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JestrJOURNAL OFJournal of Engineering Science and Technology Review 12 (1) (2019) 50- 65Engineering Science andTechnology ReviewReview Articlewww.jestr.orgBearing only Target Tracking using Single and Multisensor: A ReviewB. Sindhu1, J. Valarmathi1,* and S. Christopher21School of Electronics Engineering, Vellore Institute of Technology, Vellore, Tamil Nadu, India.2DRDO, Delhi, IndiaReceived 6 April 2018; Accepted 17 February 2019AbstractThe brief review of methods used for estimating the target state in single and multi-sensor bearing only tracking (BOT) ispresented in this paper. It deals with the target state estimation using bearing only measurements. BOT is difficultbecause of its poor observability in target state and nonlinearity in measurements. The complete survey is done onexisting techniques, involved to overcome the difficulties caused by BOT. Here, the target tracking scenarios are dividedinto three different categories based on the nature of target motion and the number of target and sensors involved. Theexisting techniques involved are reviewed in detail. Finally the future trends for BOT are also discussed.Keywords: Bearing only tracking, maneuvering target, nonlinear filters, multisensor-multitarget tracking.1. IntroductionBOT has been an active research area for several years dueto the challenges involved in it [2,4]. It is the widely usedmethod in many applications like radar, sonar basednavigation, underwater, space surveillance, ballistictrajectory estimation, submarine tracking using passivesonar, infrared (IR) sensors, wireless sensor networks andmissile guidance [3,50,65,15,29,41]. BOT involvesestimating the target state from noisy bearing measurements[83,87,10,105].The issue of poor observability caused due to BOT wasreduced by taking an appropriate ownship maneuver and itsdynamics should be higher degree than that of the target’sdynamics to gain the observability of target state[68,30,31,19]. The necessary conditions for observability oftarget state were derived and discussed in [21, 51, 85, 68,30]. Using the bearing measurements there exist manytechniques to estimate the target state [45,53]. If themeasurements are linear, then basic Kalman filter issufficient to estimate the target state [1,23]. If it is nonlinear,then special care has to be taken to linearize the nonlinearmeasurements. Thus for nonlinear measurements, differenttypes of algorithms are available in the literature and arebroadly classified into two types namely: batch processingand recursive Bayesian processing [28, 77]. In batchprocessing technique, set of measurements are consideredfor state estimation. On the other hand in recursive Bayesianmethod, each measurement is processed at a timerecursively. Later one is suitable for most of real timesystems due to its fast convergence [3, 45]. But choosingdifferent algorithms not only depends on the target motionbut also based on the scenarios. Thus in this paper we haveconsidered three category to review the techniques. First twocategories are based on the target motion (constant velocity*E-mail address: jvalarmathi@vit.ac.inISSN: 1791-2377 2019 Eastern Macedonia and Thrace Institute of Technology. All rights reserved.doi:10.25103/jestr.121.07or constant acceleration) when there exist the single targetand single ownship and third category is the extension offirst two category when there exist multiple target andmultiple ownship in the scenario.Category 1: Constant velocity target with maneuveringownshipIn this category, both batch processing and recursiveBayesian approach can be used for the state estimation.Some of batch processing algorithms include maximumlikelihood (ML) estimator, pseudo-linear (PL) estimator,batch-recursive estimator, batch maximum a posteriori(MAP) estimator [45, 37, 52]. Since recursive Bayesianapproach is best suited for real time scenario, most of thetime, this approach is preferred than batch processing. Themost widely used recursive Bayesian filter for nonlinearmeasurements is an Extended Kalman filter formulated inCartesian coordinates (EKF-Cart) [4,23]. The limitations inEKF-Cart leads to the formulation of modified sphericalcoordinates (EKF- MSC) [86] and log spherical coordinate(EKF- LSC) [2]. Other types of Kalman filters like