EP1360450A1

EP1360450A1 - A system and method for time-to-intercept determination

Info

Publication number: EP1360450A1
Application number: EP01941447A
Authority: EP
Inventors: Mary D. O'neill; William H. Wellman
Original assignee: Raytheon Co
Current assignee: Raytheon Co
Priority date: 2001-02-12
Filing date: 2001-02-12
Publication date: 2003-11-12
Anticipated expiration: 2021-02-12
Also published as: EP1360450B1; WO2002065048A1; DE60130033T2; IL152185A; DE60130033D1; IL152185A0

Abstract

A method and system of time-to-intercept determination for a radiation source using passively-sensed irradiance data. The invention provides a plurality of noise reduction features to reduce the noise present in the data and improve the accuracy of the time-to-intercept computation. The method includes reducing data noise by defining an acceptable noise level and eliminating any excessively noisy data from the time-to-intercept computation. The method further includes constantly updating the time-to-intercept computation by using irradiance values that are advanced in time. Other features of the present invention includes averaging of irradiance values over a time interval, filtering of the irradiance data received by the method, and triggering at a predetermined time-to-intercept. The invention also includes a time-to-intercept system and processor implementing the above method.

Description

A SYSTEM AND METHOD FOR TIME-TO-INTERCEPT DETERMINATION

FIELD OF THE INVENTION

The present invention relates in general to time-to-intercept

determination and more particularly to a system and a method for accurately determining a closing time between a radiation source and an

object by passively sensing the irradiance of the radiation source.

BACKGROUND OF THE INVENTION

Time-to-intercept determination has several important civilian and

military applications. Time-to-intercept (TTI) is the amount of time

remaining before an object makes contact with ("intercepts") another object. Determination of the TTI is used in civilian applications such as, for example, vehicular motion measurements, factory measurements,

astronomical measurements, satellite measurements and aircraft collision avoidance systems. One military and civilian use for TTI determination is in missile warning systems (MWS). In this age of increased conflict and terrorism, both civilian and military aircraft are especially vulnerable to

missile attack, particularly from infrared guided missiles. In fact, over

ninety percent of military aircraft losses worldwide since 1980 have been

the result of infrared guided missile attacks, and there also have been attacks on civilian aircraft. Due to the lack of missile warning, most pilots of the downed aircraft were not aware of the missile firing until the actual

hit occurred, thus could not initiate evasive or protective actions. A MWS

carried by an aircraft also enhances the effectiveness and the available duration of aircraft self-protection such as flares, which is most effective

when used a certain time before the missile intercepts the aircraft. Therefore, in order to be useful and to ensure maximum self-protection and facilitate use of available self-protection resources, the MWS must

have an accurate TTI determination. In both civilian and military applications it is important that the TTI

be determined as accurately as possible to avoid possible disaster. For

example, an error in the TTI determination may result in lack of

effectiveness for a self-protect system, if a flare is dispensed too late or too early. This may mean the loss of an aircraft and human lives. Thus, there exists a need for an accurate, effective and low-cost system and

method for TTI determination. One way to determine the TTI is by using a passive sensor system. This type of system is generally preferred over other types of systems

because of the disadvantages associated with the other systems. For

example, an active sensor system detects range by measuring pulse- doppler returns. The active sensor system, however, is relatively complex, heavy and costly because of the rangefinding equipment that must be used. Similarly, TTI determination using a triangulation system is costly,

slow and requires two sensors with the same field of regard placed far enough apart to achieve the high angular accuracy. Unlike an active sensor system that employs radar, lidar or other

direct range-measuring equipment, a passive sensor system cannot directly measure the TTI and must indirectly measure the TTI. However, TTI can be determined from fundamental physical laws, if the object has a

uniform radiation emission (such as thermal self-emissions,

electromagnetic transmitting or reflected power). These radiation

emissions may be from natural sources (such as the sun) or from artificial sources (such as laser, radar and searchlights).

For example, a passive ultraviolet sensor system indirectly measures the TTI by observing photon scattering effects that are inherent in these short ultraviolet wavelengths. As two objects approach each

other this causes a noticeable "diffusion". The main disadvantage of this passive ultraviolet sensor system, however, is that it is not useful in the infrared spectrum where this scattering is virtually nonexistent. Moreover,

the detection range in the ultraviolet spectrum is quite short due to the

limited transmittance of the atmosphere in this spectral region.

Another type of passive sensor system indirectly measures the TTI by sensing the irradiance associated with an object. In general, this type

of system measures the irradiance of the object at two instances in time

and computes the TTI from an equation relating irradiance and time. This

type of system can use infrared detection, which is advantageous for long-range detection (for example, at the time a missile is launched). Long-range detection is a useful feature of a TTI determination system because it gives the other object (such as a target aircraft) time to use

countermeasures (such as evasive maneuvers and infrared jamming

devices).

