# How to estimate the time to intercept for homing missiles?

I have been reading the book Tactical and Strategic Missile Guidance by Zarchan, and a notice that he frequently uses the time to intercept $$t_{go}$$, and in his simulations he fixes the final time.

My question is if $$t_{go}$$ also is used in practice, and if it is not the case what is done instead?

The reason for me asking this is that I have doubts about the practicality of estimating $$t_{go}$$ as it could change dramatically if the target does an unexpected manoeuvre. Additionally estimating $$t_{go}$$ requires that we compute a predicted impact point which seems cumbersome in an endgame scenario compared to proportional navigation on the form $$a_c = N V_c \dot{\lambda}$$. Any references to how $$t_{go}$$ can be computed is also appreciated.

• Boringly I suspect the answer to this is not going to be found on the public parts of the internet, however assuming steady course and speed is right for a large number of cases (drone/unaware human), and attempts to predict likely target response would be very prone to gaming/countermeasures. Jan 23 at 12:36
• That makes sense @GremlinWranger I know from experience that certain missile has a lot of stuff going on behind the scenes, but I was afraid I was completely overlooking something basic Jan 24 at 13:56
• @pedernv perhaps I should add to my answer that I frequenly saw this value used in missile simulation, although in missile guidance and control it is still used. Nevertheless the concept of calculation is exactly as I laid out below. Aug 11 at 16:54
• @pedernv No Mr ! There is an explanation to your problem regarding this matter and it is understandable and valid. Yes, in practice things tend to go technical rather than theoretical. Please read my answer below.
– user64784
Aug 13 at 11:56

The time-to-go $$t_{go}$$ for missiles is an important factor for missile guidance and control, as modern missiles adapt their behavior based on this number. (for example as in the case of the MBDA Meteor, in order to maximize the kill probability by dynamically adapting its speed). There is no alternative, but of course, the designers are smart enough to know that the target may maneuver (1).
The simplest way to calculate the $$t_{go}$$ is by dividing your velocity by remaining distance $$t_{go} = \frac{x_{go}}{V_{missile}}$$. You further improve this estimate by factoring in your expected loss of velocity over time due to air drag. Interestingly, this is not as easy to solve analytically, as you are trying to solve $$t_{go} = \frac{x}{\int^T_0{V} dt }$$, but with the help of a computer you can simply predict the velocity of your missile along its flight path and divide the remaining length of this path by the predicted flight velocity $$\Delta t_{go} = \sum_0^i \frac{x_i}{V_i}$$. Another approach based on PN guidance, factoring in sensor noise with the help of a kalman filter is described in this paper. Especially modern missile do contain the necessary computing power to carry out these kinds of calculations and they use it! For example look at the different flight profiles of a Javelin missile or read around a bit on the different modes and functionalities of modern missiles, you will be amazed of what kind of complex designs and logic trees these include.