Modifiedgain Extended Kalman filter (MGEKF) [6] and UnscentedKalman filter (UKF) can also be used for the nonlinearmeasurements. Other than this, some of the researchersrecommended Particle filter (PF), Particle flow filter (PFF),pseudo linear Kalman filter (PLKF), and any of thenonlinear filters with multiple model approach (MM)[80,26]. The review of all these methods, their advantagesand disadvantages are discussed briefly in section 2.Category 2: Constant acceleration target withmaneuvering ownshipThis category deals with the techniques involved inestimating the state of maneuvering target. Since batchprocessing cannot manage the target maneuvers, it is rarelyrecommended [7,45]. Hence, the most widely usedtechnique is Interactive Multiple Model (IMM) along withnonlinear filters [65, 45]. It works by switching betweenmultiple dynamic models according to the target maneuver
B. Sindhu, J. Valarmathi and S. Christopher/Journal of Engineering Science and Technology Review 12 (1) (2019) 50 - 65[78, 71]. Depending upon the situation any one of thenonlinear filters mentioned in category 1 may be used alongwith IMM [78,65,71]. More detailed explanation of thetechniques involved are reviewed briefly in section 3.proposed that can integrate the received information fromdifferent sensors to identify the number of targets and itslocation in the surveillance region [88, 81]. The recursivealgorithms include Multiframe assignment algorithm(MFA), Multi-target Multi-scan algorithm and Multiplehypotheses tracking (MHT) algorithm [81,64,32]. Each ofthese methods uses nonlinear filters mentioned in category 1to estimate the target state. The more detailed explanationsare given in section 4.In forthcoming sections this paper presents the completesurvey on evolution of different algorithms applied toestimate the target state in BOT for the above mentionedthree categories.The outline of the paper is as follows. Section 2describes the brief review of the techniques involved incategory 1. Section 3 concentrates the evolution of thetechniques involved in state estimation for category 2.Similarly, section 4 reviews the techniques involved incategory 3. Finally section 5, gives the conclusion and futurework.Category 3: Multiple moving targets with multipleownships (maneuvering/non-maneuvering target)This category review the techniques involved in multiplemoving targets with multiple sensors (ownship) irrespectiveof the target motion. Since multiple sensors are involved,observability is not a major issue [88, 99]. But tracking aparticular target in a multiple moving target scenario makesthe process complicated. Because, target detection by eachsensor will be independent and the measurements areobserved at random times, ambiguity may occur whether theobserved data may originate from the target being tracked orfrom the clutter or any new target [64, 35]. This will lead tothe problem of measurement origin uncertainty [81]. Toresolve these issues, batch processing algorithms likeMaximum likelihood (ML) estimator and ML probabilisticdata association (ML-PDA) are used. Since the batchprocessing techniques may not be applicable for scenariosinvolving three or more targets, the recursive algorithms are2. Review of techniques for category 1Fig.1. Techniques involved for constant velocity target. MLEMIVPLEPLLSMAPEKFUKFPFSRFCKF- Maximum Likelihood estimate- Modified-instrumental variable- Pseudo-linear estimate- Pseudo linear least square- Maximum a posteriori- Extended Kalman filter- Unscented Kalman filter- Particle filter- Shifted Rayleigh filter- Cubature Kalman filter(a)51
B. Sindhu, J. Valarmathi and S. Christopher/Journal of Engineering Science and Technology Review 12 (1) (2019) 50 - 65different techniques used for target state estimation in airspace application and satellite application.2.1. Air space applications:BOT is widely used in air space applications for trackingaircrafts, ballistic trajectory tracking and satellite tracking.The techniques used in literature are explained briefly in theupcoming subsections.Target state estimationThe observability requirements for BOT in air space arederived and explained briefly in [75, 30, 21, 85]. Sameanalysis for linear discrete time BOT is explained in [56]. Itis a direct approach and uses simple linear algebraicformulation for observability analysis of a moving target.The possible ownship maneuvering patterns are shown inFig. 