A disadvantage of this type of prior-art system is their succeptability to noise, since the initial irradiance signal measurement is measured at a

long range (when the two objects are some distance away from each

other, and the signal is weak) is used throughout the computation of the TTI, making the calculations inaccurate. In fact, a major deficiency of

prior-art irradiance-based passive sensor systems is that they either

completely ignore or inadequately compensate for the adverse effects of noise. Noise can cause significant accuracy problems in the TTI determination.

Therefore, what are needed are a system and a method for TTI

determination using an irradiance-based passive sensor system that recognizes, addresses, and adequately compensates for the adverse

effects of noise, thereby increasing the accuracy and efficiency of the TTI determination.

SUMMARY OF THE INVENTION

To overcome the limitations in the prior art as described above and other limitations that will become apparent upon reading and

understanding the present specification, the present invention includes a

method and a system for accurately determining a closing time (or time-

to-intercept) between a radiation source and an object. The present invention utilizes a plurality of features to reduce the noise present in the

time-to-intercept computation and thus improve the accuracy of the time-

to-intercept determination while still remaining relatively inexpensive and

simple.

In a preferred embodiment, the invention includes a method for time-to-intercept determination that includes computing the time-to-

intercept using at least three irradiance values of a radiation source and reducing noise in this computation by employing a variety of measures. For example, noise present in the irradiance data is monitored to

eliminate the use of any excessively noisy data in the computation of the

time-to-intercept. Preferably this is accomplished by computing a signal-

to-noise ratio value for each irradiance value and comparing this value to

a threshold signal-to-noise ratio value. Any signal-to-noise ratio values that do not meet this threshold criteria are rejected; only those irradiance values within an acceptable noise tolerance (threshold) are used in the time-to-intercept computation. This noise reduction helps improve the

accuracy of the time-to-intercept calculation.

The method also includes an averaging feature that further

enhances accuracy. For example, a minimum time interval is defined by

the resolution of the computing device, to prevent singularities and to minimize sample-data noise in the time-to-intercept computation. The time interval between irradiance values having acceptable noise levels is

determined. If this time interval is less than the minimum time interval this

irradiance data is not directly used in the time-to-intercept computation.

Instead, the irradiance data is averaged over the time interval thus providing additional noise suppression and improved accuracy in the time-to-intercept computation.

The time-to-intercept computation is constantly updated by using irradiance data that is advanced in time. This updating means that the previous time-to-intercept computation is replaced with an updated time-

to-intercept computation that was computed using irradiance data taken

later in time. Since interception is preceeded by closing distance, and

since signal strength naturally increases significantly as distance decreases, this updating significantly enhances signal-to-noise ratio, which improves TTI accuracy, without updating, as in prior art schemes,

computations are based on initial observations made when the radiation

source (such as a missile) is first detected at long range and the signal is

just at the acceptable level, hence the noise in the irradiance data is typically still high and the accuracy of the time-to-intercept computed using this data is accordingly low. By constantly updating the computation using irradiance data of the missile as it comes closer, the

accuracy of computation is markedly improved.

The time-to-intercept is computed using equations that relate the

irradiance values to the time-to-intercept. In addition, the computation

uses signal-strength normalization in order to remove the effects of

radiation source size (or absolute signal strength). Normalization is based upon assumptions of whether the closing rate follows a constant acceleration or a constant velocity trajectory. Equations for both constant

acceleration and constant velocity assumptions have been developed. The method can signal a warning system when a predetermined time-to-intercept is reached, which takes full advantage of the aforesaid

updating process. The likelihood of false trigging, another aspect of TTI

accuracy, is reduced, because the accuracy of the time-to-intercept

determination is improved by the present invention. It is desirable that the warning system be triggered at a specific time-to-intercept, so that it can cue a prearranged response. For example, if a missile is approaching an

aircraft and the time-to-intercept reaches a predetermined time, the

warning system can cue the aircraft to release flares or other engage other protective anti-missile techniques at a time of optimum effectiveness. By releasing flares only when they are effective and necessary, limited countermeasure resources can be conserved so the

usefulness of the countermeasure system can be extended.

Other features of the invention also improve the accuracy of the

invention. For example, filtering of the irradiance data prior to use by the invention helps improve the accuracy of the incoming data and eliminate

any extraneous signals. In addition, this filtering can be included in the

detection system and can be a continuous filtering. This invention works with irradiance data that is provided as a continuous data stream, as a

periodically-sampled data set, or as an aperiodically-sampled data set.

The method of the present invention can be implemented in a system for time-to-intercept determination. This system includes a detection system for providing irradiance data, a timing device for

providing timing data, a time-to-intercept processor for providing time-to-

intercept data, and a warning system for triggering countermeasures and warning the pilot of impending danger.

