PERFORMANCE ON THE EXPANDED TIME BEARING PLOT AS A FUNCTION OF BEARING ACCURACY. GaryM. Olson, LT, MSC, USN and Kevin Laxar

Transcription

1 PERFORMANCE ON THE EXPANDED TIME BEARING PLOT AS A FUNCTION OF BEARING ACCURACY by GaryM. Olsn, LT, MSC, USN and Kevin Laxar NAVAL SUBMARINE MEDICAL RESEARCH LABORATORY REPORT NUMBER 716 Bureau f Medicine and Surgery, Navy Department Research Wrk Unit MF DX5G.01 Reviewed and Apprved by: Apprved and Released by: Charles F. Gell, M.D,, D.Sc.(Med) Scientific Directr NavSubMedRschLab R. L. Sphaif, CDR MC USN Officer in Charge, Acting NavSubMedRschLab Apprved fr public release; distributin unlimited

2 SUMMARY PAGE THE PROBLEM T evaluate the effects f varius kinds and amunts f statistical nise in raw snar bearings n perfrmance in the expanded time bearing plt. FINDINGS Perfrmance fr bth human pltters and a simple mathematical curve fitting rutine was affected similarly by the characteristics f the nise, but verall perfrmance f.the mathematical rutine was superir n simple prblems while humans were better n mre cmplicated prblems and at the ends f prblems. APPLICATION This research shuld prvide empirical supprt fr the develpment f interactive systems which explit the special abilities f bth human and autmated prcedures in a cmplicated infrmatin prcessing task. ' ADMINISTRATIVE INFORMATION This investigatin was cnducted as part f Bureau f Medicine and Surgery Research Wrk Unit MF DX5G - Man as an Infrmatin Prcessr. The present reprt was apprved fr publicatin n 26 June It is Reprt N. 1 n the indicated Wrk Unit and has been designated as Naval Submarine Medical Research Labratry Reprt N PUBLISHED BY THE NAVAL SUBMARINE MEDICAL RESEARCH LABORATORY LI

3 ABSTRACT Tw experiments analyzed the effects f statistical nise in raw snar bearings n perfrmance in a labratry versin f the expanded time bearing plt«accuracy f faired bearings and bearing rate estimates were taken as the measures f perfrmance. Greater amunts f nise led t prer perfrmance, but these decrements were smaller when the nise was randm than when it was crrelated. Human perfrmance was cntrasted with that f an rthgnal plynmial curve-fitting rutine designed t d the same task. The mathematical rutine was affected by the nise in the same way as humans were. Hwever, n simple plts the mathematical rutine prvided superir slutins while n curves f mre cmplex shapes r at the ends f curves humans were superir. Thus, in certain situatins the human's perceptual and cgnitive abilities gave him a distinct advantage ver the mathematical rutine. iii

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5 PERFORMANCE ON THE EXPANDED TIME BEARING PLOT AS A FUNCTION OF BEARING ACCURACY INTRODUCTION One f the functins f the submarine's fire cntrl party is that f determining a ptential target's curse, range, and speed n the basis f passive snar bearing inputs. Elabrate techniques have been develped t accmplish this, using bth human and cmputer infrmatin prcessing capabilities. The expanded time bearing plt, ne f several manual snar plts in the fire cntrl system, is f central imprtance in this analysis since its utputs are used by several key statins in the system. In this plt the raw cmpass bearings btained frm snar are pltted against elapsed time since initial cntact. Then a curve is sketched which captures the central tendency f the pltted pints, and frm this curve the rate f change f the bearings is estimated using a specially designed bearing rate template. The bearing rate is an especially critical input t the fire cntrl party's analysis f target mtin. Changes in current technlgy and peratinal gals have made it pssible t track targets at great ranges, and as a result the raw bearings transmitted frm snar may be subject t greater distrtin than previusly. Further, since the bearing rates at greater ranges are smaller, the effects f distrtins will be crrespndingly larger. These distrtins shw up in the time bearing plt as dispersins f the pltted pints arund sme centrally tending curve. The pltter attempts t recapture this by fairing a curve thrugh the pltted pints. The investigatins reprted here fcussed n the effects f distrtins in the bearings n time bearing pltter perfrmance, under cnditins simulating lng-range, lw bearing rate cntacts. The nise {we shall hereafter use this infrmatin theretic term t refer t the distrtins in the bearings) can have varying characteristics. This nise can vary in its magnitude, and in fact when it gets t great, the snar peratr will switch his mde f reprting until he is nce mre cnfident he can track the target cntinuusly. The nise can als vary in kind. It may be essentially randm, as thugh it had been generated by a stchastically independent randm nise generatr. Here the magnitude and directin f a particular raw bearing's deviatin frm its crrespnding actual bearing is independent f any ther bearing's deviatin. A mre prbable kind f nise in peratinal situatins is that which is stchastically nnindependent r crrelated. With such nise the magnitude and directin f any given raw bearing's deviatin is related t r crrelated with that f ther bearings near it in time. This wuld appear as a slw drift in the bearings, first t ne side and then t the ther, arund the actual bearings. This type f errr is ptentially mre serius, since it is less nticeable n visual inspectin {the crrelatin tends t smth the curve) and culd lead t systematic biases in the estimates f faired bearings and bearing rates. Either kind f nise

