Multi-sensor Multi-target Tracking using Out-of-sequence Measurements

Multi-sensor Multi-target Tracking using Out-of-sequence Measurements1 Mahendra Mallicka, Jon Kranta, Yaakov Bar-Shalomb ALPHATECH, Inc., 50 Mall Road, Burlington, MA 01803, U.S.A. b University of Connecticut, Storrs, CT 06269-2157, U.S.A. [email protected], [email protected], [email protected] a

linear dynamic and measurement models. Orton and Marrs [8] are the first to address the multi-target tracking with arbitrarily delayed OOSMs. Their work is also the first application of the particle filter (PF) to the OOSM tracking problem. OOSM filtering algorithms belong to two distinct classes, (i) single-model [1]-[11] and (ii) multiple-model [5] OOSM algorithms. A single kinematic filtering model is generally not sufficient for maneuvering targets. It is now a standard practice to use the interacting multiple model (IMM) estimator [12][13]. Single and multiple kinematic models are used in the single-model and multiple-model OOSM algorithms, respectively. For each class, the algorithms can be further divided into single-lag and multiple-lag OOSM algorithms [5]. The single-lag OOSM algorithm is applicable when the OOSM z (k ) observed at time t (k ) lies between the latest two measurements. The multiplelag OOSM algorithm is applicable for the general case when the OOSM z (k ) can have an arbitrary time delay

Abstract - Out-of-sequence measurements (OOSMs) arise in a multi-sensor central-tracking system due to communication network delays and varying preprocessing times at the sensor platforms. During the last few years a great deal of research has focussed attention on the OOSM filtering problem. However, research in the multi-sensor multi-target OOSM tracking involving data association, filtering, and hypothesis management is still lacking. Some previous efforts have used buffering and measurement reprocessing to handle the OOSMs. In this paper, we present single-model multiple-lag OOSM algorithms for data association, likelihood computation, and hypothesis management for a dwell-based multi-sensor multi-target multi-hypothesis tracking (MHT) system that handles missed detections and clutter. We present numerical results using simulated multi-sensor ground moving target indicator (GMTI) radar measurements. Keywords: Out-of-sequence measurement (OOSM), OOSM filtering, OOSM tracking, multiple hypothesis tracking (MHT), ground moving target indicator (GMTI) measurements.

1

and thus lies between measurements z (k − l − 1) and

z (k − l ) observed at times t (k − l − 1) and t (k − l ) , respectively. In this paper, we present multi-target multi-sensor OOSM tracking algorithms for ground targets assuming data from each sensor arrives at the central tracker in dwells or scans. This is typical of ground moving target indicator (GMTI) radar sensors [14]-[16]. Each dwell contains zero or more reports, a single observation time, and a single measured sensor state (e.g. position, velocity). Each dwell has an associated coverage area on the ground within which the sensor reports are located. The reports in a dwell include detections from actual targets and false alarms. The GMTI sensor can detect a target when the magnitude of the radial component of velocity is greater than the minimum detectable velocity (MDV). Therefore, a GMTI sensor can not detect a target when the radar line-of-sight (RLOS) is orthogonal or nearly orthogonal to the target velocity. In certain cases, the terrain can obstruct the RLOS between the target and the sensor. In such a case a target is not detected by a GMTI sensor due to occlusion of the RLOS by the terrain.

Introduction

Out-of-sequence measurements (OOSMs) can arise in a multi-sensor centralized tracking system due to delays in communication network and varying pre-processing times at the sensor platforms [1]-[5]. The OOSM algorithms can be classified into two types, (i) OOSM filtering algorithms and (ii) OOSM tracking algorithms. The OOSM filtering algorithm addresses the update of the state and covariance using the OOSM. Many researchers [1]-[11] have primarily focussed attention on the OOSM filtering algorithms during the last few years. The OOSM filtering algorithms do not address the issues associated with data association, presence of clutter, probability of detection ( PD ) less than unity, and hypotheses management that arise in a realistic multitarget multi-sensor tracking problem. Challa, Evans, and Wang [6] use a fixed-lag smoothing framework for processing the OOSM in the presence of clutter with 1

Proc. Fifth International Conference on Information Fusion (Fusion 2002), Annapolis, MD, U.S.A.