The time-to-intercept processor of the present invention includes an

input module for receiving and filtering data, a noise threshold module for

further reducing noise in the data, and an averaging module for averaging the data over a time interval. In addition, the processor includes a calculation module for calculating the time-to-intercept, and an update

module for constantly updating the time-to-intercept using irradiance data that is advanced in time together with clock data to interpolate time-to-

intercept between the times of irradiance measurements.

Other aspects and advantages of the present invention as well as a more complete understanding thereof will become apparent from the

following detailed description, taken in conjunction with the accompanying

drawings, illustrating by way of example the principles of the invention.

Moreover, it is intended that the scope of the invention be limited by the

claims and not the preceding summary or the following detailed

description. BRIEF DESCRIPTION OF THE DRAWINGS

The present invention can be further understood by reference to the following description and attached drawings that illustrate the preferred

embodiments. Other features and advantages will be apparent from the

following detailed description of the preferred embodiments, taken in

conjunction with the accompanying drawings, which illustrate, by way of

example, the principles of the invention.

Referring now to the drawings in which like reference numbers represent corresponding parts throughout: FIG. 1 is an overview diagram of a missile warning system (MWS)

incorporating the present invention.

FIG. 2 is a structural block diagram of the present invention.

FIG. 3 is a flow diagram illustrating the functional operation of the

present invention. FIG. 4 is a functional flow diagram of a working example of the noise threshold function of the present invention.

FIG. 5 is a functional flow diagram of a working example of the

averaging function of the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

In the following detailed description of the invention, reference is made to the accompanying drawings, which form a part hereof, and in which is shown by way of illustration a specific example whereby the invention may be practiced. It is to be understood that other

embodiments may be utilized and structural and functional changes may be made without departing from the scope of the present invention.

I. Introduction

The present invention includes a system and method for time-to- intercept (TTI) determination using a passive sensor system to measure

the irradiance of a radiating source. The TTI is determined by measuring the irradiance from the radiating source at two points in time and

subsequently calculating the TTI using an equation that relates the irradiance measurements and the TTI. Later in time the irradiance is measured again at a third point in time and an updated TTI is calculated.

By such updating, at least three irradiance values at three respective

times are employed to compute TTI. This continuous updating of the TTI

calculation is accomplished by using advancing (in time) irradiance

measurements. These irradiance measurements can be obtained either as a continuous data stream or an intermittently sampled (periodically or aperiodically) data set.

From the fundamental physics, this invention reveals that TTI is proportional to the ratio of the detected irradiance of the target with respect to the rate of change of the detected irradiance. This equation does not include any of the effects of the radiating source size.

The present invention also includes a plurality of modules and functions to compensate for noise.

One example of noise compensation used in the present invention is continuous filtering of the measured irradiance signals. This continuous

filtering ensures that many extraneous signals not associated with the

radiating source are filtered from the measurements. Another example is

that excessively noisy signals are not used in the TTI calculation. An "excessively noisy" signal may be defined as any signal having a signal-

to-noise ratio (SNR) below a certain threshold signal-to-noise ratio

SNR_thre_{s o}i_d- The SNR is the ratio of the amplitudes of a desired signal to a noise signal at a point in time. If the SNR of an irradiance signal is below

the SNR_thres_hoi then the signal is discarded and another measurement is obtained. Elimination of noisy signals prior to the TTI calculation gives

the present invention improved accuracy and speed.

Still another example of noise compensation used in the present invention is averaging. In particular, additional accuracy is achieved by the present invention by averaging those measured signals that have a

SNR greater than SNR_hreShoi_d. over some minimum time interval. These noise compensation techniques help the present invention achieve a highly accurate and efficient TTI determination.

II. Structural Overview FIG. 1 illustrates one example of how the present invention may be

utilized. In particular, FIG. 1 is an overview diagram of a missile warning system (MWS) 100 incorporating the present invention. In this example

the radiating source is a missile 110 and the target object is an aircraft

115. The missile 110, shown in flight, has been launched from a ground- based launch facility 118 and is on an intercept path with the aircraft 115. The MWS 100, which is carried on the aircraft 115, can be carried on a

variety of host vehicles (such as an aircraft, a ship, etc.) or be located at a

stationary host location (such as a building). The MWS 100 can detect

and provide warning of the approaching missile 110, as well as determine

the TTI between the missile 110 and the aircraft 115. If the TTI is less

than a specified time the MWS 100 reacts in a predetermined manner (for

example, by activating countermeasure devices such as flares).

The MWS 100 includes a passive sensor system 120 that detects

irradiance from the missile 110 and outputs detected irradiance signals.

These signals can be a continuous data stream or an intermittently

sampled (either periodically or aperiodically) data set. In this example, the passive sensor system 120 measures irradiance in the infrared spectrum and sends the measured data to the Tracking and Timing

processor 140. When a threat is declared, the Tracking and Timing

processor sends the irradiance and timing data to a TTI processor 130.

