Guidance Law and DCS?

[Kazansky222]

Hello, below you will see a few links, the main link is for a PDF on a mod I helped with a long time ago. Along with a couple support links from the PDF's author to help better explain everything, In the PDF please scroll down the the section on Homing laws.

 

After you have done that please discuss what you think?

Does anyone know the math behind DCS's implementation of PN and APN? How similar or dissimilar is it to these equations?

 

Links:

https://drive.google.com/file/d/1krnJxq4zk2peUGI1K9ZXj9N_xDFsgeXI/view?usp=sharing

https://www.moddb.com/members/blahdy...igation-part-i

https://www.moddb.com/members/blahdy/blogs

 

Here's an excerpt from the Homing laws portion of the PDF

 

PROPORTIONAL NAVIGATION

 

Also known as Collision Homing or a form of ‘lead-pursuit’, Proportional

Navigation (PN) is simple to implement and very effective, where:

Acceleration = Closing Velocity * LOS Rotation Rate * NC

NC = Navigation Constant (typically 3 to 5)

 

• PN forces the missile to “lead” its target, without having to know

anything about the target’s speed, or range to target.

 

• Very effective and simple to implement on any missile, even on heat- seeking missiles that don’t have a radar. Missile always leads the target

no matter what.

 

• PN means that as you are chasing your target, your running-path rotation

rate is faster than the LOS rotation rate by a constant multiplier – the

Navigation Constant (NC).

 

• Higher the NC, the faster you correct your path early in the flight, and less

corrections are needed near the end.

 

• Under PN guidance, the missile and the target appear to be on a mid-air

collision course, where both objects appear to look “frozen” in state as

they merge closer.

 

Simple PN as described earlier assumes constant air speed. Under maneuvering

or accelerating situations, lead is ineffective.

 

• Even against non-maneuvering target, a non-maneuvering target still has an

upward sensible acceleration of 1G.

To produce a more efficient intercept trajectory, the PN equation in FLINT engine

is modified by an additional term:

Acceleration = Closing Velocity * LOS Rotation Rate * NC + ( NC / 2 ) * at

 

• This is also known as Augmented Proportional Navigation (APN)

 

• Under APN, the missile violently wiggles to align itself on the LOS to target,

immediately after launch. Corrections in flight are minimal as it approaches

closer to target. The missile collides onto the target in a near straight line.

 

 

PREDICTIVE GUIDANCE

 

Predictive Guidance (PG) can be argued as an advanced derivative of Proportional Navigation

(PN), typically used by radar-guided missiles (i.e. AIM-120C, AGM-114L, MIM-104, PAC-3, etc).

 

• Real world versions of these missiles use similar in concept, but much more advanced forms

of PG, though actual details are classified.

 

• We use a simpler elementary form of PG that is publicly known, but very

effective for game presentation.

 

Proportional Navigation (PN) works without knowing the range to target, nor any kinematics

data. Predictive Guidance augments PN by taking kinematics parameters and range into

consideration.

Zero Effort Miss (ZEM)

In deriving homing guidance laws, it’s useful to know what the miss distance would be if the

missile and the target did nothing but continue on their current courses. This is called Zero

Effort Miss or ZEM.

The logic behind ZEM is that if we know how far a missile will miss its target without effort, an

acceleration command can be applied to reduce that miss. A homing guidance law can then

be deriving using ZEM by repeating the following process:

1. Find ZEM

2. Compute missile acceleration to reduce ZEM

3. Repeat until ZEM becomes zero.

 

ZEM is closely related to the LOS Rotation Rate (LOSr), which we used earlier for

Proportional Navigation guidance.

ZEM’s relationship to LOS rate (LOSr) can be presented as follows:

LOSr = ZEM / ( LOS * Tgo

2 )

Alternatively,

ZEM = LOS * Tgo

2 * LOSr

 

• LOS Rotation Rate is easy to derive, as missile seeker itself can measure the

change in angular rate of sightline (as all PN-guided missiles do).