ISIF © 2002

135

(2 − 4)

Trees and buildings can also obstruct the RLOS. In this paper, we do not consider occlusion due to trees and buildings, since these data are difficult to obtain for most parts of the world. We use the nearly constant velocity model (NCVM) in two dimensions [2], [13] for the target kinematic model on the surface of the earth. Target tracking is performed in a topographic coordinate frame (TCF) [17] whose origin lies on the WGS84 reference ellipsoid [18] with geodetic longitude (λ 0 ) , geodetic

(2 − 5)

following form: (2 − 6)

3

[

p ky

v kx

v ky

1 q2 (∆ j )3 3

q1∆ j

1 q2 (∆ j ) 2 2

0

p T ∈ ℜ3 : Cartesian components of the target position vector relative to the TCF origin and coordinatized in the TCF ,

v T ∈ ℜ 3 : Cartesian components of the target velocity relative to the TCF and coordinatized in the TCF, s T ∈ ℜ 3 : Cartesian components of the sensor position vector relative to the TCF origin and coordinatized in the TCF. Let

]′ ,

[

model

(3 − 2)

v T := [x&

derived from the continuous time dynamics of the state for the NCVM is described by [2], [5] ,[13], [19]

(3 − 3)

s T = s xT

where p kx := p x (t k ), p ky := p y (t k ), v kx := v x (t k ), and discrete-time

kinematic

(2 − 2) x j = Φ( j , j − 1) x j −1 + w( j , j − 1),

noise [5], [19]. The state transition matrix and the integrated process noise for the NCVM are given by

1 0 0

0 1 0

y&

s Ty

pz

]′ ,

′ z& ] ,

]

′ s zT .

position p z is determined using the terrain dada. Formally, the nonlinear GMTI measurement model for the measurement z (k ) ∈ ℜ m is

and w( j, k − 1) := w(t j , t j −1 ) is the integrated process

0 ∆j

[

py

Given ( p x , p y ) , the Z component of the target

where Φ( j, j − 1) := Φ(t j , t j −1 ) is the state transition matrix

1 0 (2 − 3) Φ ( j , j − 1) :=  0  0

   1 q2 (∆ j ) 2  2 .  0   q2 ∆ j   0

GMTI Measurement Model

p T := p x

The

0

0

(3 − 1)

v ky := v y (t k ).

1 q1 (∆ j ) 2 2

0

Define

Let xk ∈ ℜn denote the state of the target at discrete time k := t k . The state consists of two-dimensional position and velocity:

x k := p kx

Q(∆ j ) = 1 3  3 q1 (∆ j )   0  1 2  2 q1 (∆ j )   0 

Kinematic Model

(2 − 1)

E{ w( j , j − 1) w′(l , l − 1)} = δ jl Q(∆ j ).

Q(∆ j ) is the covariance of the process noise with the

latitude (φ 0 ) , and zero geodetic height (h0 = 0) . The Z components of position and velocity are not estimated in the filter. However, given X and Y components of target position, the Z components of position obtained from terrain data is used in the GMTI measurement model. The Z component of velocity is assumed zero in the measurement model. The terrain data and sensor state are assumed error-free. The outline of the paper is as follows. Sections 2 and 3 present the kinematic model and GMTI measurement model, respectively. Section 4 summarizes the multiple-lag OOSM filtering algorithm SNB l [11] using a single kinematic model and nonlinear measurement model. Section 5 describes OOSM tracking algorithms which include gating, likelihood computation, and hypotheses management. Finally, Sections 6 and 7 present numerical results and conclusions.

