Adaptive Signal Processing Class Project Adaptive Interacting Multiple Model Technique for Tracking Maneuvering Targets Viji Paul, Sahay Shishir Brijendra, Krishnamoorthy Iyer, Meles Gebreyesus

Adaptive Signal Processing Class Project Outline of the Presentation Introduction to the problem Multiple Model Technique IMM and the models used Multiple Target Scenario Simulation results Adaptive Cancellation of Oscillation Effect Simulation results

Adaptive Signal Processing Class Project Outline of the Presentation Introduction to the problem Multiple Model Technique IMM and the models used Multiple Target Scenario Simulation results Adaptive Cancellation of Oscillation Effect Simulation results

Adaptive Signal Processing Class Project Radar site Observed Position Predicted Position Error Target Tracking Using Surveillance radar

Adaptive Signal Processing Class Project Target Tracking Using Surveillance radar

Adaptive Signal Processing Class Project In the MM estimation, it is assumed that the possible system behavior patterns, called system modes, can be represented by a set of models. A bank of filters runs in parallel at every time, each based on a particular model, to obtain the model-conditional estimates. Overall state estimate is a certain combination of these model-conditional estimates. Multiple Model Estimation

Adaptive Signal Processing Class Project Multiple Model Estimation A Bayesian framework starting with prior probabilities of each model being correct (i.e. the system is in a particular mode) is used. The model, assumed to be in effect throughout the process, is one of r possible models (the system is in one of r modes)

Adaptive Signal Processing Class Project Multiple Model Estimation The prior probability that is correct (i.e. the system is in mode j) is j = 1…….r where is the prior information; and

Adaptive Signal Processing Class Project Multiple Model Estimation The output of each mode-matched filter: Mode-conditioned State Estimate Associated State Error Covariance Matrix Mode Likelihood Function

Adaptive Signal Processing Class Project Multiple Model Structure

Adaptive Signal Processing Class Project Output Estimate After the filters are initialized, they run recursively on their own estimates. Their likelihood functions are used to update the mode probabilities. The latest mode probabilities are used to combine the mode-conditioned estimates and covariances.

Adaptive Signal Processing Class Project Output Estimate The combination of mode-conditioned estimates is therefore done as follows And the covariance of the combined estimate is

Adaptive Signal Processing Class Project Multiple Model Approach for Switching Models Consider an example with two models, and at time, k =2 one has possible histories

Adaptive Signal Processing Class Project Multiple Model Approach for Switching Models The mode history – or sequence of models – through time k is denoted as where is the model index at time k from history l. It is important to note that number of histories increases exponentially with time.

Adaptive Signal Processing Class Project Interacting Multiple Model Algorithm

Adaptive Signal Processing Class Project Steps in IMM One cycle of the algorithm consists of the following: Step 1: Calculation of the mixing probabilities. Step2: Mixing- Calculation of mixed initial conditions Step3: Mode matched filtering. Step4: Mode probability update. Step5: Estimate and covariance combination

Adaptive Signal Processing Class Project Block Diagram of the Tracking Routine Model j Kalman Filter j = 1…r IMM Block State estimates for established target State estimate covariance for established target Model probabilities for established target Sensor measurements

Adaptive Signal Processing Class Project Tracking Maneuvering target A weaving target track constructed of linked coordinated turns

Adaptive Signal Processing Class Project IMM One cycle of the algorithm consists of the following: Step 1: Calculation of the mixing probabilities. The probability that mode was in effect at time k-1 given that is in effect at k, conditioned on is:

Adaptive Signal Processing Class Project IMM Algorithm The above are the mixing probabilities, which can be written as Where the normalizing constants are j = 1,…,r.

Adaptive Signal Processing Class Project IMM Algorithm Step 2: Mixing. Starting with one computes the mixed initial condition for the filter matched to j = 1,…,r

Adaptive Signal Processing Class Project IMM Algorithm The covariance corresponding to the above is

Adaptive Signal Processing Class Project IMM Algorithm Step 3: Mode-matched filtering. The estimate and covariance are used as input to the filter matched to which uses to yield and The likelihood functions corresponding to the r filters are computed using the mixed initial condition and the associated covariance

Adaptive Signal Processing Class Project IMM Algorithm Step 4: Mode probability update. This is done as follows

Adaptive Signal Processing Class Project IMM Algorithm Step 5: Estimate and covariance combination. Combination of the model-conditioned estimates and covariances is done according to the mixture equations

Adaptive Signal Processing Class Project There are total four targets moving with different kinematics. Initial Range : Range of the target at time zero. Initial Theta : Azimuth of the target at time zero. Split no : Number of splits into which time is partitioned. No of Scans : Number of scans in each time split. Start Scan : Starting scan number of each partition of time. End Scan : Ending scan number of each partition of time. IMM Estimator for Tracking Multiple Targets: Parameters used for scenario generation

Adaptive Signal Processing Class Project Turn Rate : Amount of course change in degree per second. Velocity : Velocity in each partition of time. Acceleration : Acceleration in each partition of time. Heading : Heading in each partition of time. IMM Estimator for Tracking Multiple Targets: Parameters used for scenario generation

