" their orientation in space. A target lock is established pre or post launch and then maintained by missile sensors, and the sensor signal is then used to calculate necessary maneuvers to steer towards the target.
Any information regarding where in space and in what alignment in reference to earth the missile actually is, is useless: only the position with regards to the target is of importance, as reaching the target is a matter of actions within the frame of reference of the missile, not the earth: the target exist in certain three dimensional(* point in space in relation to the missile sensor. The guidance system updates this "situational image" at certain intervals (several times a second) and the difference between images is used to calculate the rate of change and then the necessary steering inputs.
Adding sensors and algorithms relating to spatial situation with regard to earth's frame of reference add unnecessary complexity (and thus extra fail modes) to this kind of weapons. Within the maneuverability envelope of these missiles the "direction" of gravity is not of crucial importance.
*)To be precise, whether 3-, or just 2-dimensional situation image is actually necessary is an interesting question, as the missiles of this sort are not "throttle-able", so they speed on at full power until target is destroyed or fuel is depleted. Actual or relative speed are therefore of no importance. However, some missiles do not need to impact the target to detonate, so they must have some way to determine the sufficient proximity to the target to arm and explode.
Modern missiles pretty much all determine their orientation via some sort of IMU. Note that you do not need super-expensive RLG-IMU, but you might get away with cheaper MEMS-based IMUs (*1). However (and I cannot stress this enough), it all depends on your specification:
But again, it depends on your specifications. With very tight specifications, you generally need to achieve very high performance in your control loops, which is only possible if you have very good (e.g. expensive) sensor available. If you need to hit the third screw from the left of your target, then you need very precise and expensive sensors. If your warhead is powerful enough to obliterate the target in a 2km radius, you can figuratively just close your eyes and aim in the general direction.
The take-home message is (especially for closed loop control of any flying vehicle) is: Performance and robustness of a control loop are interchangable. The more performance you demand of a control loop, the less robust against sensor noise, external disturbances, system dynamic uncertainties etc. it will be. There are plenty of ways to overcome limitations of missing sensors etc. in order to do something cheaper, however it is up to the designer to check if the product is still be able to perform its task as intended.
Foonotes:
(*1): Expensive and cheap in the military context are a bit different. A cheap MEMS IMU might still cost several thousands of USD. (*2): Of course you do not need an IMU to close a control loop. Early missile designs directly coupled the angle-to-target (as determined by the seeker) with corresponding fin-deflection. However the addition of an IMU and the corresponding data streams offers more data for possible control loops.
To expand on the answer given by @Jpe61, homing missiles use a technique called 'Proportional Navigation'. It is a surprisingly simple algorithm in which the missile attempts to keep the target on a constant bearing. As long as the missile is reducing the distance to the target this guarantees a hit.
This technique can be implemented using a PID controller where the error signal is the deviation from a constant bearing (detected on a photocell in the case of an IR seeker). The PID output then drives the control fin motors.
Active Skyflash quoting the relevant part where it describes how the missile tracks the target:
http://www.ausairpower.net/skyflash-slammer.html
The Active Skyflash seeker feeds the missile's Integrated Power and Control Unit (ICPU) with serial signals proportional to target line-of-sight difference from the missile's boresight in yaw and pitch, and with a signal proportional to target range. The missile is steered by cruciform wings, a pair each generating yaw and pitch inputs, with one pair differentially controlled to provide roll stabilisation. The wings are actuated by solenoid controlled hydraulics, the solenoids driven by DC amplifiers fed from digital to analogue converters (D/A).
Basically, the missile boresight, orientation, and where the seeker head is telling it the target is.