Alternatively, other spectra, such as radar, acoustic, visible light, and ultraviolet, for example, may be measured. The passive sensor system

120 using infrared detection is suitable for long-range detection and, in

this example, the missile was detected at the moment it was launched from the ground-based facility 118. A system clock resident in the Tracking and Timing processor 140 provides clock and time data to the MWS 100 that is used in the

calculation of the TTI. Data from the system clock is sent to the TTI

processor 130, where, as explained in detail below, the TTI processor 130

uses this data and data from the passive sensor system 120 to calculate and continuously update the TTI. When the TTI is less than a

preprogrammed time the TTI processor 130 can output a signal to a

warning system 150 that determines what action to take. For example,

when the TTI of the missile 110 and the aircraft 115 is less than the preprogrammed time the warning system 150 can provide a visible or

audible alert to the pilot or automatically implement countermeasures.

FIG. 2 is a structural block diagram of a TTI processor 200 (an example of a TTI processor 130 was shown in FIG. 1). The TTI processor 200 receives data from a timing device 210 and a detection

system 220. For example, this data can be a time value and an

irradiance value of a radiating source measured at an instant in time. The

input module 230 receives the incoming data and passes the data to a

noise threshold module 240 for elimination of any excessively noisy data. The data that meets this criterion is sent to an averaging module 250 and

then to a calculation module 260 where the TTI is calculated. If the data does not meet this criterion, the last TTI is decremented by the timing

device 210 in the calculation module 260. The update module 270

replaces the old TTI value with the updated TTI calculation and sends a

signal to the warning system 280 if the TTI value is less than a

predetermined value.

III. Functional Overview The present invention can be implemented in hardware or software.

The TTI processor (for example, the TTI processor 200 of FIG. 2) can be

implemented in hardware using a dedicated logic circuit or a field

programmable gate array (FPGA). Alternatively, the TTI processor may

contain a microprocessor and memory (such as RAM, ROM and EPROM) for storing and carrying out the method of the present invention.

FIG. 3 is a flow diagram illustrating the functional operation of the TTI processor of the present invention. Irradiance data (box 310) from a radiating source is detected and measured by a detection system such

as, for example, an infrared-based passive sensor system. As discussed

earlier, however, signals in spectra other than infrared may be detected by the detection system and used in this invention. Because the irradiance data may contain extraneous noise, the data is filtered (box 320) to reduce any noise present in the signal. For example, if the

irradiance signal is from a missile any extraneous noise (such as photon or electronics noise) is filtered.

Time data (box 330), which may come from a timing device, is used

to provide timing information. The time data and the irradiance data is received as input data (box 340).

Noise Threshold Function

The present invention includes a noise threshold function to

eliminate any excessively noisy detected irradiance signals from the TTI

determination. This function can be implemented, for example, within the

noise threshold module 240 of FIG. 2. In general, the noise threshold function calculates a noise function of incoming detected irradiance signals relative to a threshold noise values, and eliminates any signals

that are less than this threshold. The threshold noise value can be user-

selected, determined dynamically or preprogrammed into the function. The present invention does not consider noisy irradiance signals in the calculation of the TTI thus making the TTI calculation more accurate.

As shown in box 350 of FIG. 3, a noise operator of an irradiance

signal is calculated to determine if a desired threshold noise value has been exceeded (box 350). Preferably, the noise operator is a signal-to- noise ratio (SNR) of the detected irradiance signal and is compared a

certain threshold noise operator (such as a threshold SNR value

SNR hres_hoid)- If the noise operator of the detected irradiance signal is less than the threshold noise operator then the detected irradiance signal is

rejected and the noise threshold function returns to box 340 to input a new irradiance signal at a later time (e.g., Z[t + delta t] at a new time [t +

delta t].

FIG. 4 is a working example of the noise threshold function. In this

example, the irradiance signal is a detected irradiance at an instant in

time, t, and is represented by Z(t). In box 410 the detected irradiance,

Z(t), is received by the noise threshold function. This signal is passed to

box 420 where the signal-to-noise ratio of Z(t) is calculated. In box 430

the SNR is compared to a threshold SNR value and, if the calculated SNR of the detected irradiance is greater than the threshold SNR value, the

detected irradiance is passed to box 440 for output to the next function

(for example, the averaging function). Otherwise, the SNR is less than or equal to the threshold value (indicating that the detected irradiance is too noisy to use in the TTI determination) and the noise function returns to

box 410 to input another detected irradiance.

Averaging Function

The averaging function of the present invention can be implemented within the averaging module 250 shown in FIG. 2. In

general, as shown in box 360 of FIG. 3, the averaging function

determines whether a pair of usable irradiance signals has been

measured over some minimum time interval. Usable irradiance signals refer to a pair of signals that have passed through the noise threshold

function and have minimal noise content. One purpose of imposing a minimum time interval between measured signals is to prevent the

possibility of division by zero in the TTI calculation. The time interval

must be long enough so that any truncation or rounding off of the time

interval will not result in division by zero in the TTI calculation. In addition, a short time interval amplifies the effect of noise in the TTI calculation.