2

E{w( j , j − 1)} = 0,

(3 − 4)

z ( k ) = hk ( xk , skT ) + n( k ),

where hk : ℜ n × ℜ 3 → ℜ m and n(k ) ∈ ℜ m ~ N (0, Rk ) are the measurement function and zero-mean Gaussian measurement noise, respectively. The components of z k

0 ∆ j  , ∆ j = (t j − t j −1 ), 0  1

for the GMTI sensor are slant range ( z kr ) , azimuth

136

( z kα ) , and range-rate ( z kr& ) . The components of the measurement function hk are range (hkr ) , azimuth (hkα ) , and range-rate (hkr& ) . The components of the measurement noise vector nk are measurement noises for range (nkr ) , azimuth (nkα ) , and range-rate (nkr& ) . Each component of nk may be the sum of independent error sources. Thus z k := [z kr

(3 − 4)

hk := [hkr

(3 − 5)

nk := [nkr

(3 − 6)

z kα

z kr& ]′ ,

hkα

hkr& ]′ ,

nkα

(3 − 11) hα (r L ) :=  tan −1 (r1L , r2L ), if tan −1 (r1L , r2L ) > 0 , 0 ≤ α < 2π .  −1 L L tan (r1 , r2 ) + 2π , if tan −1 (r1L , r2L ) < 0, The azimuth is defined using the components of r L , not r T . Therefore, we need to transform r T to r L using the TCF to LLF rotational transformation TTL . We compute TTL as follows: L T (3 − 12) TTL (λs , φ s ; λ 0 , φ 0 ) = TE84 (λs , φ s )[ TE84 (λ0 , φ 0 ) ]′,

nkr& ]′ .

(3 − 13)

L TE84 (λs , φs ) = F (λ s, φs ),

(3 − 14)

T TE84 (λ0 ,φ0 ) = F (λ 0,φ0 ),

We assume that Rk is diagonal: where 2 σ kr

 Rk =  0  0 

(3 − 7)

0

σ k2α 0

  , 2  σ kr& 

0 0

(3 − 15) F (λ , φ )  − sin λ :=  − sin φ cos λ  cos φ cos λ

where σ kr , σ kα , and σ k&r , are the GMTI measurement noise standard deviations for range, azimuth, and rangerate in the k th dwell, respectively.

(3 − 16)

r T ∈ ℜ 3 : geometric range vector from the sensor to the target, coordinatized in the TCF, r L ∈ ℜ 3 : geometric range vector from the sensor to the target, coordinatized in the local level frame (LLF) [17], r : geometric range from the sensor to the target, u T ∈ ℜ3 : unit vector along the geometric range vector, coordinatized in the TCF.

(3 − 17)

hr& ( x, s T ) = (v T )′ u T = (u T )′v T ,

where we have dropped the arguments of simplicity.

4 r T = pT − sT .

TTL for

Single Model Multiple-lag OOSM Algorithm

The OOSM z (k ) observed at time t (k ) arrives at the central tracker after the measurement z (k − 1) observed

Dropping the measurement subscript k and ignoring the atmospheric refraction correction

(3 − 10)

r L = TTL r T .

The measurement function for the range-rate is

Then

(3 − 9)

cos φ cos λ

0  cos φ , sin φ 

The transformation of r T to r L is

Define

(3 − 8)

cos λ − sin φ sin λ

at time t (k − 1) . In general, the measurement time t (k ) may be l lags behind, t (k − l − 1) < t (k ) < t (k − l ) , l =

hr ( x, s T ) = r = [(r T )′r T ]1 / 2 ,

1,2…. Before the out-of-sequence measurement z(k ) is received, we have the last measurement updated state xˆ (k − 1 | k − 1) and the corresponding estimate

u T := r T / r.

covariance P(k − 1 | k − 1) at time t (k − 1) :

The azimuth angle is defined in the LLF [17] and is given by

(4 − 1)

137

xˆ (k − 1 | k − 1) := E{x(k − 1) | Z k −1 },

For the B - type algorithms [11], we use the approximation

P(k − 1 | k − 1) := cov{x(k − 1) | Z k −1 },

(4 − 2)

where ( 4 − 3)

Z

k −1

zˆ SNB ( k | k − 1) ≈ hk (Φ ( k , k − 1) xˆ ( k − 1 | k − 1))

( 4 − 14)

:= {z (1), z ( 2),..., z (k − 1)}.

