Trajectory Estimation of AESA Radar Seekers using Kalman Filter

This report delves into the trajectory estimation of objects in space using Airborne Active Electronically Scanned Array (AESA) radar, focusing on military and weather applications. It discusses the complexities of tracking moving targets, the role of AESA radar in transmitting and receiving reflected waveforms, and the challenges posed by low signal-to-noise ratios. The report explores trajectory estimation methodologies, including the 'track before detect' approach and Kalman filter implementation, highlighting the importance of factors such as object weight, center of mass, and radar parameters. A MATLAB simulation is mentioned, involving tracking an aircraft from a military airbase using AESA radar with a Kalman filter. The document emphasizes the radar's capability to provide information on target velocity, spatial location, and composition, while also addressing limitations related to noise and false alarms, aiming to provide a comprehensive understanding of AESA radar-based trajectory estimation.

AESA Radar Seeker Trajectory Estimation
Student Name
Institutional Affiliation
Date of submission

Airborne AESA Radar
Airborne AESA Radar
INTRODUCTION
Weather applications and military organizations globally are interested in tracking objects
in space while in motion. It is quite a complex task and it requires that the surveillance
applications use a trajectory algorithm that is well-optimized to track the movement of the target
object [1]. The radar transmits the modulated pulses towards the target and it receives the
reflected waveforms transmitted by the target. In practice, the small objects have a very low
signal-to-noise ratio. It is required that the AESA radar receiver obtain a number of response
signals as considered from the associated reflection coefficient summation across them. There
are a number of object moving in space and the identification and tracking algorithm ought to
determine the specific object and follow it through consistently either real-time or through
imaging.
The radar facilities transmit radio waves to detect the reflection obtained from the target.
The received signal is able to provide information such as velocity, spatial location, composition,
structure, and vibration [2]. The radar can only measure up to 50,000 objects a day and is neither
affected by daytime nor weather conditions. The AESA radar needs to be a phased array radar to
perform space surveillance. The location is given using the azimuth and elevation while the
range rate is given by the measurement of the two-way doppler shift, radar cross-section,
material, shape, and orientation. The most suitable radar used has different sensor sizes and it
works for bi-static and multi-static systems [3].
TRAJECTORY ESTIMATION BASED ON AESA RADAR
A projectile for a mobile target in space is modelled while in flight. The target’s initial
location is obtained using based on the McCoy’s howitzer’s firing position coordinate system for
the modern exterior ballistics. The object in space moves in both the rotational and translational
motion. The trajectory algorithm must focus on the weight of the object in space as well as its
location of center of mass. The array antenna focus energy, directivity, towards the object in
space using isotropic elements [4]. The AESA radar is arranged in a manner to provide a full

Airborne AESA Radar
scan such that it can reach up to ± 900from the broadside. The radiation impedance changes with
the scan and in many implementations only a ± 600 is covered.
d ≤ λmin
1+sin θmax+ sin θ00
2
[ m ]
The radar has high power amplifiers, circulators, T/R modules, phase shifters, and
attenuators to scan the objects. One approach to trajectory estimation using the scatter measure is
the track before detect approach. It either uses a series of images or a singular image. For a
moving object, the sequence images are used and the pixel size of the image is considered for the
fixed velocity and further data acquisition purposes [5]. The approach does not allow for real-
time processing of the images but they can be processed in batches periodically using control
applications. The approach embraces the scatter in auto-comparison of periodic time series.
x ( n )=x ( n+ L )=…=x ( n+ mL ) m−integer number
The measure of scatter is given by the coefficient,
S= 1
T ∑
j=1
T ||X j −A ||p A−centroid vector T −finite
of periods
¿
¿
Sxx ( l )=S ( l ) = 1
T (l ) ∑
j=1
T (l)
||X j− A||p
¿ ¿
The algorithm can be implemented to determine a single-line trajectory estimation such that,
( x , y , α , l )=argmin S(x , y , α ,l)
Several Monte Carlo tests are done to determine the low peak detection of the moving
target. The amount of power directed towards the target determines if a waveform gets to the
target and it reduces the amount of noise reflections obtained by the receiver [6]. The radar can
track the object when the standard deviation of the background noise is less than 0.8 for a
maximum period of 200. Further one can perform a likelihood locality ratio test to determine the
location of the target while in flight,

Airborne AESA Radar
Using the algorithm, the radar can coherently integrate the reflections within a coherent
processing interval in all the configurations. The received reflection signal is a complex value as
it contains the sum of the reflection coefficient and background noise. The noise samples are a
key limitation to attaining a clear signal from the target on its location, velocity, and range from
the radar or the earth’s atmosphere. The Kalman filter is able to determine the target’s 6 DOF
trajectory estimation. The probability of having a false alarm for the target test variable and
threshold is obtained as,
MATLAB Simulation
Tracking an aircraft from the base station at the military airbase using the AESA radar with a
Kalman filter implementation.