Hardware in the loop simulation of infrared ranging system
GORAN D. DIKIC1, BRANKO D. KOVACEVIC2, MILORAD M. MILOVANOVIC3
1MilitaryAcademy, Ratka Resanovica 1, 11000 Beograd
2Faculty of Electrical Engineering, Bulevar kralja Aleksandra 73, 11000 Beograd
3Military Technical Institute, Kataniceva 15, 11000 Beograd
SERBIA AND MONTENEGRO
Abstract: - In this paper, the possibility that passive IR seekers of surface-to-air homing missiles can be applied for hidden target tracking and its range estimation is verified by the experimental test results. Combination of hardware in the loop (HIL) and off-line simulation results in all confirm the idea that complete target kinematics states can be observed by the strategy based on use of two passive IR sensors, the triangulation method and the appropriate stochastic state estimator.
Key-Words: - automatic control,target tracking, IR sensor
1 Introduction
Traditionally, air target detection and tracking in modern combat systems are based on radar sensing. However, an active sensor can be investigated and attacked from a considerable distance. Use of passive infrared (IR) sensors can be a better solution for a real situation on the battlefield [1]. They are recognised as providing precise bearing-only target location. Through fusion of data from two or more such sensor range information can also be extracted 2. Possible solution, based on using of passive sensors that respond to a small target signal as in some (nonimaging) missile seekers in ground-to-air or air-to-air systems, is suggested in paper [3,4].
Fig. 1 Geometry relations among target and passive sensors
The estimation of target position, in this system, is based on target azimuths 1, 2 and elevations 1, 2 relative to the passive sensors that are placed on the ends of a baseline d (see Fig. 1). This is a well-known triangulation method. Actual solution includes two sensors with overlapping detection zones inside a region defined by their maximum scanning angles and maximum detection range of an expected target. When the primary sensor M detects the target, its azimuth and elevation are communicated to the secondary sensor S that begins to operate in commanded mode.
In this mode, the secondary sensor searches the line of sight (LOS), the direction of the line-joining target and the primary sensor, starting from a range defined by the maximum visual detection range of a target detected in the IR range. It is assumed that this point contains an assumed target that moves towards the real target (scanning process of the secondary sensor). Bearing in mind the well defined relationships between the angles 2, 2 and 1, 1 the movement of the secondary sensor is synchronised on both plains with the aim of preserving the LOS of the primary sensor within its own field-of-view (FOV) using the data received from the primary sensor. When the target is detected by the secondary sensor it switches to tracking mode.
Good results of the "off-line" simulation of suggested system in [3,4] induced the authors to check the validity of that solution in situations much closer to the reality by using HIL simulation. Considering the existence of physical limitations only one real sensor is used through HIL simulations. The second sensor function was simulated using the appropriate software.
There are several crucial problems that must be solved through the development of concrete real system. According to the construction of applied sensor the space within angles of 900 to 1400 can be covered during the searching, without changing the platform orientation. The target range estimation based on passive sensors, at the same time, requires the existence of the target in FOV of two or more sensors. However, the tracking system inertia and narrow detector FOV (less than 40) make difficulties in initialisation and during the tracking process.
This paper was written as a result of verification process of the IR sensor applicability in a real system. The results of HIL simulations have shown that target range can be estimated using passive IR seekers of homing missiles. In intention that minimal state estimation errors be achieved and positioning accuracy of the tracking system be maximal, the processing of the appropriate measurements is based on using of interacting multiple model (IMM) estimator [5]. The three extended Kalman filters based on different target state space models, are used in the concrete simulated system. Considering that positioning of real sensor, during experiments, is based on “off-line” simulation results, it should be mentioned that partial HIL simulation is realised. Development of the appropriate software for real-time processing is in progress.
2 Sensor description
The target tracking, in IR homing missile seekers, usually is based on LOS displacement, relative to the sensor optical axis. The automatic tracking system consists of co-ordinator and the appropriate servo. The co-ordinator consists of optical system, modulation disc (spinning reticle), and single IR detector. It is placed on rotor rotating in gimbals of “free” gyro (with three degrees of freedom). The entrance optics provides an image of the small target onto an image plane where the modulation disc is placed. The modulation disc is intended to provide a temporal modulation that corresponds to the target position. This modulation is provided chopping the small target IR signature by a complex reticle pattern that encodes target position. The chopped target IR energy is collected by condensing optics and is converted to electric signal by single IR detector. This signal is analysed by processor to determine the radial target position. The orientation of the sensor optical axis follows the change by target direction.
Tracking servo usually consists of two identical channels that form closed control loop providing independently displacement of co-ordinator optical axis in planes that are normal to each other. Usually it is gyro servo system. Fig. 2 shows the simplified structural scheme of that system (for one control channel). The appropriate coefficients are: KK co-ordinator amplification, KM, TM and UM amplification, time constant and output signal of power amplifier, K0, T0amplification and time constant of gyro servo, and H kinetic moment of gyro. Angle stands for LOS angle. Through analyse of the appropriate transfer function:
(1)
it can be viewed that tracking error is proportional to the angle rate d/dt.