= h k ( xˆ ( k | k − 1)).

For tracking applications we need the following measurement updated state estimate and covariance for each track hypothesis at time t (k − 1) by processing

( 4 − 15)

A(k , k − 1) := H k ( xˆ (k | k − 1))Φ(k , k − 1),

(4 - 16)

z (k ) :

xˆ ( k | k − 1) = Φ ( k , k − 1) xˆ ( k − 1 | k − 1).

(4 − 4)

xˆ (k − 1 | k ) := E{x(k − 1) | Z k },

(4 − 17)

(4 − 5)

P(k − 1 | k ) := cov{x(k − 1) | Z k },

( 4 − 18)

H j ( xˆ ( j | j − 1)) :=

∂h j ( x) ∂x

x = xˆ ( j | j −1) ,

j = 1,2,.., k .

PxzSNBl (k − 1, k | k − 1)

SLBl = [ P (k − 1 | k − 1) − Pxw (k − 1; k , k − 1 | k − 1)] A ′(k , k − 1),

where

l = 1,2,... k

(4 − 6)

Z := {Z

k −1

, z (k )}.

( 4 − 19) PzzSNB l ( k , k | k − 1) = A(k , k − 1)[ P (k − 1 | k − 1) + Q(k − 1, k )

Details of the single model nonlinear measurement based multiple-lag OOSM filtering algorithm, SNB l are given in [11]. For clarity, we summarize the algorithm for updating the state estimate and covariance here.

( 4 − 7)

SNBl SNBl − Pxw ( k − 1; k − 1, k | k − 1) − Pxw (k − 1; k − 1, k | k − 1) ′] A′( k , k − 1) + R( k ), l = 1,2,...

where

xˆ (k − 1 | k ) = xˆ (k − 1 | k − 1) + K (k − 1, k | k − 1)[ z (k ) − zˆ(k | k − 1)],

(4 − 20)

( 4 − 8) P (k − 1 | k ) = P ( k − 1 | k − 1) − Pxz ( k − 1, k | k − 1) Pzz (k , k | k − 1) −1 Pxz ( k − 1, k | k − 1) ′,

Pxw (k − 1; k , k − 1 | k − 1) := E{~ x (k − 1 | k − 1) w(k , k − 1) | Z k −1 }.

We show in [11] that SNBl (4 − 21) Pxw (k − 1; k , k − 1) = M (k − l )Q(k − l , k ; k − l , k − 1)

where K ( k − 1, k ) := Pxz (k − 1, k | k − 1) Pzz (k , k | k − 1) −1,

( 4 − 9)

+

l −1

∑ M (k − j )Q(k − j, k − j − 1; k − j, k − 1),

l = 1,2,...

j =1

(4 − 10)

Pxz (k − 1, k | k − 1) = cov{x(k − 1), z (k ) | Z k −1 },

( 4 − 11)

Pzz ( k , k | k − 1) = cov{ z ( k ), z ( k ) | Z k −1 }.

(4 - 22) Q(k − j , k − j − 1; k − j, k − 1) := E{w(k − j , k − j − 1; k − j ) w(k − j, k − j − 1; k − 1)' }, B ( k − 1), j =1  ( 4 − 23) M ( k − j ) :=  D ( k − j + 1 ) B ( k − j ), j = 2,3,..., l 

Using (3-4) and (2-2), we get ( 4 − 12 ) z ( k ) = h k (Φ ( k , k − 1)[ x ( k − 1) − w( k − 1, k )])

(4 − 24)

+ n ( k ).