2 and the necessary conditions for ownship maneuverwas derived in [30,56,68,85]. Using this condition anoptimal ownship maneuver is framed in [31,33] and theyalso proved the enhancement in system observability andaccuracy through results [54]. Since, BOT is a nonlinearproblem, linear analysis is not suitable for practicalscenarios. There are various types of batch and recursivealgorithms proposed to solve the single target BOT problem[52,3]. Next subsection briefs the literature survey of batchprocessing techniques used in BOT following which thereview of recursive algorithms for the same.(b)2.1.1. Batch processing techniquesThis type of algorithm processes the batch of measurementsfor a particular time period to estimate the target state [28].Nardone et al. [69] have used three technique namelymaximum likelihood estimate (MLE), modified-instrumentalvariable (MIV) and pseudo-linear estimate (PLE) for 2DBOT. The performances of three algorithms are tested forlarge range-to-baseline scenario. For this scenario, CramerRao bound is derived analytically. The simulation resultsindicate, for lower effective noise all three algorithms showssimilar results and for higher effective noise, PLE showsdegraded performance compared to MLE and MIV. In [70],Nardone has proposed the closed form pseudo linearsolution to overcome the observability issue caused due tosingle sensor tracking. It was developed based on theobservable parameters which includes bearing, bearing rateand range rate divided by range. Using the observableparameters, normalized polar coordinate state was derivedand the results are generated using bearing onlymeasurements. Although this method produces good resultsfor high observability conditions, in case of poorobservability the estimates are biased. Later, Kumar et al.[28] also used the modified instrumental variable (MIV)estimate by taking care of missing bearing measurementseither randomly or continuously. Performance of the methodwas evaluated through error bounds. Analogous to [69],Zhang et al. [97] have derived and evaluated theinstrumental variable (IV) algorithm based on the covariancematrix. Similar to [69,70,97], Dogancay [18] has proposedweighted instrumental variable (WIV) and compared theperformance with MLE, MIV, PLE. He stated that MLE hasthe disadvantage that, it does not converge to a closed formsolution. He also stated that MLE has to be implementediteratively with the initialization close to the true solution.PLE converges with larger estimation bias. He also addedthat MIV converges with high computational time. Out ofthe four techniques used, he proved that the proposed WIVestimator has the closed form solution for the smaller(c)(d)Fig.2. Maneuvering patterns of ownship to track single target when it ismoving at constant velocity (Courtesy [2], [21], [56], [31]).Fig. 1 shows the block diagram of various techniquesused for category 1. Fig. 2 illustrates the different ownshipmaneuvering patterns to gain the observability of the targetmoving with constant velocity. For this category if theownship does not move and change its velocity to take amaneuver, there will not be a relative velocity between thetarget and ownship. The relative motion between the targetand ownship at each time will just be a linear trajectory withthe fixed angle of arrival [106]. Hence the system will beunobservable, the relative position and velocity of target willnot be determined. Thus the ownship takes differentmaneuver to gain observability in range and target state[62,24,58] as shown in Fig.2. Following sections briefs the52
B. Sindhu, J. Valarmathi and S. Christopher/Journal of Engineering Science and Technology Review 12 (1) (2019) 50 - 65bearing noise variance with less computational time and lessbias. This method will also diverge with high bearing noisevariance [70,52]. Analogous to [18,69,70], Wang et al. [90]have described the pseudo linear least square (PLLS) batchprocessing method. This method requires no targetinitialization. The equations for the target state estimationusing batch of measurements are derived using standardlinear least square method. They proved that, PLLSeffectively minimizes the squared norm of the error vector.Huang et al. [37], proposed a