The minimum SNR and minimum time interval are related to the total

error in the TTI calculation.

If the time interval between a pair of usable detected irradiance

signals is greater than the minimum time interval then the time data and the irradiance data are passed to the calculation function (box 380). If the time interval is less than or equal to the minimum time interval then the

pair of irradiance signal is averaged over the time interval. This averaging

of the irradiance signals over the time interval further enhances the accuracy of the TTI determination by effectively decreasing the relative noise content of the irradiance signal.

FIG. 5 is a working example of the averaging function of the present

invention. In this example, the time interval (delta t) is the interval

between a pair of usable detected irradiance signals (for example, greater than a SNR threshold value as defined in the noise threshold function). In mathematical terms, the delta t is equal to the absolute value of t_n minus

t_n.ι, where t_n and t_n-ι are the respective times at which usable irradiance

signal measurements have been made.

In box 510 the averaging function receives time data and irradiance

data. In this example, the irradiance signal data is again represented by measured detected irradiance, Z_n and Z_n._1t at times \_n and t_n.-, .

Delta t is computed in box 520 by, for example, subtracting t_n.ι from t„ . In

box 530 delta t is compared to a minimum time interval. If delta t is

greater than the minimum time interval, then the time data and the

detected irradiance data from the averaging function are sent by box 540

(for example, to the calculation function). If delta t is less than or equal to the minimum time interval then an average of the detected irradiances are computed over the time interval delta t in box 550. This average detected

irradiance value is used in box 560 to update the time data and the

detected irradiance data.

Calculation Function

The calculation function can be implemented within the calculation module 260 of FIG. 2. As shown in FIG. 3, the calculation function

includes the calculation of the TTI (box 380) and is performed if the time is greater than a minimum time interval (box 360). The calculation

function calculates the TTI using only sequential (in time) irradiance

measurements, thus eliminating the need to calculate the range or closing

velocity between the radiating source and the target object. This greatly

simplifies and increases the speed of the TTI calculation while providing

improved accuracy.

In addition, the calculation function includes signal strength

normalization to eliminate any effects of the radiating source size. Thus,

whether the radiating source is large or small is irrelevant in the TTI

calculation. Moreover, the calculation of the TTI is easier and more

accurate because, as explained further below, the calculation function assumes that the radiating source has either a constant acceleration or a constant velocity.

In general the calculation function uses a fundamental equation

derived from first principle physics that relates the irradiance of a radiating

source to the TTI. If constant acceleration is assumed, an equation can

be derived that uses time data, irradiance data and an empirical constant to calculate the TTI. If a constant velocity is assumed, then a different equation can be derived and used to calculate the TTI using time data

and irradiance data. Both the constant acceleration and constant velocity

equations include a ratio of a pair of measured irradiance signals. The

TTI calculation is discussed in greater detail below in the mathematical

description of the invention section and the working example section.

Update Function

The update function of the present invention can be implemented within the update module 270 of FIG. 2. As shown in FIG. 3, after the TTI has been calculated the update function (box 390) updates the earlier TTI

value. Preferably, after every TTI calculation a previous value of the TTI

is updated with a current TTI value. Because the radiating source is

approaching the target object the irradiance signal is stronger and

contains less noise, and the accuracy of the TTI calculation should be improving over time. Thus, constantly updating the TTI calculation

provides continuously improving TTI calculations as the radiating source approaches the target object.

IV. Mathematical Basis of the Invention

The TTI calculation is derived from first principle physics and the

ability of present day detectors to produce an electrical response in accurate proportion to the radiation incident on the detector.

Irradiance (H) of a radiating source is defined as the incident

radiation per unit area and is given in units of watts per sguare centimeter

(W/cm²). Radiant intensity of the radiating source. J. is a radiant flux per

unit solid angle and is given in units of watts per steradian (W/sr). From first-principle physics, the irradiance of the detected radiating source is

related to the distance the radiating source is from the target object(range, R) by the following equation:

H t)= J(t)^ (1)

Where:

J(t) = radiating source radiance, time-dependent, W/sr

R(t) = slant range to radiating source, or distance from intercept, m H(t) = detected irradiance of radiating source, W/cm2 a = atmospheric absorption coefficient, m^" t = elapsed time in flight, sec, =total flight time-time to go = t_fl - t_go

Equation (1 ) is the fundamental equation relating the irradiance of the

radiating source to the distance between the radiating source and the target object. In this derivation, the irradiance and the attenuation due to

atmospheric absorption are constant over the time interval when detection measurements are made. The development of the equation relating the

TTI to the irradiance of the radiating source depends on whether a

constant acceleration assumption or a constant velocity assumption is used.

Constant Acceleration Assumption

A constant acceleration assumption is valid if the radiating source is

either in constant acceleration or deceleration. For example, if the radiating source is a missile, the constant acceleration assumption is usually valid because missiles accelerate and decelerate due to

aerodynamic forces (such as drag and propulsion) and in-flight

maneuvers.