6 culd cnceal discntinuities in the time bearing curve which are indicative f target maneuvers r culd lead the pltter t falsely reprt a target maneuver when nne existed. Previus investigatins f time bearing perfrmance were cncerned with either the lder vertical pltting system r with nise-free bearings. The tw experiments reprted here examined perfrmance n the expanded time bearing plt with variatins in bth the level and kind f nise in the raw bearings. A simple versin f the peratinal time bearing plt was designed fr experimental purpses in rder t see the best a human pltter can d under varying cnditins f signal degradatin. All prblems simulated lng-range cntacts with lw bearing rates. Thus, pltters were never frced t change their pltting scales during a prblem. Further, n maneuvers by wn ship r by target were simulated and the pltter wrked at his wn pace rather than in real time. Thus, perfrmance under these; cnditins culd be interpreted as the best a pltter culd d given the signal characteristics, since the additinal factrs invlved in an actual peratinal plt wuld nly serve t magnify the perfrmance errrs fund here. The details f the plts used will be discussed in the next sectin. ' METHOD The tw experiments shared a general methdlgy, and this will be described separately frm their unique design characteristics. Descriptin f the Task A special experimental versin f the expanded time bearing plt was created which departed frm actual peratinal plts in several ways. All pltting was dne n a single sheet f 11 x.16-1/2 in. graph paper ruled every tenth f an inch. Several cnstraints had t be intrduced because the smaller pltting sheet was used. Each prblem simulated a prtin f a time bearing plt in which a cntact had already been made and was being tracked. This cntact was fllwed in the experimental prblem fr 15 minutes f hypthetical time, these times being labeled frm 0:00 t 15:00 fr pltting purpses but nt necessarily crrespnding t the first 15 minutes f cntact. Similarly, the range f pssible bearings was restricted s that the entire plt culd be dne n a single sheet f pltting paper withut any change f scale (a ne degree per inch by ne minute per inch scale was used thrughut). Thus, fr any given prblem the raw bearings were nt allwed t change by mre than 10.5 degrees in the 15 minutes Of hypthetical time. In additin, there were n changes in the directin f the bearing rate (right t left r vice versa), the target was assumed t be n a cnstant curse with n target r wn ship maneuvers, and the bearing rate was nt allwed t get very large (generally being less than ne degree per minute in these prblems). Several prcedural changes were intrduced fr experimental purpses which als differed frm prcedures used in peratinal tasks. Subjects were presented all the raw bearings at nce n a cmputer printed sheet and allwed t