B(k − j ) = I − K (k − j ) H (k − j ),

j = 1,2,3,..., l

(4 − 25) D(k − j + 1) := C ( k − 1)C ( k − 2)...C (k − j + 1), j = 2,3,..., l ,

Thus the predicted measurement is (4 − 13) zˆ(k | k − 1)

(4 − 26) C (k − j ) = B(k − j )Φ(k − j , k − j − 1), j = 1,2,..., (l − 1).

= E{hk (Φ(k , k − 1)[ x(k − 1) − w(k − 1, k )]) | Z k −1}.

138

An alternate form for PzzSNB l (k , k | k − 1) is

( 4 − 27 )

PzzSNB l (k , k | k − 1)

SNB l = A(k , k − 1)[ P ( k − 1 | k − 1) − Pxw ( k − 1; k − 1, k | k − 1) SNB l − Pxw ( k − 1; k − 1, k | k − 1) ′] A ′( k , k − 1) + Pek , l = 1,2,...

( 4 − 28 )

Pek := E{e( k )e ′( k )} = A( k , k − 1)Q ( k − 1, k ) A ′( k , k − 1) + R ( k ).

5

Multi-sensor Multi-target OOSM Tracking Algorithms

In the MHT approach, the association of reports with track hypotheses using more than one dwell of data is used to determine the best association of reports to tracks. This delayed decision making feature of the MHT algorithm, until more data is processed, enables to make more accurate track to report assignment in complex tracking scenarios. In our MHT tracking, hypothesis management includes several key components: gating, hypothesis generation, likelihood computation, track hypothesis likelihood update, and hypothesis pruning. Given a dwell segment packet, we process dwells sequentially.

5.1

Gating

If the dwell time t (k ) for a dwell containing one or more reports is less than the latest dwell time t (k − 1) in the tracker, then we identify that the dwell contains OOSMs. If the delayed dwell at time t (k ) does not contain any reports, then no OOSM processing is performed. If t ( k ) > t ( k − 1) , then standard tracker operations are performed. Let z (k ) be a measurement in the dwell time

The multi-target GMTI OOSM tracking algorithms must address the presence of false alarms, missed detections, non-observability of targets with magnitude of the radial velocity less than the MDV, occlusion of RLOS by terrain, data association for target detections, computation of the track likelihood, and hypothesis management. The central tracker must process the OOSM data in a consistent way that is realistic in nature with the data structure of received data. We assume that the central tracker receives a dwell segment packet at a time from a sensor platform. A dwell segment packet can contain one or more dwells of data. A basic assumption for the dwell data is that no more than one report arises from a single target in a dwell. Some reports in a dwell may be false alarms. A dwell may not contain any report. For each dwell, a dwell time, observed sensor state (measured sensor position and velocity from inertial navigation (INS)/global positioning system (GPS)), possibly sensor state covariance, and GMTI measurement error covariance are available. The dwells in a dwell segment are usually time-ordered. If the sensor operates in multiple modes (e.g. wide area search (WAS) mode, sector search (SS) mode), the dwells in a dwell segment packet may not be time-ordered. Since all the dwells in a dwell segment packet are received at the same time at the central tracker, out-of-sequence dwells in a dwell segment packet can be always time-ordered at the central tracker. Therefore, we assume without loss of generality that the dwells in a dwell segment packet are time-ordered. We use a track-oriented multiple-hypothesis tracking (MHT) algorithm [2], [19] to process the OOSMs. In the track-oriented MHT framework, each target has a tree structure with track hypotheses as the branches. The tracker computes the estimated state, covariance, and track hypothesis likelihood ratio. The MHT algorithm forms one or more global hypotheses by using a set of track hypotheses such at most one track hypothesis is selected from each target tree and the reports in a track hypothesis do not occur in any other track hypothesis in the global hypothesis.