bank of batch maximum aposteriori (MAP) estimates to reduce the linearization errorscaused due to nonlinear filters and for handling the multihypothesis tracking. The MAP uses the availablemeasurements in each step to compute the state estimate [9,11]. Each MAP estimator in the bank is initialized by eachmode. All the modes are computed analytically byconverting the nonlinear cost function into the polynomialform. Thus high probable hypothesis are tracked and therebyincreasing the accuracy of the estimation process. Eventhough MAP batch processing increases the estimateaccuracy, these techniques are not preferred due to the largermemory requirement with more computational time forsimple scenarios.compared the performance of the particle filter (PF) withEKF-MPC and RPEKF. The authors stated that, PF showsbetter performance compared to EKF-MPC. Although theRPEKF performance is nearly equivalent to PF it exhibitslarger error initially due to lack of initial target range. Theother method which is similar to EKF-MPC is the log polarcoordinate (EKF-LPC) and was used by B.L. Scala et. al[83] for BOT. The authors have compared three differenttracking algorithms namely EKF-LPC, RPEKF-LPC andGaussian sum measurement approximation filter. Theperformance was analyzed using root mean square (RMS)position error, root-time averaged mean square (RTAMS)and number of divergent tracks. The simulation resultsindicate that, all three filters has similar performance.Another form of EKF is the progressive correction (PC)technique (PC-EKF) and was implemented by Wang et al[90]. They compared the performance of PC-EKF with EKF,RPEKF in MPC (RPEKF-MPC) and PLLS. They showedthat, PLLS has better performance than PC-EKF for smallerinitial ranges of the target. However at 100km EKF, PCEKF and PLLS gives biased estimates of the target. Overallthe authors stated that, RPEKF-MPC shows better resultscompared to other filters irrespective of ranges.Later, Franken in [20] have explained about the filterinitialization of EKF using log spherical coordinates (LSC)and regression based batch estimator. LSC considers bothazimuth and elevation measurements and is the 3D versionof LPC used in [83]. Filter initialization using LSC is theone-point initialization technique which consider onemeasurement pair. Whereas, batch estimator is the multiplepoint initialization technique which consider multiplemeasurement pairs. The other three estimators considered inthis paper are, EKF-Cart initialized with 1. Converted prior2. Quadratic regression estimator and 3. General non-linearleast squares. To validate these techniques, authors haveconsidered two scenarios for target tracking, one is on thepassing course and the other is course close to collision.Among all algorithms, EKF-LSC and batch estimatorperforms better for two scenarios considered. The algorithmwhich is similar to LSC is modified spherical coordinate(MSC) which is the 3D version of MPC. Mallick et al. [60]have used MSC and LSC for angle only tracking (AOT) in3D.Authors have presented the new derivation forcontinuous to discrete EKF-MSC and EKF-LSC filteringalgorithms. The derivation for MSC and LSC are presentedusing first order nonlinear stochastic differential equationsand has shown its equivalence with the nearly constantvelocity model (NCVM) in Cartesian coordinates. Inaddition, the authors have presented the new derivation forthe predicted covariance which follows the Brownian motionprocess and it is integrated numerically and jointly to thepredicted state estimate to provide better numericalaccuracy. Simulations were performed for three differentbearing and elevation measurement error standard deviations(0.001, 0.005 and 0.015 radian) and performance of EKFMSC and EKF-LSC were compared with EKF-Cart. Fromthe results the authors stated that, for high measurementaccuracy (0.001 radian) EKF-Cart performs better whereasfor medium and low accuracy (0.005 and 0.015 radian)EKF-MSC and EKF-LSC performs better.The other alternative filtering technique to EKF is theMGEKF. It was initially proposed and derived by [84] andlater the derivation of modified gain function was madesimple by [22]. Huang et al. [38] has presented the iteratedMGEKF, which combines the MGEKF and iterationmethod. In IMGEKF the new updated state and its2.1.2. Recursive nonlinear