7 plt at their wn pace, s that althugh a 15-minute time slice was examined,' pltting was nt dne in real time. Similarly, they were asked t prduce faired bearings and estimates f the bearing rate at prespecified intervals and write this in apprpriate spaces n the same cmputer printut. Raw bearings were presented every 30 secnds frm time 0:00 t 15:00 inclusive, yielding a ttal f 31 pints t be pltted. Faired bearings were requested every whle minute frm time 1:00 t time 14:00 fr a ttal f 14 faired bearings, while estimates f the bearing rate were requested fr alternate whle minutes frm times 2:00 t 12:00 inclusive fr a ttal f six bearing rate estimates. Subject t these cnstraints, a set f twelve standard prblems was created fr use in these experiments. Each prblem was derived either frm sme apprpriate mathematical functin r frm a set f line segments which yielded a curve apprximating the characteristics f curve segments frm peratinal plts. The set f twelve prblems are shwn in Figure 1. Independent Variables These studies were designed t investigate the effects f nise in the raw bearings upn subjects' ability t estimate actual bearings and bearing rates n the basis f the time bearing plt. Tw aspects f such nise were examined: (1) The level f nise was manipulated by cntrlling the standard deviatin f the nise in a special cmputer prgram which generated the pseud-randm degradatin. (See Appendix A fr details n the prcedure used t generate the nise.) Examples f lw, medium, and high levels f nise are shwn in Figure 2. The kind f nise was als manipulated, and this referred t crrelatins between the signed magnitude f the degradatin fr successive raw bearings. In the randm nise cnditin the magnitude f the errr intrduced fr any given bearing was statistically independent f the magnitude f the errr fr any ther bearing. This is in cntrast t the crrelated nise cnditin where the magnitude f the degradatin fr any particular bearing is related t r crrelated with the magnitude f the degradatins fr bearings near it. Figure 2 als illustrates this difference. A third independent variable was time, r the place in the prblem where the subject prvided an estimate. There were furteen bearing estimates (minutes 1-14) and six bearing rate estimates (even minutes frm 2 t 12). Nte that time refers t the hypthetical time represented by the rdinate f each plt, nt actual elapsed time in the experimental situatin. Dependent Variables Subjects' perfrmance was cmpared with tw kinds f criteria. One cmparisn invlved cntrasting their estimates with the actual bearings and bearing rates btained frm the mathematical functins characterizing each f the 12 standard prblems (see Figure 1). This prvided a measure f hw well the subjects culd recver the "true" state f affairs that was bscured by the statistical nise. The secnd cmparisn invlved cntrasting subjects' estimates with the best estimates

8 BEARING 10 0 UJ Fig. 1. The set f time bearing prblems, withut degradatin, shwing nly right bearing rates. prduced by a mathematical curve-fitting technique. This cmparisn prvided an indicatin f hw subjects' perfrmance deviated frm that f an analytic curve-fitting prcedure. Tw types f measures were btained fr bth bearing and bearing rate s. The ' 'true'' under lying para-' meter was subtracted frm ä subject's estimate f a parameter, and this signed scre was a measure f algebraic errr. It shuld be pinted ut that algebraic errrs were cmputed by subtracting the actual bearing frm the estimated bearing. In ther wrds, a negative value indicates that the estimated bearing was smaller than the actual bearing while a psitive value means the estimated bearing was larger. Greater than and less than were defined with respect t

9 MEDIUM CORRELATED MEDIUM RANOOM Fig. 2. Examples f the three levels and tw kinds f bearing degradatin (nise), with the actual underlying curve shwn. the value f the actual bearing, with the cnventin that if an estimate were just belw 360 and the actual just abve 000, r vice versa, the estimate was first translated t the scale f the actual by adding r subtracting 360 as apprpriate. The abslute value f this scre was a measure f abslute errr. A third measure was used fr bearing rates nly. The abslute errr was divided by the true underlying bearing rate t yield a prprtin abslute errr. These varius measures are summarized in Table I. General Prcedure In bth experiments, subjects were scheduled as grups fr tw-hur