 

• Tgo represents Time to Go (estimated time to intercept), which can be calculated

from the missile’s radar range to target and its velocity measured by IMU.

 

Knowing the ZEM and Time to Go, which accounts for missile’s range to the target, the

acceleration command should be proportional to the Zero Effort Miss and inversely

proportional to the square of Time to Go until intercept as:

 

Acceleration = NC * ZEM / Tgo

2 + ( NC / 2 ) * at

 

• Predictive Guidance (PG) produces one of the most efficient collision-lead intercept

trajectory, by combining the concept of Proportional Navigation (PN) and LOS

rotation rate, with engagement geometry and kinematics data (Time to Go).

 

• Time to Go estimation can be augmented with various forms as seen fit, using range

to target and kinematics parameters.

 

• Missiles using PG produce a straight-line intercept flight path, where the target

appears to be being smacked by a meteor.

Edited May 15, 2020 by Kazansky222

[Chizh]

In DCS, most missiles have a proportional navigation method. Some air defense systems such as Tunguska have a three-point navigation. All Russian ATGMs use the three-point too. Recently, we began to introduce an adaptive proportional navigation method for modern air-to-air missiles like AIM-120 or R-77.

Edited November 12, 2019 by Chizh

[Kazansky222]

In DCS, most missiles have a proportional navigation method. Some air defense systems such as Tunguska have a three-point navigation. All Russian ATGMs use the three-point too. Recently, we began to introduce an adaptive proportional navigation method for modern air-to-air missiles like AIM-120 or R-77.

 

Thanks for the reply Chizh.

 

The 3 point navigation method for some systems such as Tunguska, are you describing a guidance law that is basically PN with known distance or time to go added to the basic PN equation?

 

Also I'm curious about the ED APN equation, is is more similar to a PN style system with known distance or is it more like Predictive Guidance (PG) with zero effort miss & time to go taken into consideration to find most optimal flight path?

 

I made / borrowed from some academic pages a basic PG script which seems to work pretty well for finding optimal paths, I haven't tried to add anything to it such as kalman filters or anything yet, it does seem to take a bit more cpu then I would have hoped but I think I can slow down the interval of the script a little bit to ease the cpu load while not slowing it down soo much to break the navigation.

[Kazansky222]

In DCS, most missiles have a proportional navigation method. Some air defense systems such as Tunguska have a three-point navigation. All Russian ATGMs use the three-point too. Recently, we began to introduce an adaptive proportional navigation method for modern air-to-air missiles like AIM-120 or R-77.

 

Hey Chizh, I know its been a while

 

I've just been studying the ED's new loft API implemented on the SD-10

 

I am very impressed, it seems like you guys have worked out the most efficient trajectory to carrier the most energy to a target. Do you have plans on also adding something similar to non lofted shots, something along the vein of Predictive Guidance posted above?

[TAW_Blaze]

Hey Chizh, I know its been a while

 

I've just been studying the ED's new loft API implemented on the SD-10

 

I am very impressed, it seems like you guys have worked out the most efficient trajectory to carrier the most energy to a target. Do you have plans on also adding something similar to non lofted shots, something along the vein of Predictive Guidance posted above?

 

The 120C loft looks quite efficient too, although in the Viper you don't yet have a loft cue and requires good manual pitch control to not send your missile to orbit :)

 

However the endgame guidance is still very susceptible to even arguably poor defensive maneuvering i.e. a target performing a 3-4 g slice turn chaffing only momentarily entering a notch at best, while flying at 20-30k ft with no terrain cover to be seen within 15-20 miles of missile LOS. For a missile with an active radar range of < 8 miles I'm very surprised something like that can happen, unless range gating is not simulated at all.