t (k ) . The covariance Pzz ( k , k | k − 1) of the innovations process for in-sequence measurement (ISM) and OOSM are given by

(5 − 1) Pzz (k , k | k − 1)  H ( xˆ (k | k − 1)) P (k | k − 1) H ( xˆ (k | k − 1)) ′ + R (k ),  = for ISM,  P SNBl (k , k | k − 1), = 1 , 2 ,... for OOSM. l  zz

We did not address missed detections in the filtering algorithm. In general, a track hypothesis in the tracking problem would contain a number of detections and missed detections. The presence of missed detections requires modifications in the computation of the B matrix. For detection and missed detection cases the B matrix is computed by

(5 − 2 )

B (k − j )

 I − K (k − j ) H (k − j ), for detection = for miss - detection  I,

j = 1,2,.., l.

If z (k ) satisfies the gating the condition

(5 − 3) [ z ( k ) − zˆ ( k | k − 1)]′ Pzz−1 ( k , k | k − 1) [ z ( k ) − zˆ ( k | k − 1)] ≤ χ 2p (α ),

0 < α < 1,

where zˆ (k | k − 1) = hk ( xˆ (k | k − 1) for ISM or OOSM, then the report z (k ) is associated with the given track hypothesis and a new track hypothesis branch is

139

(5 − 5) ~ z B (k | k − 1) = A(k , k − 1)[~ x (k − 1 | k − 1) − w(k − 1, k )] + n(k ).

generated at time t (k − 1). χ d2 (α ) represents the upper (100 α )th percentile of a chi-square distribution with d degrees of freedom [21].

5.2

Since the previous innovations process ~ z ( k − 1 | k − 2) B ~ and ( z (k | k − 1) are correlated, computation of the track hypothesis likelihood is difficult. Currently we ignore this correlation and compute the incremental likelihood ratio approximately for an OOSM using

New Target Hypothesis

If the gating condition is not satisfied, then a new target hypothesis is created at time t (k ) and the state and covariance are propagated to time t (k − 1).

5.3

(5 − 6) λ ( z (k ); zˆ (k | k − 1), Pzz ) N ([ z (k ) − zˆ (k | k − 1)]; 0, Pzz ) ≈ PD , µ FA ( z (k ))

Special Cases

A class of special cases arise, when a track hypothesis contains only one report and one or more missed detections as shown in Figures 1. z (k )

where PD , µ FA , Pzz are the probability of detection, false alarm density, and covariance of the innovations process for the OOSM, respectively. Future research will focus on more accurate computation of the likelihood ratio.

z (k − 1)

t (k ) t (k − 1)

Time

(a) Single-lag

6

We used the Kosovo Engineering Data Set vignettes from the Affordable Moving Surface Target Engagement (AMSTE) I program to test, validate, and evaluate the OOSM algorithms using single and multiple targets. Figure 2 shows the simulated Kosovo scenario with terrain data and two GMTI platforms. Two GMTI radar platforms collected data at a 60 degree aspect difference and a 5 second update interval. The aircraft locations are depicted on the right hand side of Figure 2. The yellow aircraft processed reports without latency, while the red aircraft had a 2-second communication latency. The measurement error standard deviations for range, azimuth, and range-rate for both sensors are 6.0 meters, 2.062 milli-radian, and 1.0 m/s, respectively. Target truth is shown as brown diamonds, tracks as red squares and reports as yellow triangles.

z (k ) z (k − 2) Miss-detection

t (k )

t (k − 2)

t (k − 1)

Time

(b) Two-lag Figure 1. Special cases of OOSM z (k ) association with an initialized track hypothesis An analysis of the derivation for Pxw ( k − 1; k , k − 1) shows that this case is generally handled by setting Q(k − l , k ; k − l , k − 1) to zero. Thus for this special case we obtain

(5 − 4)