10 Table 1. Summary f Dependent Variables - Measure Bearing Bearing Rate 1. Algebraic errr 2. Abslute errr 3. Prprtin Abslute Errr Subject's estimate - actual bearing Abslute value (algebraic errr) Subject's estimate - actual bearing rate Abslute value (algebraic errr) Abslute errr/actual bearing rate sessins during which they cmpleted fur time bearing plts. All subjects started a given plt at the same time, but were allwed t wrk at their wn speed. A new prblem was nt started until all subjects had finished the previus ne. At the beginning f a sessin each subject was given a pencil and a flexible, transparent bearing rate template identical t thse used in the fleet. When everyne was ready t begin a new plt the experimenter passed ut blank pltting paper and an individualized cmputer print-ut. Subjects had been instructed t d each plt in the fllwing manner: enter the date and subject identificatin number n bth sheets, label the axes f the graph (scales fr labeling purpses were given n the print-ut), plt the raw bearings, fair a smth curve thrugh the raw bearings, enter the required faired bearings n the cmputer printut, and estimate the required bearingrates and enter these n the print-ut. This sequence f peratins bviusly differs frm the sequence ne wuld fllw ding a plt in real time at sea. Nnetheless, by cntrlling a number f extraneus and cmplicating influences fund in peratinal versins the experimental prcedure allwed a relatively pure assessment f the effects f the independent variables. It can safely be assumed that any effects attributed t the independent variables in these experiments wuld be magnified under the mre cmplicated situatin at sea. Design Experiment I. Twelve subjects were each given 12 plts t d, fur a sessin fr each f three tw-hur sessins. The three experimental sessins had been preceded by tw tw-hur training and practice sessins in which subjects had been taught hw t d time bearing plts and had been given practice in the experimental prcedure until the experimenter was satisfied all subjects were cmpetent in all aspects f the task.

11 Three levels f nise (high, medium, and lw) were cmbined with tw kinds f nise (crrelated, randm) and tw directins f bearing rate (right, left). Kind f nise was a between-subject variable; level f nise and directin f bearing rate were within-subject variables. Each subject received all 12 standard prblems (see Figure 1), with level f nise and directin f bearing rate assigned by means f a mdified Latin squares prcedure. Thus, any given subject had fur prblems at each f the three levels f nise, half f these presented with right bearing rates, half with left. The Latin squares prcedure ensured that the assignment f values f the within-subject variables was cunterbalanced acrss subjects and prblem types. Independent randm permutatins were used t establish the presentatin rder f the twelve plts fr each subject. Experiment II. This experiment was run as part f a cmprehensive 30-day snar cnfinement study, and cnstituted ne set f perfrmance measures amng a wide variety f perfrmance, perceptual, and physilgical measures used in that study. Tw cmplete replicatins f a within-subject study f time bearing perfrmance were run, ne replicatin early and anther late in the nise prtin f the snar habitability study. In each replicatin a unique series f 12 plts was prepared fr each subject. Fur plts were dne n each f three tw-hur evening sessins during a given replicatin. A three-hur training and practice sessin was held prir t the first replicatin. Tw levels f nise (high, medium) were cmbined factrially with tw kinds f nise (crrelated, randm) and applied t three prblem types t generate the twelve plts presented t each subject. Directin f bearing rate was cunterbalanced acrss these. Each subject saw three different prblems selected frm thse shwn in Figure 1. (Tw subjects saw Prblems 6, 7, and 9, three subjects saw Prblems 2, 8, and 12, and fur subjects saw Prblems 1, 10, and 11. Prblems 3,4, and 5 were nt used in Experiment II.) Different randmizatins were used t create each new set f raw bearings, as in Experiment I. Fr a particular subject the tw sets f 12 plts he saw in the tw replica- tins differed nly in the randmizatin used t generate the set f bearings and the randm permutatin used t establish the rder f presentatin. Subjects Experiment I. Twelve Navy enlisted men waiting t begin Submarine Schl served as subjects. Nne f them had prir experience with the expanded time bearing plt r with submarine fire cntrl prblems. Experiment II. All nine subjects wh participated in the 30-day cnfinement study were used in this experiment. Fur subjects were civilians frm the lcal cmmunity wh were paid fr their participatin; nne had prir experience with submarine peratins r the Naval service in general. The remaining five subjects were Naval enlisted men. All were experienced snar technicians familiar with the expanded time bearing

