Comments on" Joint target tracking and classification using radar and ...

Download PDF
1 downloads 0 Views 268KB Size Report
Comment
The joint target tracking and classification. (JTC) filter proposed in [1] intended to improve maneuver tracking performance and classification performance ...
[34]

[35]

Himed, B., and Melvin, W. L. (1998) Analyzing space-time adaptive processors using measured data. In Proceedings of the Thirty-First Asilomar Conference on Signals, Systems & Computers, 1998, 930–935. Richmond, C. D. (2000) Performance of a class of adaptive detection algorithms in nonhomogeneous environments. IEEE Transactions on Signal Processing, 48, 5 (May 2000), 1248–1262.

and IMM filter. Because the target class is uncertain, maneuvering input sets for all possible target classes are used in the JTC filter. However, the maneuvering input set for IMM filter should be the union of all maneuvering input sets for all possible target classes. As for the simulation experiments in [1], there are two target classes, so the maneuvering input sets for JTC filter are S 1 = I0, +g, ƒgJ

Comments on “Joint Target Tracking and Classification Using Radar and ESM Sensors” (Digest)

Joint target tracking and classification (JTC) filter was presented in the abovementioned paper. A comment is made here to point out that JTC filter has no advantage over interacting multiple model (IMM) filter from a theoretical viewpoint.

The joint target tracking and classification (JTC) filter proposed in [1] intended to improve maneuver tracking performance and classification performance simultaneously by calculating the joint target state-class probability density function (pdf) recursively. However, their simulation experiments did not produce results as they had expected. The authors of [1] pointed out that it is due to inaccuracies in the numerical integration of the pdfs. Our research reveals that the inherent philosophy of [1, Theorem IV.1 (JTC Filter)] itself is imperfect. From a theoretical viewpoint, JTC filter will not have advantage over interacting multiple model (IMM) filter. We also find that there is one step of irrational approximation in the proof of [1, Theorem IV.1 (JTC Filter)]. The philosophy of JTC filter is illustrated in [1, Fig. 3], but it is our opinion that this figure has not correctly revealed the inherent philosophy of JTC filter. We believe that we could not have an insight into the inherent philosophy of [1, Theorem IV.1 (JTC Filter)] without comparing it with IMM filter. We also believe that it is important to make clear the maneuvering input sets for JTC filter and IMM filter, respectively, for it can help us to understand the relationship and difference between JTC filter

S 2 = I0, +5g, ƒ5gJ: But the maneuvering input set for IMM filter should be S = S 1 > S 2 = I0, +g, ƒg, +5g, ƒ5gJ: Therefore if we plan to compare the performance of JTC filter with that of IMM filter, be sure that JTC filter is using maneuvering input sets S 1 and S 2 , and IMM filter is using maneuvering input set S. Unfortunately, it had not been mentioned that the simulation results of position and velocity estimates of IMM filter given in [1, Fig. 4] were based on which maneuvering input set. However, it is obviously not the maneuvering input set S. It seems that maneuvering input set S 2 had been used in IMM filter. If it is true, then the simulation comparison has lost its significance. Let us also have a look at the process of calculating target state estimate and classification probability after we figure out p(xk , c = i M Yk ), which is helpful for us to find out the inherent philosophy of JTC filter, and the relationship and difference between JTC filter and IMM filter. The calculating process is as follows. Step 1 = p(xk , c = i M Y k )dxk p(c = i M Yk ) = ¥i

Step 2 p(xk M c = i, Yk ) = Step 3 xˆ ki =

= ¥i

IEEE Log No. T-AES/40/2/831403. Refereeing of this contribution was handled by X. R. Li.

c 2004 IEEE 0018-9251/04/$17.00 ’ CORRESPONDENCE

xk p(xk M c = i, Yk )dxk

Step 4 xˆ k =

Manuscript received May 12, 2003; released for publication December 15, 2003.

p(xk , c = i M Y k ) p(c = i M Y k )

s ; i=1

p(c = i M Yk )xˆ ki :

(1)

From the above calculating process (1) we know that, in order to obtain the final state estimate xˆ k , JTC filter first calculates the class-conditioned state estimate xˆ ki . Then xˆ ki is weighted by target classification probability p(c = i M Y k ). Finally 765

Fig. 1. Framework of JTC. (Take simulation example in [1] for example.)