Pxw (k − 1; k , k − 1) =

l −1

∑ M (k − j)Q(k − j, k − j − 1; k − j, k − 1). j =1

5.4

Simulation and Numerical Results

Track Hypothesis Likelihood Ratio

In the MHT algorithm, we compute the log-likelihood ratio of a track hypothesis. The log-likelihood ratio is the sum of the incremental log-likelihood ratios for a number of dwells that include reports and missed detections. The innovations process for the OOSM using the SNB l algorithm [11] is

140

Table 1 compares three approaches for processing OOSMs with the ideal non-latent case for one, three, and eight targets using the MHT algorithm. We observe that discarding the OOSM can result in large position and velocity estimation errors. A simple alternative to MHT based OOSM processing is to buffer OOSMs on the front-end, enabling the tracker to process reports in temporal order. A disadvantage to the buffering approach is that there may not be enough information available to select the right amount of buffering for real scenarios. Too small a buffer will cause many latent reports to be discarded. Too large a buffer results in the large propagation of the target tracks in the output, degrading accuracy.

Figure 2. Kosovo target tracking scenario with two GMTI radar platforms

Number of Targets

1

3

8

Table 6.1. Comparison of Algorithms for Processing Out-of-sequence Measurements RMS Position, Speed, and Heading Error Discarding Processing Processing Processing with Processing with Processing Variable

Position (m) Speed (m/s) Heading (deg) Position (m) Speed (m/s) Heading (deg) Position (m) Speed (m/s) Heading (deg)

Reports in Time Order

OOSM Algorithm (1-Lag)

Buffering Algorithm (1-Lag)

with OOSM Algorithm (2-Lag)

65.9 1.54 18.7 74.7 1.57 16.3 77.3 2.21 21.8

66.1 1.51 18.4 76.9 1.61 17.1 82.5 2.13 22.2

71.3 1.54 18.7 80.1 1.61 17.3 85.1 2.20 23.5

93.6 1.50 20.6 100.1 1.79 20.3 134.3 2.35 26.2

The OOSM tracking algorithm and buffering approaches significantly improve the position and velocity estimation accuracy compared to discarding the OOSM. Results from Table 1 show that for the single lag case, the OOSM tracking algorithm performs better than the buffering approach and is close to the optimal solution.

7

with Buffering Algorithm (2-Lag) 85.5 1.56 21.0 95.8 1.68 19.8 108.1 2.36 27.5

OOSM

158.4 2.0 32.1 152.7 1.97 23.9 197.8 3.36 35.6

Conclusions

In this paper we have developed multi-sensor multitarget OOSM dwell-based tracking algorithms which include gating, likelihood computation, and hypotheses management. We have presented preliminary results for the multi-sensor multi-target GMTI tracking problem using simulated data. Our results indicate that discarding the OOSMs in realistic multi-target GMTI tracking problems can lead to severe degradation in position and velocity estimation accuracy. On the other hand, the OOSM tracking algorithm or buffering approach provide significant improvement in tracking accuracy compared to discarding the OOSM. For the single-lag problem, the

However, for the two-lag OOSM problem, buffering seems to perform better than the OOSM tracking algorithm. More extensive test and evaluation is necessary to validate the performance of the OOSM algorithm implemented in the MHT tracker.

141

results from the OOSM tracking algorithms are close to those obtained from processing time ordered measurements and better than the results from the buffering approach. For the two-lag OOSM problem, the results of the OOSM tracking are less accurate than those from the buffering approach. We plan to investigate an improved likelihood computation algorithm and OOSM tracking algorithms using multiple model approach.

8

Target Indicator (GMTI) Tracking,” Proc. IEEE Aerospace Conference, Big Sky MT, March 2002. [11] M. Mallick and Y. Bar-Shalom, “Nonlinear Out-ofsequence Measurement Filtering with Applications to GMTI Tracking,” Proc. SPIE Conf. Signal and Data Processing of Small Targets, Orlando, Florida, April 2002. [12] H. A. P. Blom, and Y. Bar-Shalom, “The Interacting Multiple Model Algorithm for Systems with Markovian Switching Coefficients,” IEEE Transactions on Automatic Control, 22(3): 302-312, 1977.