Where the radiating source is a missile, developing the constant acceleration assumption equation,

R(t) = Rsiant- (af/z) - Vt, where a is a constant acceleration and V is the velocity and time t=0 is the start of the missile's flight such that V = V(0)+at = at, and R(0) = 3at_fl ² / 2 = R_sι_ant. This leads to the equation: W _x ^4JA ₂₁, (2)

[2R_slant -3at²]

In this example, the detected irradiance of the missile, H(t), is

converted to a measured amplitude (Z) using the formula, Z(t) = CH(t),

where C is a constant conversion factor. Equation (2) then becomes:

Where k= 4CJA.

Equation (3) can be exploited by considering the relative change of amplitude, (dZ/dt):

The ratio of measured amplitude to change in amplitude becomes:

άZ/ d t _ 2R_slant -3at² Z(t) Uat ⁾

Substituting t_rt_g0 for t and 3at_fl ²/2 for R_S|_ant results in equation (6): dZ/ dt _ ^t _go[2t_fl -t_go]

Equation (6) relates the measured irradiance to the TTI and shows

that the TTI is proportional to the ratio of the detected irradiance of the

radiating source with respect to the rate of change of the detected

irradiance. In addition, equation (6) is not a function of k and therefore

does not need to know the radiating source size, the weather conditions

or the velocity of the radiating source to determine the TTI.

Equation (6) can be rewritten in a form that is useful with irradiance data that is discretely sampled (either periodically or aperiodically), by considering the average measured amplitude over a sampling time

interval, At. A numerical differentiation formula gives the TTI at the

midpoint of this sampling time interval as follows:

2At(Z_n +Z_n__x)[t_β -t_g0] _ Atc(Z_n +Z_n__x) (Z_n -Z_n__λ)[2t_β -t_g0] (Z_n -Z_n._λ) ⁽ )

Where c= 2(t_frt_go)/(2t_frtg₀). For implementation, c is chosen to be

constant depending on the calculated TTI. Since t_go ranges from 0 seconds (at impact) to t_fl seconds (at launch), c can range from 0 to 1.OFor example, in this working example, the value of c is approximately 0.67 for initial samples, and approximately 0.86 after two seconds of time

has elapsed. In addition, the signal strength normalization provided by

equation (7) means that Z_n can be measured in convenient units without

the need for extensive calibration of the detection system or preamplifier

gain.

Note that Equation 13, like other equations to follow, use sample-

data notation wherein t_n.ι refers to a value of t at one prior sample

interval, and t_n refers to a value of t at the current time, etc. This notation

is adopted for convenience of expression, and applies to either digital or

analog computations, and to periodic or aperiodic sampling.

Constant Velocity Assumption

A constant velocity assumption is valid if the radiating source is

moving at a constant velocity. R(t) = Vt, where V is a constant velocity and time t=0 is impact between the missile and the target object such that R(0) - 0. This leads to the equation:

JA

H( = (8) [Vt]²

Similar to the constant acceleration assumption, the detected

irradiance of the missile, H(t), is converted to a measured amplitude (Z) using the formula, Z(t) = CH(t), where C is a constant conversion factor. Equation (8) then becomes:

^Z^ ⁼F (9)

Where:

CJA k = - (10)

V²

Equation (10) can be exploited by considering the relative change

of amplitude, (dZ/dt):

dZ(t) _ -2-k

(11) dt t

The ratio of measured amplitude to change in amplitude leaves a

simple result that directly expresses measured amplitude in terms of time:

Similar to the constant acceleration assumption, equation (12) is not a function of k and therefore the radiating source size, weather

conditions or the velocity of the radiating source are not needed for the TTI calculation.

Equation (12) can be rewritten in a form that is useful for discretely

sampled (either periodically or aperiodically) irradiance data by

considering the average measured amplitude over a sampling time

interval, At. A numerical differentiation formula gives the TTI at the

midpoint of this sampling time interval as follows:

(Z(t_n) + Z(t„.₁)) t go — (13) (^ -t^XZ t -Z^.,))

The signal strength normalization provided by equation (13) means

that Z_n can be measured in convenient units without the need for

extensive calibration of the detection system or preamplifier gain.

V. Working Example

In order to create data for this working example, actual proprietary IR sensor data and a linear least squares analysis was used. Actual

digitized IR sensor data was analyzed using a linear least squares analysis that determines the best k that minimizes the error in equation

A1.

where ||₂ is the Euclidean norm, Z„ is the measured amplitude given by

the equation:

and Zn is the predicted measurement based on the equation:

If we let H be a matrix representation of 1/t_n ^~, and Z be a matrix

representation of the measured values, then we solve:

k = [H^TH)^~l H^TZ (A4)

The standard deviation of the detected and system noise, w, was

determined as the standard deviation of Z„ -z„ using the k calculated in

equation (A4). A k of 1500 represents a radiating source that can be detected 4 seconds prior to intercept. The standard deviation of the system noise is

33.8. For algorithm implementation, six (6) measurements are averaged

per TTI calculation.