the weighted class-conditioned state estimates p(c = i M Yk )xˆ ki are summed to arrive at xˆ k . [1, Theorem IV.1 (JTC Filter)] together with the above calculating process (1) forms an entire JTC filter. Our research shows that the inherent philosophy of JTC filter could be illustrated as Fig. 1. (Let us take the simulation example in [1] for example.) As we can see from Fig. 1 that mode competition relationship between different target classes, like mode competition relationship between mode +5g and +g, is broken in JTC filter. However in IMM filter, all the maneuvering input sets of different target classes are combined into a whole maneuvering input set S = I0, +g, ƒg, +5g, ƒ5gJ, which make possible mode competition between different target classes. For example, if maneuvering acceleration of the target is +5g, then the class 2-conditioned state estimate xˆ k2 (using maneuvering input set S 2 ) of JTC filter will be more accurate than that of IMM filter (using maneuvering input set S), and the class 1-conditioned state estimate xˆ k1 (using maneuvering input set S 1 ) of JTC filter will be less accurate than that of IMM filter (using maneuvering input set S). Nevertheless, we could3not conclude whether the final state estimate xˆ k = si=1 p(c = i M Yk )xˆ ki of JTC filter is more accurate than that of IMM filter. It is often the case that IMM filter can arrive at the same accurate state estimate, if not more accurate, only by mode competition, without taking advantage of the target class information. It is our opinion that [1, Theorem IV.1 (JTC Filter)] is not a workable framework on which the JTC filter could be founded. We also note that there is an approximation from step 2 to step 3 in the deduce of [1, (26)], that is p(Mji (k ƒ 1) M xkƒ1 , c = i, Ykƒ1 ) = p(Mji (k ƒ 1) M c = i, Ykƒ1 ):

(2) We believe that Mji (k ƒ 1) and xkƒ1 are not independent. We know that Mji (k ƒ 1) is dependent on Ykƒ1 , and Mji (k ƒ 1) is dependent on xkƒ1 as well. 766

MEI WEI SHAN GAN-LIN WANG HONG-FENG Dept. of Electronic Engineering Shijiazhuang Mechanical Engineering College No. 97, Hepingxilu Road, Shijiazhuang PR China, 050003 E-mail: ([email protected]) REFERENCES [1]

Challa, S., and Pulford, G. W. (2001) Joint target tracking and classification using radar and ESM sensors. IEEE Transactions on Aerospace and Electronic Systems, 37, 3 (July, 2001), 1039–1055.

Authors’ Reply The following claims have been made in regard to the original paper [1]: 1) The simulation results are not “as expected.” 2) The model set should be the union of all the models across all classes. 3) There is an (erroneous) approximation in the proof of [1, (26)]. 4) The inherent philosophy of joint tracking and classification (JTC) is flawed. 5) JTC does not have any advantages over the interacting multiple model (IMM) approach. We preface our response to each of these claims with a number of facts about the IMM algorithm. 1) While often effective for the manoeuvring target tracking problem, the IMM is not an optimal filter—it is an approximation. 2) The IMM algorithm is not formulated for classification, but rather for state estimation. 3) Unlike JTC, the IMM framework does not feed back any classification information to alter the estimation of target state. This last point is also apparent in Fig. 1 of the Comments. 1) Simulation results are not as expected: Barring the response time in detecting the mode switches, our results are in line with what the joint

IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 40, NO. 2 APRIL 2004

Fig. 1. Framework of JTC. (Take simulation example in [1] for example.)