Fig. 2 The simplified structural scheme of IR sensor and the appropriate control system
In concrete application, displacement of gyro rotor and co-ordinator toward the LOS direction is disabled (locked mode). Considering that complete seeker is placed on the appropriate platform, control signals are used to control the platform rotational movement. The target direction is measured from platform orientation in vertical and horizontal planes.
3 Positioning of the secondary sensor
To describe the movement of the secondary sensor, the law of the change of azimuth is adopted as:
,(2)
where, are the values of the azimuth and angular velocity at the beginning of the sampling interval, respectively. In addition toand, it is necessary to define the movement of the assumed target along the LOS of the primary sensor. With this in mind, it is initially assumed that the assumed target begins its motion at a range of 3000m from the primary sensor and at a velocity of 300m/s. Furthermore, the rate of change of its acceleration is modelled as a response of the 2nd order shaping filter to a step function:
(3)
The choice of T0 and synchronises in time the change of the radial acceleration with the increase in the distance between the assumed target and the primary sensor. This method ensures time efficient scanning of the LOS of the primary sensor within the limits of the angular velocities which ensure detection. Elevation 2 of the secondary sensor, during the tracking of the assumed target, should follow the expression:
(4)
in order to preserve the LOS of the primary sensor within the field of view of the secondary sensor.
Positioning precision of the secondary sensor, in commanded mode, depends on the quality of the state estimates of the assumed target. Bearing in mind the stochastic nature of LOS measurement angles, non-linear Kalman filter is employed for the target state estimation. The target dynamics are modelled in state space as:
(5)
whereis the target state vector at time instance k. Matrix F in Eq. (5) is defined, for sampling interval T, as:
,
and
(6)
(7)
(8)
describe the changes that depend on the acceleration of the assumed target. The accelerations ax, ay, az are given by:
ax = acos(1) cos(1) (9)
ay= acos(1) sin(1), (10)
az = -asin(1). (11)
The random sequence v(k) is a zero-mean white Gaussian state noise with known variance Ev(k)v(j)T = Q(k,j) where:
,
q - the variance of the process or state noise,
(k,j) - the Kroneker delta symbol.
The sensor measurements are modelled as:
z(k) = hx(k)+w(k), k=0,1,2,... (12)
where z(k) is three-dimensional vector that consists of azimuth and elevation angles from the primary sensor and the azimuth from the secondary one. Non-linear function hx(k) stands for transformations from polar to Cartesian co-ordinates that are given by:
1 = tan-1(y/x) (13)
1 = tan-1-z/(x2+y2)1/2 (14)
2 = tan-1(y-d)/x (15)
2 = tan-1-z/(x2+(y-d)2)1/2 (16)
The random sequence w(k) is independent zero-mean Gaussian measurement noise with known covariance matrix, that is Ew(k)w(j)T = R(k,j) where:
and 2, 2 are the variances of angle measurement noises. The extended Kalman filter equations (in the usual notation) are [2]:
(17)
(18)
(19)
(20)
where is the Jakobijan matrix with elements expressed as a result of partial derivation of the equations (13), (14), and (15).
In tracking mode the target dynamics are modelled in the state space form as:
(21)
and appropriate elements of Jakobijan matrix in equations (18) – (20) are expressed as a result of partial derivation of the equations (13), (15) and (16).
Using both the last measurements and their predictions from (12), the state update is given by:
(22)
The appropriate state estimations are given by equation
(23)
in commanded mode, and by equation
(24)
in tracking mode.
Target movement is tracked by appropriate servo system that minimises the displacement of LOS relative to pointing direction of the sensor. For realisation of a control law, expressed by Eq. (2), the appropriate transformation of the states from Cartesian to polar co-ordinates has to be made as:
(25)
(26)
The analogue relations in vertical plane are given by:
(27)
(28)
The simplified control structure of passive IR sensor in vertical plane can be viewed in Fig. 2. In commanded mode switchers A, B and C are placed in position 1. In this way the positioning of co-ordinator (the change of angle k) is achieved according to the sensor movement (locked mode). At the same time sensor elevation s is changed by the servo system whose transfer function is Gs(s). In this mode elevation angle is changed according to the law described by equation (4). When the target appears in FOV of the secondary sensor this one switches to tracking mode and the appropriate switchers A, B and C are in position 2. In contrast to the commanded mode, when co-ordinator follows the change of sensor elevation s, in tracking mode co-ordinator follows the target movement, that is the change of angle . In other words, the appropriate servo system ensures, in this mode, that rotation of complete sensor follows the co-ordinator movement and so the target at the same time.
A quality of the estimation depends on the validity of model dynamics and assumed covariance matrices Q and R. With this in mind, the use of IMMalgorithm is suggested for the estimator in order to obtain the best possible tracking performance [5].