techniques:These techniques outperform the batch processingalgorithms and produces closed form and unbiased estimates[39]. The common recursive filter used is Kalman filter (KF)for the linear problems. Since BOT is the nonlinear problem,it cannot be used here. The most widely used recursivenonlinear filter is EKF in Cartesian coordinates. Theliteratures indicate that EKF in Cartesian coordinates mayexhibit large error in the target state estimate due to lack ofinitial range information [69,45]. There are variousmodifications proposed in EKF to overcome this. Other thanthis new type of Kalman filter namely UKF, CKF are alsoproposed in the place of EKF. Apart from Kalman filterextensions, SRF and PF are also proposed to estimate thetarget state in BOT. Following subsection gives the briefreview on the proposed extended methods for target stateestimation in BOT using the above mentioned nonlinearfilters.A. EKF and its extensionIt is a sub-optimal filter and linearizes the nonlinearmeasurement model using Taylor series approximation.Aidala et al. [2] have used EKF in modified polarcoordinates (EKF-MPC) and the results are compared withEKF-Cart and pseudolinear filter.The authors haveassumed the scenario of constant velocity with an arbitrarymotion. They showed that, EKF-Cart fails to estimate thetarget state for long and short range scenario. Similarly,pseudolinear filter produces biased estimates for long rangescenario, whereas the EKF-MPC filter shows betterperformance in all scenarios but they didn’t give the analysisfor nearly zero or very high bearing rate scenarios. The otherrobust method used to overcome the drawbacks of abovementioned EKF is Range parameterized–EKF (RPEKF)which was proposed by Peach [74]. This was implementedby dividing the large range uncertainty region into subintervals and the set of weighted EKF is used each withdifferent initial range estimate to obtain the best rangeestimate [80,42,96]. The author has compared theperformance of RPEKF with EKF-MPC, EKF-Cart andproved that, RPEKF performs better for nearly zero or veryhigh bearing rate scenarios. Branko et. al. [3], have53
B. Sindhu, J. Valarmathi and S. Christopher/Journal of Engineering Science and Technology Review 12 (1) (2019) 50 - 65corresponding covariance are obtained by re-linearizing themeasurement function. The other nonlinear filters used areEKF, IEKF, MGEKF. The performances of all the filters arecompared with CRLB. The authors stated that IMGEKF hasbetter performance than other filters. However, since thismethod depends on the updated state for iteration, thedisadvantage occurs when the system is unobservable duringthe initial period of trackingmeasurement [5]. Sanjeev et.al [5] have used SRF forMaximum bearing rate (MBR) scenarios. The authors haveinvestigated the performance of SRF with EKF, UKF and PFfor the above mentioned scenario. SRF uses the directionalcosines of bearing measurement and augmented to obtain theexact conditional mean and covariance. From the simulationresults, it is stated that EKF and UKF shows divergent tracksfor low MBR whereas SRF and PF does not shows divergenttracks even with increased MBR. Hence SRF achievesperformance similar to PF. Ozelci et al. [15] have used SRFfor target tracking from noisy measurements in the presenceof clutter, and was named as SRF for 3D bearingmeasurement with clutter (SRF3C). The authors havecompared performance of proposed SRF3C with EKF,RPEKF, UKF and Particle filter with local EKF linearization(EKPF), considering high bearing rate scenario. Thesimulation results indicate EKF, UKF and RPEKF performpoor whereas EKPF has the comparable performance to thatof SRF3C but has higher computational time nearly 4 ordersof magnitude compared to SRF3C. Hence it is stated that,the proposed SRF3C performs better in case of poor targetinitialization, high probability of clutter and high bearingrate scenarios.B. UKF and its extension:The other techniques used for constant velocity target stateestimation are Sigma point Kalman filter (SPKF) otherwiseknown as UKF for BOT. It uses the sigma point to linearizethe nonlinear dynamic or measurement model, this filterovercomes the divergence problem in EKF [40,59]. Sadhu etal. [82] have made comparison between SPKF, EKF andIEKF. The authors deal with implementation of nonlinearfilters