Constant Acceleration Assumption

After data was obtained for this working example, a threshold SNR

value was determined. Predicted TTI degrades rapidly as TTI increases. This indicates the necessity for a threshold SNR value at which the

predicted TTI becomes valid. The SNR is defined as:

where σ_w is the variance of the white Gaussian noise, w. The error, ε, on

TTI is given as:

where t_go is the actual TTI and t_g0 is the predicted TTI given in equation

13.

A SΝR of 23 dB corresponds to an ε of +/-0.36 seconds and is

approximately one seconds prior to intercept. The resolution of the

predicted TTI is related to the sample time. Because the averaging

function was not used in this working example, and the chosen sample time was 0.5 second, the resolution on predicted TTI can be further

improved by interpolating and averaging between samples with the

system clock.

The TTI algorithm was applied to 7820 runs of the simulated data.

The critical time to be determined was 1.5 seconds. The t_g0 error had the

following characteristics:

Table 1

In this working example, the present invention correctly predicted the 1.5

second value to within 0.4 second 97% of the time. In addition, it should

be noted that the present invention had a tendency to underestimate t go .

This slightly early prediction is generally preferable, however, to a late

prediction since a slightly early release of a flare or decoy is still acceptable.

Constant Velocity Assumption

After data was obtained for this working example, a threshold SNR

predicted TTI becomes valid. The SNR is defined as:

where σ_w is the variance of the white Gaussian noise, w. The error, ε, on

TTI is given as:

ε= t_g0 -t_g0 (A5)

where t_g0 is the actual TTI and t_go is the predicted TTI given in equation

13.

A SΝR of 27 dB corresponds to an ε of +/-0.25 second and is

approximately two seconds prior to intercept. The resolution of the

predicted TTI is related to the sample time. Because the averaging

function was not used in this working example, and the chosen sample

time was 0.5 second, the resolution on predicted TTI can be further

improved by interpolating and averaging between samples with the

system clock.

The TTI algorithm was applied to 7789 runs of the simulated data.

The critical time to be determined was 1.5 seconds. The t_so error had the

following characteristics: Table 1

In this working example, the present invention correctly predicted the 1.5

second value to within 0.25 second 97% of the time. In addition, it should

be noted that the present invention had a tendency to underestimate t_g0.

This slightly early prediction is generally preferable, however, to a late

prediction since a slightly early release of a flare or decoy is still

acceptable.

The foregoing description has described the principles, preferred

embodiments and modes of operation of the present invention. However,

the invention should not be construed as being limited to the particular

embodiments or working examples discussed herein. As an example, the

above-described invention can be used with other types of systems

utilizing TTI determination, as well as missile warning systems. Thus, the

above-described embodiments should be regarded as illustrative rather

than restrictive, and it should be appreciated that variations may be made in those embodiments by workers skilled in the art without departing from

the scope of the present invention as defined by the following claims.

Claims

WHAT IS CLAIMED IS:

1. A method of determining a time-to-intercept for a

radiation source using irradiance values of the radiation source, the

method comprising:

computing the time-to-intercept using at least three irradiance

values; and

reducing noise in the time-to-intercept computation by using a continuously-updated calculation, based upon recent values, and upon

initial values.

2. The invention as set forth in claim 1 , wherein reducing

noise further comprises selecting a threshold noise function to improve

the accuracy of the time-to-intercept computation.

3. The invention as set forth in claim 2, further

comprising:

determining a noise function of each irradiance value; and

comparing the noise function of each irradiance value to a

threshold noise function value.

4. The invention as set forth in claim 3, wherein the noise

function of each irradiance value is a signal-to-noise ratio value, the noise

threshold value is a threshold signal-to-noise ratio value and each

irradiance value is a respective detected irradiance value of the radiation

source.

5. The invention as set forth in claim 4, wherein

computing the time-to-intercept further comprises:

using detected irradiance values having a signal-to-noise

ratio value greater than the threshold signal-to-noise ratio value.

6. The invention as set forth in claim 5, wherein the

threshold signal-to-noise ratio value can be 27 decibels.

7. The invention as set forth in claim 1 , further comprising:

filtering of each irradiance value to reduce noise in the

irradiance values.

8. The invention as set forth in claim 7, wherein:

filtering of the irradiance values is continuous; and

each irradiance value is a respective detected irradiance

value of the radiation source.

9. The invention as set forth in claim 1 , further

comprising:

determining whether a time interval between irradiance

values is greater than a minimum time interval; computing an average irradiance value over the time interval

if the time interval is greater than the minimum time interval.

10. The invention as set forth in claim 1 , wherein

calculating the time-to-intercept further comprises: using an equation relating the irradiance values to the time-

to-intercept.