12 plt and submarine fire cntrl prblems, but nly ne man reprted having extensive experience. RESULTS AND DISCUSSION Fr each dependent variable, the apprpriate set f scres was btained fr each time segment f each f the prblems. Special difficulties were encuntered in the analysis f Prblem 4 in Experiment I. Therefre, this prblem was excluded frm the main analysis and it will be discussed in a separate sectin. Fr a given subject, an average scre n each dependent variable fr each f the three levels f nise and each f the time segments (six fr bearing rate, 14 fr bearing) cnstituted his input t the analyses abut t be reprted. Preliminary analyses indicated there were n effects due t directin f the bearing rate, s this variable was ignred in all subsequent analyses. Similar average scres were btained fr each subject in Experiment II. Once again directin f bearing rate was ignred since preliminary analyses indicated it had n effect n perfrmance. Since there were n differences in perfrmance fr the early and the late sessins, these data were als cmbined. Thus, fr each subject, a set f scres was btained fr each dependent variable by averaging ver prblems and replicatins fr each cmbinatin f level (high vs. medium) and kind (randm and crrelated) f nise at each f the time samplings. The data fr each dependent variable in Experiment I were subjected t a ne-between (tw levels f kind f nise), tw-within (three levels f amunt f nise, either six r 14 levels f time f estimate) mixed design analysis f variance (Winer, , sec. 7.3)* Thse frm Experiment II were subjected t a three factr (tw levels f kind f nise, tw levels f amunt f nise, either six r 14 levels f time f estimate) cmpletely-crssed withinsubject analysis f variance, (Winer, , sec. 7.5)... Estimatin f Bearings Figures 3 and 4 summarize the perfrmance f subjects at estimating bearings, and are separated accrding t the independent and dependent variables. The lwer panels f these figures shw that the algebraic errrs tended t remain fairly clse t zer in bth experiments. The deviatins frm. zer appear t be unsystematic. Thus, there was n verall bias in the directins f the errrs subjects made with respect t the actual underlying bearings. Furthermre, the analyses f variance fr algebraic errrs in estimating bearings revealed that there were n significant effects fr any f the independent variables r their interactins in either experiment. In sum, the average signed deviatin f the subjects' estimates did nt depart systematically frm zer and were nt influenced by any f the independent variables (kind, level, time)., The upper panels f Figures 3 and 4 shw the data fr abslute deviatins. This measure is an index f hw much n the average an estimated bearing deviated frm the actual bearing, regardless f the directin f deviatin.

13 a. a. (X. UJ z a: < CD RANDOM NOISE * 4 HIGH MEDIUM LOW <t f 1 1 h- H h H 1 1 t- H 1 i H 2- OC -f I a. ÜJ UJ CD UJ 2-- -I H H 10 H 1 h H 1 h H H NOMINAL TIME (min.) H 14 Fig. 3. Errr in bearing estimates fr Experiment I at three levels f nise. These panels shw that there were systematic differences in the size öf these deviatins, and statistical analyses cnfirmed that a number f these differences were reliable, hi bth experiments the average abslute deviatins were greater when the nise was crrelated than when it was randm (Exp. I: Fl,10 = 8.16, p<.05; Exp. H: Pi 8 = , p<.001). Itshuldbe recalled that in Experiment I this was a between-subject variable, while in Experiment II it was a within-subject ne. In either case perfrmance was significantly affected. Similarly, the average abslute deviatin increased as the level f nise was increased (Exp. I: F2,20= 77.15, p<. 001; Exp. II: Fl,8 = 23.78, p<. 01)7 In Experiment I these tw factrs had a significant interactin (F2 20 = ^5* 23» fi <. 001), and inspectin f the upper panel in Figure 3 reveals that this was due mainly t the size f the difference 9

14 -s 5- CORRELATED NOISE *»HIGH RANDOM NOISE *»HIGH - MEDIUM IT (E UJ t H t I H ) i- -i H H 1-.2 a. UJ.1 - m er < -.1 m UJ -+ h- H h H H 1- H i ( NOMINAL TIME (min.) Fig. 4. Errr in bearing estimates fr Experiment II at tw levels f nise. between the medium and high levels f nise in the tw cnditins, randm and crrelated. N such interactin existed in Experiment n. In bth experiments perfrmance was reliably different as a functin f the hypthetical time in the prblem (Exp. I: T?i$ t 130 = 2.11, p <05; Exp. II: F l3 ; 104= 3.42, p<.001). In Experiment I, but nt in Experiment II, the interactin between time and level f nise was als significant ( 26, 260 = 2-56 > P<.01). Again, inspectin f Figure 3 suggests this was due largely t the cntrast f the highly bwed curve fr the high-crrelated cnditin with the curve fr the high randm cnditin. N ther interactins in either experiment were statistically reliable. Althugh the algebraic errrs indicated that there was n tendency fr the subjects' average bearing estimates t deviate frm the true bearings, analysis f the abslute errrs shwed that there were systematic effects n the quality f the bearing estimates as a functin f bth the level and the kind 10