for severe nonlinear system with uncertainty in initialconditions. The track lose criterion was taken into accountfor performance comparison. Simulation results indicate,superiority of SPKF compared to EKF and IEKF. Thefrequency of track loss in SPKF is 0.014% whereas for EKFit is 0.28%. The track loss for SPKF can be reduced bychanging the . The term refers to the spread of sigmapoints. The minimum failure occurs at 0.6. Therefore theauthors recommend using SPKF for BOT with acceptableincrease in computational time. Analogous to [5,15], Strakaet al. [87] has introduced UKF with adaptive scalingparameter. The adaptation was done by means of Maximumlikelihood (UKFML) or Maximum posterior probability(UKFMPP) and has compared with EKF, UKF and SRF forthe constant velocity target. The authors have consideredthree scenarios with different ownship motion patterns. Inscenario 1 the ownship follows the straight line motion. Theownship is assumed to take a maneuver in scenario 2. Inscenario 3 the ownship follows unit circle centered at origin.From simulation results the authors stated that only inscenario 1, SRF performance was slightly better than UKF’swhereas in other scenarios UKF with adaptive scalingparameter performance was good compared to others. Morespecifically UKFMPP achieves better performance.E. Particle filter and its extension:It is the recursive Monte Carlo method which represents theposterior density of target [62,66]. Gordon et al. [25] havedescribed the sampling based method and auxiliary PF forBOT problem. The performances were compared with EKF.From results, the best performance is achieved by auxiliaryPF whereas EKF estimate diverges. Later, Karlsson et al.[41] have used PF in MSC and Cartesian. The comparisonwas made between RPEKF and PF in Cartesian and MSC.The results indicate the good performance of PF in bothMSC and Cartesian with more computational time thanRPEKF. Mallick et al. [61] have used UKF and PF in MSC.This work is an improved version of his work in [60]reviewed in subsection (2.1.2.A). In this paper an improvedfilter initialization algorithm was discussed. The authorshave used EKF, UKF and Bootstrap particle filter (BPF) inCartesian and MSC. The simulation results indicate for highmeasurement accuracy, EKF and UKF in MSC performsmarginally better than EKF and UKF in Cartesian. For lowmeasurement accuracy best performance was achieved byEKF-MSC and UKF-MSC compared to others. WhereasBPF shows severe computational complexity than others andperformance was not better than EKF-MSC and UKF-MSC.The authors stated that, the poor performance of BPF can beincreased by adding particles but this will further increasecomputational time. Similar to [60,61], Gupta et al. [29]considered PFF along with deterministic Ensemble Kalmanfilter (DEnKF) and stochastic Ensemble Kalman filter(sEnKF) in Cartesian and MSC and compared the resultswith EKF, UKF, BPF in Cartesian and MSC. In the case oflow measurement accuracy, the simulation results indicatesbetter performance for PFF in Cartesian and MSC whereassimilar performance was achieved by EKF, UKF andDEnKF only in MSC and not in Cartesian. Also PFFperforms better with less number of particles compared toparticles used in BPF.Ristic et. al [79] have discussed the improved andmodified form of PF called Bernoulli PF and is used forownship motion control under the consideration of falsealarm and missed detection. Problem is to identify theappearance and disappearance of target during ownshipmotion. To solve this problem, Bernoulli filter was used.C. Cubature Kalman filter (CKF):The method of approximating the posterior distribution ateach time step with a Gaussian distribution is known asCKF. Cubature is the approximation in a multi-dimensionalproblem [94]. Analogous to [67], Wu et al. [92] has usedCKF along with range parameterized (RP) method. In thispaper the sample set of points in the CKF with an orthogonaltransformation was designed and used when there is a highdegree of nonlinearity in the measurement function. Theauthors refer to these points as orthogonal simplex cubaturepoints (OSCPs). This paper also used the rangeparameterized (RP) method with different initial estimates,which deals with fuzzy initial estimation problem. The RPtracker has demerits in terms of computational complexity,due to the usage of series of sub-filters. Authors tried toreduce the computational cost by setting the threshold andremoval of unstable sub-filters. But still the authors statedthat the proposed RPOSCKF has high computationalcomplexity but performs better than other conventionalnonlinear filters used.D. Shifted Rayleigh filter (SRF) and its extension:It is a moment matching algorithm used for BOT to calculatethe exact conditional mean and covariance for the given54