Adaptive Signal Processing Class Project --- Target data ---1 Initial Range : Initial Theta : Split no : Scan no : Start Scan : End Scan : Turn Rate : Velocity : Accelaration : Heading : IMM Estimator for Tracking Multiple Targets: Parameters used for scenario generation

Adaptive Signal Processing Class Project --- Target data ---2 Initial Range : Initial Theta : Split no : Scan no : Start Scan : End Scan : Turn Rate : Velocity : Accelaration : Heading : IMM Estimator for Tracking Multiple Targets: Parameters used for scenario generation

Adaptive Signal Processing Class Project --- Target data ---3 Initial Range : Initial Theta : Split no : Scan no : Start Scan : End Scan : Turn Rate : Velocity : Accelaration : Heading : IMM Estimator for Tracking Multiple Targets: Parameters used for scenario generation

Adaptive Signal Processing Class Project --- Target data ---4 Initial Range : Initial Theta : Split no : Scan no : Start Scan : End Scan : Turn Rate : Velocity : Accelaration : Heading : IMM Estimator for Tracking Multiple Targets: Parameters used for scenario generation

Adaptive Signal Processing Class Project Maneuvering Models Constant Velocity Model For small sample intervals T, the following model is commonly used (Blackman & Popoli, Sec ):

Adaptive Signal Processing Class Project Maneuvering Models Constant Acceleration Model

Adaptive Signal Processing Class Project Maneuvering Models Coordinated Turn Model

Adaptive Signal Processing Class Project Multi Target Scenario

Adaptive Signal Processing Class Project Variation of Model weights For Target 1

Adaptive Signal Processing Class Project Variation of Model weights For Target 2

Adaptive Signal Processing Class Project Variation of Model weights For Target 3

Adaptive Signal Processing Class Project Variation of Model weights For Target 4

Adaptive Signal Processing Class Project Tracking From Unstable Platform The environment strongly impacts radar performance

Adaptive Signal Processing Class Project Platform Oscillations Roll, Yaw and Pitch Only Roll has been considered in this simulation. All the three motions are sinusoidal or DC shifted sinusoidal. At max, frequency of the sinusoid is about 1/10 Hz.

Adaptive Signal Processing Class Project Physically stabilized beam

Adaptive Signal Processing Class Project Tracking Maneuvering target A weaving target track constructed of linked coordinated turns. Perturbations are seen because of platform motion.

Adaptive Signal Processing Class Project Target Tracking Data Flow Estimated State Target Sensor (Obsvn Device) Signal / Data Pre- Processor Tracker (State Estimation / Data Association) Electro Magnetic or Acoustic Energy Channel Signal / Raw Data Tracking Algorithm Data Conversion Decoupling Detection- Subsystem Typical Target tracking system

Adaptive Signal Processing Class Project Measurement corrupted by Oscillations Increased deterioration at larger ranges.

Adaptive Signal Processing Class Project For Target 1 Model weight variations due to Platform Oscillations

Adaptive Signal Processing Class Project For Target 2 Model weight variations due to Platform Oscillations

Adaptive Signal Processing Class Project For Target 3 Model weight variations due to Platform Oscillations

Adaptive Signal Processing Class Project For Target 4 Model weight variations due to Platform Oscillations

Adaptive Signal Processing Class Project Target Tracking Data Flow with Adaptive Compensation Estimated State Target Sensor (Obsvn Device) Signal / Data Pre- Processor Tracker (State Estimation / Data Association) Electro Magnetic or Acoustic Energy Channel Signal / Raw Data Tracking Algorithm Data Conversion Decoupling Detection- Subsystem Typical Target tracking system Motion Sensor LMS based Algo

Adaptive Signal Processing Class Project Measurements corrupted by a proportional multiplication of oscillation

Adaptive Signal Processing Class Project Reminds You of Something ??? Output from the Gyro Modified form of Gyro output Signal from the radar

Adaptive Signal Processing Class Project Compensated for Platform Oscillation

Adaptive Signal Processing Class Project Its OK in Theory but is the Target a Sitting Duck ? Operational Solution: Sea state does not change drastically. Ships are always in formation during an operation. During the pre-detection phase, i.e. while approaching the Theatre of Operation, the weights of the Adaptive Filter can be “set” using the LMS Algorithm. The same weights can then be used during the Target Detection phase. Ship with Surv Radar Friendly Ship in Company

Adaptive Signal Processing Class Project Compensated for Platform Oscillation For Target 1

Adaptive Signal Processing Class Project Compensated for Platform Oscillation For Target 2

Adaptive Signal Processing Class Project Compensated for Platform Oscillation For Target 3

Adaptive Signal Processing Class Project Compensated for Platform Oscillation For Target 4

Adaptive Signal Processing Class Project Conclusion Analyzed Multiple Model Technique IMM based estimation is implemented Generated a Multi Target Scenario Applied IMM Verified the algorithm Introduced Platform Oscillations Added LMS based adaptive compensation

Adaptive Signal Processing Class Project Thank you