15 f nise. This was true fr subjects wh saw nly ne kind f nise, as in Experiment I, r thse wh saw bth kinds, as in Experiment n. There was n systematic tendency fr level and kind t interact in any way suggestive f a psychlgically meaningful prcess. The ne departure frm additivity shwn in Figure 3 which cntributed t the significant interactin f level and kind with abslute errrs in Experiment I has n plausible explanatin. In additin, perfrmance was cnsistently and reliably different as a functin f where the subject was in the prblem. Trend analysis cnfirmed that the effect f time n abslute errrs was largely due t inferir perfrmance at the ends f the plts. (All trend analyses in this reprt are based n the methds discussed in Winer, 1971^, sec. 7.6, using rthgnal plynmials t partitin the main effects int unique trend cmpnents. ) In Experiment I there were bth significant linear and quadratic cmpnents (linear: Fj 130 ~ 4. 02, p<.05; quadratic: Fi,l30 = 19.85, p <.001), These tw cmpnents accunted fr 87% f the variance due t time, hi Experiment n there were significant linear and quadratic trends (linear: F ls10 4 =27.75, p<.001; quadratic: Fj 104 = 9.64, p<.01) and these accunted fr 84% f the variance due t time. Inspectin f the data in Figures 3 and 4 suggests that the mst parsimnius way f describing these trends is t say that perfrmance was mst affected at the beginnings and ends f prblems. This wuld be expected since subjects had fewer data pints n which t base their estimates f initial and final bearings than in the middle f a plt. This difference between the ends and the middle is highly significant in peratinal cntexts. When the plts are dne in real time, mst estimatin takes place near the end f a cntinuusly grwing curve. The estimatin f bearings cnsists f a cmbinatin f tasks beginning with the initial pltting f the raw bearings and ending with the recrding f the faired bearings (in these experiments) n a data sheet. Cnsistent with earlier findings, inspectin f the raw data in these experiments indicates that the effects prduced by the independent variables were nt due t systematic errrs in either pltting raw bearings r in reading f faired bearings and entering them n the data sheets. Thus, the lcus f the effects is in the actual fairing r subjective curve-fitting that the subject engages in. A full discussin f the human subject as a subjective curve-fitter must await the analysis f the capabilities f bjective, mathematical curvefitting with the present prblems. This discussin will be presented later in this reprt. Estimatin f Bearing Rates The perfrmance f subjects at estimating bearing rates in these experiments are shwn in Figures 5 and 6. Althugh algebraic errrs, shwn in the center panel f each figure, lie near zer, there were sme tendencies in the data which were cnfirmed as reliable by statistical analysis. In bth experiments the level f the nise was a significant factr (Exp. I: F2 20 " 5.02, p<. 05; Exp. H: Fj 8 = 9'.28, p <. 05). Hwever, inspectin f the center panels in bth figures reveals 11

16 If 15 CORRELATED NOISE «HIGH MEDIUM «LOW RANDOM NOISE * «HIGH «MEDIUM - LOW mi I 1 h -t h +.1- O c g = S 9.6- m & NOMINAL TIME (min.) Fig, 5, Errr in bearing rate estimates fr Experiment I at three levels f nise. that there is n cnsistent rdering f the curves as a functin f level f nise, making this effect difficult t interpret. In sum, there was at least n straightfrward bias in the directin f the average errrs. In Experiment I, kind f nise als prduced a significant effect n the algebraic errrs (Fl, 10 = 3.40, p<. 05) and kind interacted with level (F2,20' 5. 07, p<. 05). In gen- eral, crrelated bearings led t estimates f bearing rates which tended t slightly exceed the actual bearing rates, while randm bearings prduced estimates slightly less than the actual bearing rates. There was als a significant effect in Experiment I due t the time at which the bearing rate was estimated (F , p<.05), and trend analysis cnfirmed that this 12