the weighted class-conditioned state estimates p(c = i M Yk )xˆ ki are summed to arrive at xˆ k . [1, Theorem IV.1 (JTC Filter)] together with the above calculating process (1) forms an entire JTC filter. Our research shows that the inherent philosophy of JTC filter could be illustrated as Fig. 1. (Let us take the simulation example in [1] for example.) As we can see from Fig. 1 that mode competition relationship between different target classes, like mode competition relationship between mode +5g and +g, is broken in JTC filter. However in IMM filter, all the maneuvering input sets of different target classes are combined into a whole maneuvering input set S = I0, +g, ƒg, +5g, ƒ5gJ, which make possible mode competition between different target classes. For example, if maneuvering acceleration of the target is +5g, then the class 2-conditioned state estimate xˆ k2 (using maneuvering input set S 2 ) of JTC filter will be more accurate than that of IMM filter (using maneuvering input set S), and the class 1-conditioned state estimate xˆ k1 (using maneuvering input set S 1 ) of JTC filter will be less accurate than that of IMM filter (using maneuvering input set S). Nevertheless, we could3not conclude whether the final state estimate xˆ k = si=1 p(c = i M Yk )xˆ ki of JTC filter is more accurate than that of IMM filter. It is often the case that IMM filter can arrive at the same accurate state estimate, if not more accurate, only by mode competition, without taking advantage of the target class information. It is our opinion that [1, Theorem IV.1 (JTC Filter)] is not a workable framework on which the JTC filter could be founded. We also note that there is an approximation from step 2 to step 3 in the deduce of [1, (26)], that is p(Mji (k ƒ 1) M xkƒ1 , c = i, Ykƒ1 ) = p(Mji (k ƒ 1) M c = i, Ykƒ1 ):

(2) We believe that Mji (k ƒ 1) and xkƒ1 are not independent. We know that Mji (k ƒ 1) is dependent on Ykƒ1 , and Mji (k ƒ 1) is dependent on xkƒ1 as well. 766

MEI WEI SHAN GAN-LIN WANG HONG-FENG Dept. of Electronic Engineering Shijiazhuang Mechanical Engineering College No. 97, Hepingxilu Road, Shijiazhuang PR China, 050003 E-mail: ([email protected]) REFERENCES [1]

Challa, S., and Pulford, G. W. (2001) Joint target tracking and classification using radar and ESM sensors. IEEE Transactions on Aerospace and Electronic Systems, 37, 3 (July, 2001), 1039–1055.

Authors’ Reply The following claims have been made in regard to the original paper [1]: 1) The simulation results are not “as expected.” 2) The model set should be the union of all the models across all classes. 3) There is an (erroneous) approximation in the proof of [1, (26)]. 4) The inherent philosophy of joint tracking and classification (JTC) is flawed. 5) JTC does not have any advantages over the interacting multiple model (IMM) approach. We preface our response to each of these claims with a number of facts about the IMM algorithm. 1) While often effective for the manoeuvring target tracking problem, the IMM is not an optimal filter—it is an approximation. 2) The IMM algorithm is not formulated for classification, but rather for state estimation. 3) Unlike JTC, the IMM framework does not feed back any classification information to alter the estimation of target state. This last point is also apparent in Fig. 1 of the Comments. 1) Simulation results are not as expected: Barring the response time in detecting the mode switches, our results are in line with what the joint

IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 40, NO. 2 APRIL 2004

formalism predicts. We discussed at length in [1] our interpretation of the simulation results between the three approaches of direct identity fusion (DIF), JTC, and IMM. In particular we pointed out that, due to the nonlinear/non-Gaussian nature of the filtering equations, the quality of numerical approximation is a key factor in the implementation of a JTC filter. The effects on performance of the relatively coarse grid used in the simulations in [1] are not easy to quantify but are thought to be significant. We suggested alternative implementation approaches in the concluding remarks. A number of authors have already taken up the proposed basic formalism as a starting point for particle filter realisations of the JTC [2, 3]. 2) The model set should be the union of all the models across all classes: In our formulation of JTC we considered a problem where the total number of classes was known and the model set for each class was also assumed to be known. By definition, and in line with physical considerations, the model set assumed by one class is different from the model set assumed by a different class (although some models may be common to several classes). We also assumed that the target under consideration belonged to one and only one of the classes. Under this assumption it would be illogical to use all the union of model sets (of all the classes) to track a single target that belongs to only one class. Recent research on variable structure IMM algorithms [4] suggests that it is detrimental to use either more or fewer than the true number of models for optimal tracking performance. This goes against the idea of using the union of all model sets when there is uncertainty about the number of classes. 3) Made an approximation in the proof of (26): In (2) of the Comments a dependence between Mji (k ƒ 1) and xkƒ1 is elicited. In our system definitions [1, (1) and (2)], of [1]), the manoeuvre input at time k ƒ 1 for model j and class i, ukƒ1 = Mji (k ƒ 1), influences the state xk at time k and not xkƒ1 , and manoeuvres satisfy a class-dependent but state-independent Markov chain ¡ (i). In other words xkƒ1 has no bearing on the realisation of the particular manoeuvre input ukƒ1 . Thus, given the target class and past measurements, the model set Mji (k ƒ 1) is conditionally independent of xkƒ1 . While it may be useful to define a classand state-dependent Markov process, this level of complexity seems unnecessary for the JTC approach. 4) Inherent philosophy of JTC is flawed: An oversight in the Comments relates to step 3 of the JTC calculations where the following assumption appears to have been made: = = i k xˆ k = xk p(xk M c = i, Y )dxk = xk p(xk M c = i, Y k )dxk : ¥i