11. The invention as set forth in claim 10, wherein the

equation uses signal strength normalization.

12. The invention as set forth in claim 11 , wherein:

signal strength normalization includes having a ratio of the

irradiance values;

each irradiance value is a respective radiation intensity value

of the radiation source.

13. The invention as set forth in claim 10, wherein the equation is derived using a constant acceleration assumption.

14. The invention as set forth in claim 10, wherein the

equation is derived using a constant velocity assumption.

15. The invention as set forth in claim 1 , wherein computing the

time-to-intercept further comprises: computing a first time-to-intercept value using first and

second irradiance values; and updating the fime-to-intercept by computing a second time-to-

intercept value using a third irradiance value taken later in time than the

first and the second irradiance values.

16. The invention as set forth in claim 15, further comprising:

repeating the time-to-intercept updating with subsequent irradiance

values that are later in time until a predetermined time-to-intercept value

is reached.

17. A method of determining a time-to-intercept for a radiation source, comprising:

providing irradiance data relating to the radiating source;

minimizing noise associated with the irradiance data so as to provide usable irradiance data;

computing the time-to-intercept using the usable irradiance

data; updating the time-to-intercept computation using updated usable irradiance data derived from updated irradiance data.

18. The invention as set forth in claim 17, wherein

minimizing noise further comprises:

computing a noise function value for each irradiance data;

and comparing respective noise function values to a threshold noise function value; wherein each usable irradiance data has an associated noise

function value greater than the threshold noise function value.

19. The invention as set forth in claim 18, wherein:

the noise function value is a signal-to-noise ratio of the associated irradiance data; the threshold noise function value is a threshold signal-to- noise ratio value.

20. The invention as set forth in claim 19, wherein irradiance data includes the detected irradiance of the radiation source.

21. The invention as set forth in claim 17, wherein irradiance data is provided as one of: (a) a continuous data stream; or (b) a periodically sampled data set; or (c) an aperiodically sampled data set.

22. The invention as set forth in claim 17, wherein computing the time-to-intercept further comprises using an equation having signal strength normalization.

23. The invention as set forth in claim 22, wherein the equation assumes a constant acceleration.

24. The invention as set forth in claim 22, wherein the equation assumes a constant velocity.

25. The invention as set forth in claim 18, further comprising:

computing a time interval between successive usable

irradiance data;

comparing the time interval to a minimum time interval; and

averaging the irradiance data over the time interval if the time

interval is approximately less than the minimum time interval.

26. A system for determining a time-to-intercept of a radiation

source, comprising:

a detection system detecting successive irradiance values of

the radiation source;

a calculation module that calculates the time-to-intercept

using the irradiance values;

an update module that updates the time-to-intercept

calculation using irradiance values that are advanced in time.

27. The invention as set forth in claim 26, further comprising:

a noise module that minimizes noise in the irradiance values;

and

an averaging module that averages irradiance values over a

time interval.

28. The invention as set forth in claim 27, wherein the irradiance value is a detected irradiance of the radiation source.

29. The invention as set forth in claim 27, wherein the calculation module uses an equation that assumes constant acceleration.

30. The invention as set forth in claim 27, wherein the calculation module uses an equafion that assumes constant velocity.

31. A time-to-intercept processor for determining a time-to- intercept of a radiation source, comprising: means for providing irradiance values of the radiation source

successively in time;

means for reducing noise present in the irradiance values to

produce usable irradiance values; and means for calculating the time-to-intercept using the usable

irradiance values.

32. The invention as set forth in claim 31 , further

comprising: means for averaging the usable irradiance values over a time interval if the time interval is less than a minimum time interval.

33. The invention as set forth in claim 31 , further

comprising:

an update module for updating the time-to-intercept

calculation using irradiance values that are advanced in time.

34. The invention as set forth in claim 33, wherein the

means for providing irradiance values is an input module that inputs irradiance values into the time-to-intercept processor.

35. The invention as set forth in claim 34, wherein the input

module inputs irradiance values as at least one of: (a) a continuous data

stream; (b) a periodically sampled data set; (c) an aperiodically sampled

data set.

36. The invention as set forth in claim 33, wherein the means for

reducing noise is a noise threshold module that compares a noise

function value of each irradiance value to a threshold noise function value

to produce usable irradiance values.

37. The invention as set forth in claim 36, wherein the noise

function value is a signal-to-noise ratio of the respective irradiance values and the threshold noise function value is a threshold signal-to-noise ratio.

38. The invention as set forth in claim 36, wherein the means for

calculating is a calculation module that uses an equation relating the irradiance values to the time-to-intercept.

39. The invention as set forth in claim 38, wherein a constant

acceleration is assumed.

40. The invention as set forth in claim 38, wherein a constant

velocity is assumed.

41. The invention as set forth in claim 38, wherein the irradiance

value is a radiation intensity of the radiation source.