References

[1] R. D. Hilton, D. A. Martin, and W. D. Blair, “Tracking with Time-Delayed Data in Multisensor Systems,” NSWCDD/TR-93/351, Dalhgren, VA, August 1993.

[13] Y. Bar-Shalom, X. R. Li and T. Kirubarajan, Estimation with Applications to Tracking and Navigation, Wiley & Sons, 2001.

[2] S. Blackman and R. Popoli, Design and Analysis of Modern Tracking Systems, Artech House, 1999.

[14] J. N. Entzminger, Jr., C. A. Fowler, and W. J. Kenneally, “Joint-STARS and GMTI, Past, Present, and Future,” IEEE Transactions on Aerospace and Electronic Systems, vol. 35, pp. 748-761, April 1999.

[3] Y. Bar-Shalom, “Update with Out-of-Sequence Measurements in Tracking: Exact Solution,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 38, July 2002.

[15] T. Kirubarajan, Y. Bar-Shalom and K. R. Pattipati, “Ground Target Tracking with Variable Structure IMM Estimator,” IEEE Transactions on Aerospace and Electronic Systems, January 2000.

[4] J. R. Moore and W. D. Blair, “Practical Aspects of Multisensor Tracking,” in Multitarget-Multisensor Tracking: Applications and Advances, Volume III, Y. Bar-Shalom and William Dale Blair, (ed.) pp. 1-76, Artech House, 2000.

[16] W. Koch, “GMTI-Tracking and Information Fusion for Ground Surveillance,” Signal and Data Processing of Small Targets: Proceedings of SPIE, vol. 4473, August 2001.

[5] M. Mallick, S. Coraluppi, and C. Carthel, “Advances in Asynchronous and Decentralized Estimation,” Proc. IEEE Aerospace Conference, Big Sky MT, March 2001.

[17] M. Mallick, “Maximum Likelihood Geolocation using a Ground Moving Target Indicator (GMTI) Report”, Proc. IEEE Aerospace Conference, Big Sky MT, March 2002.

[6] S. Challa, R. J. Evans and X. Wang, “A Fixed Lag Smoothing Framework for Target Tracking in Clutter Using Out of Sequence Measurements,” DASP 2001, Australia.

[18] Department of Defense World Geodetic System 1984, Its Definition and Relationships with Local Geodetic Systems, NIMA WGS 64 Update Committee, NIMA TR 8350.2, Third Edition, 4 July, 1997.

[7] E. W. Nettleton and H. F. Durant-Whyte, “Delayed and Asequent Data in Decentralized Sensing Networks,” The University of Sydney, Australia, 2001.

[19] A.Gelb, ed., Applied Optimal Estimation, M.I.T. Press, 1996.

[8] M. Orton and A Marrs, “A Bayesian Approach to Multi-target Tracking Data Fusion with Out-of Sequence Measurements,” 2001.

[20] T. Kurien, “Issues in the Design of Practical Multitarget Tracking Algorithms,” in MultitargetMultisensor Tracking, Y. Bar-Shalom (ed.), pp. 43-83, Artech House, 1990.

[9] Y. Bar-Shalom, M. Mallick, H. Chen, and R. Washburn, “One-Step Solution for the General Out-ofSequence Measurements Problem in Tracking,” Proc. IEEE Aerospace Conference, Big Sky MT, March 2002.

[21] R. A. Johnson and D. W. Wichern, Applied Multivariate Statistical Analysis, Communications, Prentice Hall, 1992.

[10] M. Mallick, T. Kirubarajan, and S. Arulampalam, “Out-of-Sequence Measurement Algorithm using the Particle Filter with Application to Ground Moving

142