4 IMM filtering algorithm
The IMM algorithm requires several sub filters, say N, each of which may model different possible target motions. A concise description of the IMM algorithm is given below. It involves four steps:
a) Interacting: It is assumed that there is a possibility of jumping between sub-filters. The output of the interactive estimated state vector of the jth sub filter at time (t-1), is given by
(29)
where is the output of the ith sub filter at (t-1), is the transition probability from the ith sub filter to the jth sub filter, and is the weighting of the ith sub filter at (t-1). Similarly, the interactive covariance matrix of estimation error for the jth sub filter at (t-1) is given by:
(30)
where:
(31)
is the normalisation constant at (t-1).
b) Filtering: Each filter uses a mixed estimate (29), (30) and the same measurement to compute a new estimate and likelihood for the model within the filter.
c) Weighting: Weighting factors are given by:
(32)
where:
(33)
is the likelihood function calculated from the innovation (n is the measurement dimension) and covariance matrix of innovation - .
d) Estimate combination: In this step, the final estimate at instance t is a combined estimate from all of the sub filters
(34)
and the estimate error covariance matrix is:
(35)
5 HIL simulation
HIL simulation is realised using the configuration that is symbolically illustrated by Fig. 3. The applied software supports the next activities:
- the control of missile flight simulator frames (the IR seeker is placed on one of these frames and connected through A/D converter with appropriate electronic module),
- the control of target flight simulator (through D/A converter),
- the acquisition of angular frames movements that control the pitch and yaw position of IR seeker,
- the acquisition of angular frames movements that control the pitch and yaw position of simulated target,
- the acquisition of angular rate of all frames in simulator,
- the dynamic compensation of all frames in simulator according to requested precision during experiments and etc.
Fig. 3 Global structure of HIL simulation model of tracking process with two IR seekers
The basic hardware simulator components are:
- the missile flight simulator consisting of three axes (in concrete case it is used for positioning of IR seeker in vertical and horizontal plane),
- the target flight simulator consisting of two axes (for positioning of IR source),
- the control console,
- the connector panel with appropriate A/D and D/A converters,
- personal computer and hydraulic servo.
During the simulation, we have used three extended Kalman filters of the form (17)-(25) with different orders (second order filter without manoeuvre, and two third order filters with different manoeuvres [3, 4])
6 Simulation results
HIL simulation of target capture and tracking processes are realised with assumption that its positioning simulate the movement of real target at rate Vc = 300 m/s from position on co-ordinates C(x,y,z) = (2,5,-1) km, in horizontal plane, in direction of -900 relative to x – axis of geodetic co-ordinate system. It is evident that flight direction is chosen to be parallel relative to the y – axis of co-ordinate system (Fig. 1). The sensors that follow the target movement are placed at points whose co-ordinates are M(x,y,z) = (0,0,0) km and S(x,y,z) = (0,2,0) km. The flight in time interval of 10s is watched. The sampling of the appropriate measurements is adopted to be in intervals of 20ms.
It is well known that every HIL simulation starts with appropriate calibration procedure that depends on mass and dimensions of hardware mounted on simulator platform. In our experiment surface-to-air missile passive IR seeker is used as a sensor. Every servo amplifier in simulator with five degrees of freedom (roll, yaw, pitch, elevation, and azimuth) must be adjusted through calibration procedures. The sensor orientation is synchronised according to the “off-line” simulation results. Fig. 4 and 5, show the angle position of the target direction relative to the secondary sensor S and its orientation during the tracking initialisation and target tracking.
Fig. 4 Elevation angles (off-line simulation results)
From Fig. 6, the existence of differences can be viewed among measured frames angle rates and the angle rates requested according to “off-line” simulation results. The frame dynamics and calibration inaccuracy are some of the reasons for differences between the target appearance instances in the secondary sensor FOV achieved by HIL and “off-line” simulations, respectively.
Fig. 5 Azimuth angles (off-line simulation results)
Fig. 6 The change of sensor frames angle rates: doted lines (“off-line” simulation results), solid line (HIL simulation).
Fig. 7 Signal on sensor output (value is determined by LOS displacement relative to co-ordinator optical axis)
In the case of HIL simulation the target appearance in sensor FOV is reached after about three seconds (Fig. 7), that is not same as in “off-line” simulation (Fig. 4 and 5). The other reasons
for differences in results of HIL and “off-line” simulations probably are in physically limitations of experiment (short distance between sensor and IR source, the narrow IR detector FOV). In “off-line” simulation these effects are neglected.
7 Conclusion
The HIL simulation results confirm the assumptions about realisation of the target range estimation using triangulation method based on application of passive IR sensors (the homing missile seekers, for example). The results are reached in partial HIL simulation. Complete simulation will be made with hardware that has to provide implementation of state estimator in real time. We shall try to do it without using of special digital signal processors. The experiments are in progress and results will be published in future papers.
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