B. Sindhu, J. Valarmathi and S. Christopher/Journal of Engineering Science and Technology Review 12 (1) (2019) 50 - 65Since Bernoulli filter does not form a closed-form solution itis implemented based on the particle filter with diffuse prior.Further observer motion was controlled using the output ofBernoulli PF. The simulation was done with two differentaverage number of false detections λ 0.5 and λ 5. Theresults indicate that for λ 0.5, the RMS error is very closeto theoretical bound and for λ 5 the estimation errorincreases. Overall the performance of Bernoulli PF showsbetter performance in track maintenance. Analogous to [79],Morelande [66] has developed marginalized particle filter(MPF) for 2D BOT. This paper considers the improvementof PF known as marginalization technique. This can be doneby replacing the Monte Carlo approximation with analyticalcomputation. In this paper Euler approximation is used fordynamical equation and thus only three elements of the statevector needs to be sampled. The proposed MPF in MPC(MPF-MPC) was compared with MPF in Cartesian (MPF-C)and Bootstrap filter in Cartesian (BF-C) and MPC (BFMPC). From the simulation results, MPF-MPC shows bestperformance compared to others with one 10th of sample sizebut with greater computational time.measurements. Hence smoothing process is betteroptimization than filtering [1]. The process of smoothing isapplied to BOT and is discussed by few authors. In analogyto [38], Qian et al. [73] has proposed a smoothing MGEKF(sMGEKF) based on Rauch-Tung-Stribel (RTS) smoothing.The authors stated that, RTS algorithm is a fixed intervalsmoothing and it has two steps forward filtering andbackward propagation process. The forward filteringemploys the usual filtering algorithm and backwardprocessing propagates the statistics of the filter backward intime and obtains the smoothed states. The nonlinear filtersused in this paper are, EKF, IEKF, smoothing EKF (sEKF),MGEKF and sMGEKF. From simulation results, the authorsconcluded that sMGEKF performs better during the initialperiod when the target is not observable and also reduces theestimation error. Similar to [73], Meiqin et al. [67] havecombined the RTS smoother and Cubature Kalman filter andpresented the Cubature Rauch-Tung-Striebel (CRTS)smoother. Based on this the authors has proposed the newtechnique cubature Rauch-Tung-Striebel (CRTS)-U. Thiswas performed to check the optimal ownship maneuverusing the determinant of covariance matrix and the trace ofit. CKF, CRTS and CRTS-U algorithms were compared andproved. CRTS-U has superior performance with less RMSerror.F. Kernel based filter (KBF):This method is mainly used for signal propagation timedelay. Yunfei et al [27] have used online parameterestimation (OPE) method embedded into a nonlinear filterfor tracking moving target. Along with OPE the authorshave used improved range parameterized EKF (IRP-EKF) inwhich adaptive weight adjustment is introduced. Furtherinstead of EKF, they used Kernel-based filter (KBF) andregularized particle filter (RPF) to improve the filterperformance. The proposed OPE-IRP-KBF based estimationis compared with OPE-RPEKF and OPE-regularized particlefilter (OPE-RPF). The authors stated that proposed methodruns four parallel KBF during the initial stage and removethe low-weight sub-intervals and produces better fusionresult. During the normal tracking stage it produces highestimation accuracy, compared to other methods but thecomputational time is higher. Thus the authors stated that
2 DRDO, Delhi, India Received 6 April 2018; Accepted 17 February 2019 _ Abstract The brief review of methods used for estimating the target state in single and multi-sensor bearing only tracking (BOT) is presented in this paper. It deals with the target state estimation using bea
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