 

Overall I think the general guidance has improved a lot, especially at early and mid flight, but next to no changes in the endgame and this tends to outweight what was gained in other areas. It seems there is still no extrapolation in case the target is lost, it just rather tends to overpull the same way quite consistently resulting in unsolvable geometry, even if it finds the target again. One would expect that a modern missile such as the 120 family has smart enough ECCM to deal with a lost target for 100-200 ms that had a steady previous data, indicating that it is performing a somewhat "stable" maneuver i.e. targets pulling consistent g without any sudden jinks.

[PE_Tigar]

The 120C loft looks quite efficient too' date=' although in the Viper you don't yet have a loft cue and requires good manual pitch control to not send your missile to orbit :)[/quote']

 

AIM-120C goes into orbit invariably if the target turns cold :).

[Shadow KT]

The 120C loft looks quite efficient too, although in the Viper you don't yet have a loft cue and requires good manual pitch control to not send your missile to orbit :)

 

However the endgame guidance is still very susceptible to even arguably poor defensive maneuvering i.e. a target performing a 3-4 g slice turn chaffing only momentarily entering a notch at best, while flying at 20-30k ft with no terrain cover to be seen within 15-20 miles of missile LOS. For a missile with an active radar range of < 8 miles I'm very surprised something like that can happen, unless range gating is not simulated at all.

 

Overall I think the general guidance has improved a lot, especially at early and mid flight, but next to no changes in the endgame and this tends to outweight what was gained in other areas. It seems there is still no extrapolation in case the target is lost, it just rather tends to overpull the same way quite consistently resulting in unsolvable geometry, even if it finds the target again. One would expect that a modern missile such as the 120 family has smart enough ECCM to deal with a lost target for 100-200 ms that had a steady previous data, indicating that it is performing a somewhat "stable" maneuver i.e. targets pulling consistent g without any sudden jinks.

 

https://forums.eagle.ru/showthread.php?t=269854

[Kazansky222]

https://www.researchgate.net/publication/316942493_Predictive_Missile_Guidance_with_Online_Trajectory_Learning

 

Is a link to a PDF you can download that is a very well written academic paper written by the Department of Aeronautics and Astronautics, Istanbul Technical University. Its easy enough to understand by just looking at the pictures but it is also written in a way that is easy to learn as well.

[Маэстро]

I don't know why the formula with ZEM called the PG in above links. In fact it's just an alternative(vector) form of PN. Both laws with LOS rate or ZEM will provide the same trajectories in similar conditions. The main advantage of using vector form that it more useful for INS-based guidance systems. Also vector form provides more handy way for optimal control theory using and filters synthesis. Finally, vector form allows to define terminal conditions such as desired miss distance or velocity vector direction(JDAM has that option).

 

APN implementation requires detailed model of seekers and different filters/maneuver estimators development because target acceleration can not be directly measured IRL(of course in simulation it can, but that's not the way we go). APN also can be modified and improved. For example, additional accounting for missile longitudinal acceleration provides more straight path. Modern optimal control theory provides many other interesting features.

 

Currently most of DCS weapons use conventional proportional navigation, but we will improve guidance model with time.

Edited June 17, 2020 by Маэстро

[nighthawk2174]

Good to hear, though with APN something i'm curious about you guys have used the term adaptive PN while in western literature the term is augmented PN. What are the differences if any? And as far as i'm aware very modern missiles like the 54C, 7P, 120b|c, should use some form of optimal control with kalman filtering. Is this planned to be added at some point down the road?

Edited June 18, 2020 by nighthawk2174

[Маэстро]

Good to hear, though with APN something i'm curious about you guys have used the term adaptive PN while in western literature the term is augmented PN. What are the differences if any?

There is no difference. Just a typo or wrong term.

 

And as far as i'm aware very modern missiles like the 54C, 7P, 120b|c, should use some form of optimal control with kalman filtering. Is this planned to be added at some point down the road?

 

Optimal control/guidance is a broad concept. For example, conventional PN is an optimal guidance, but only for non maneuvering target. But anyway, some variants of Kalman filtering will be implemented because APN(and more advanced guidance laws) requires target acceleration estimation, which can be obtained using Kalman filter.