The integral is over the flight envelope for class i, which is clearly influenced by the class-conditioned CORRESPONDENCE

manoeuvre model set. Thus the decomposition shown in Fig. 1 is not valid as the manoeuvre model set influences the state estimates, which then determine the amount of overlap of the joint probability density p(xk , c = i M Y k ) with the flight envelopes, influencing in turn the target classification probability. Conversely the target class probability influences the significance of the model sets, which impacts on the state estimates. These effects require a joint state-class probability density, and cannot be arbitrarily separated. Both the state estimates and class probabilities are obtained using marginalization of this joint pdf. The observation made in the Comments that “mode competition is broken” is seen to be false. Fig. 1, which resembles the feed-forward DIF approach (when the ESM classifier is removed), reflects a lack of appreciation of the role of flight envelopes in the JTC filter (or some equivalent class-to-state coupling). 5) JTC does not have any advantages over IMM: In proposing what is essentially a feed-forward structure based on standard IMM algorithms, the authors of the Comments have failed to recognize the fundamental differences between JTC and IMM filters. We have tried to make it clear that the JTC formalism has a sound basis. The paper [1] necessarily deals with the issues of developing a coherent framework for the JTC problem and the theory governing the JTC filter, rather than focusing on numerical implementation issues. It is seen that the claim that “the JTC filter will not have advantages over IMM filter” is flawed as the two filters serve different purposes. While the IMM filter is an approximation to a multiple-model branching filter for target tracking with a known model set, the JTC filter is at the outset an optimal filter that treats tracking and classification in a joint probabilistic context. In particular the IMM does not provide information on target class unless it is cascaded with an ad hoc manoeuvre-based classifier. Moreover, it is widely acknowledged that the choice of the model set has a large bearing on the tracking performance of the IMM [4, 5]. The literature on variable structure IMM methods is an indication of the importance of this problem [4, 6]. In JTC, model sets that are more consistent with the target dynamics should receive more weight, leading to better overall estimation. Effort should be directed at determining practical suboptimal implementations of JTC filters that retain the bidirectional class-state coupling. REFERENCES [1]

Challa, S., and Pulford, G. W. (2001) Joint target tracking and classification using radar and ESM sensors. IEEE Transactions on Aerospace and Electronic Systems, 37, 3 (July 2001), 1039–1055. 767

[2]

[3]

[4]

[5]

768

Gordon, N., Maskell, S., and Kirubarajan, T. (2002) Efficient particle filters for joint tracking and classification. Proceedings of SPIE Signal and Data Processing of Small Targets, 4728 (2002), 439–449. Herman, S. (2002) A particle filtering approach to joint passive radar tracking and target classification. Doctoral dissertation, Dept. of Electrical and Computer Engineering, University of Illinois at Urbana Champaign, 2002. Li, X. R. (1999) Engineers’ guide to variable-structure multiple-model estimation. In Y. Bar-Shalom and W. D. Blair (Eds.), Multitarget-Multisensor Tracking: Advances and Applications, Vol. 3, Dedham, MA: Artech House, 1999. Pulford, G. W., and La Scala, B. F. (2002) MAP estimation of target manoeuvre sequence with the expectation-maximisation algorithm. IEEE Transactions on Aerospace and Electronic Systems, 38, 2 (Apr. 2002), 367–377.

[6]

Wang, X., Challa, S., Evans, R., and Li, X. R. (2003) Minimum sub-model set switching algorithm for multi-model estimation. IEEE Transactions on Aerospace and Electronic Systems, 39, 4 (Oct. 2003). SUBHASH CHALLA Computer Systems Engineering Faculty of Engineering The University of Technology Sydney NSW Australia E-mail: ([email protected]) GRAHAM W. PULFORD Thompson Marconi Source Sydney NSW Australia E-mail: ([email protected])

IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 40, NO. 2

APRIL 2004