17 .25 r.20- CORRELATED NOISE * * HIGH MEDIUM RANDOM NOISE * * HIGH MEDIUM ~.15 I?.10 I H 1- H h t n QC a v,s <* CD a> +.I H (- H cs' NOMINAL TIME (min.) Fig-, 6. Errr in bearing rate estimates fr Experiment Hat tw levels f nise. was largely due t the tendency fr the estimated bearing rate t drp belw the actual rate at the ends f prblems. The test fr quadratic trend was significant, F lf 50= 7.2V, p<.01. N ther trend cmpnents reached significance. The effects due t level and kind f nise n algebraic errrs were small, smewhat marginal, and nt very systematic, and as a result are exceedingly difficult t interpret. The falling ff in the curves in Figure 5 at the last time segment is the mst significant effect in terms f the actual pltting task, since it indicates a tendency t underestimate the bearing rates as these rates increase (as they tended t d at the end f mst prblems). 13

18 Further, it indicates sme difficulty in estimating the bearing rate at the end f the faired curve, and this is the mst realistic cnditin in terms f real-time perfrmance f this task at sea. Hwever, again this effect was relatively small in magnitude and marginal, and did nt shw up in Experiment II, s shuld be viewed with cautin. The upper panels f Figures 5 and 6 shw perfrmance as measured by the abslute difference between the actual bearing rate and the estimated bearing rate. As with the bearings, these curves indicate that bth the kind and the level f nise affected the quality f the estimates. Larger average deviatins were assciated with crrelated nise as ppsed t randm, and higher as ppsed t lwer levels. Hwever, the effect f kind f nise reached statistical significance nly in Experiment II (Exp. I: Fi } i = 1.21, n.s.; Exp. II: F 1} 8 = 6.57, p<. 05) while the effect f level f nise reached significance nly in Experiment I. (Exp. I: F2 20 = 13.81, p<. 001; Exp. II: F lj 8 = 4.97,,05<p<,10). The nly ther reliable effect in either experiment was the time f estimate, and this was significant in bth experiments (Exp» I: F 5 5 ~ 3 «5^» p<.01;exp. H: F 5] 40 = -.6."57> p<.001).. N ther effects r interactins reached acceptable levels f statistical reliability. Unlike the data shwn in the center panels fr algebraic errrs, the data fr abslute errrs revealed that each f the three independent variables had systematic, rderly effects n the average quality f the estimated bearing rates. The" effects fr kind and level f nise were nt as cnsistently reliable as with the bearing data cnsidered earlier, but appear nntheless t be imprtant effects. The effect f time f estimate was reliable in bth experiments. Trend analysis indicated that the effect f time f estimate culd largely be attributed t the relatively mre severely degraded perfrmance at the beginning and end f prblems (Experiment I: linear cmpnent, Fj 50= 5.50, p<.05, quadratic cmpnent, Fj 50 = 11.60, p <. 01, the linear and quadratic cmpnents accunting fr 96% f the variance due t time; Experiment n: linear cmpnent, Fj" 40=27.89, p<.001, quadratic cmpnent, Fj 40 = 4.99, p <,05, the linear and quadratic cmpnents accunting fr 99% f the variance due t time). The ends f these curves represent thse prtins f the prblems where the bearing rate was, in general, either lwest r highest. Hwever, the effect f magnitude f the bearing rate n the accuracy f bearing rate estimatin must be examined explicitly befre this can be discussed in detail. The ends als represent, f. curse, thse prtins f the time bearing curve where the cntextual infrmatin is minimal. The lwer panels in Figures 5 and 6 present the data in a third frmat. Here the abslute difference between the actual and estimated bearing rates have been divided by the actual bearing rate, translating an abslute measure int a relative ne. The rdinates n these panels represent the amunt f errr in estimatins f the bearing rates as a prprtin f the actual underlying bearing rate. Level f nise systematically rdered these curves, the curve fr a higher 14

19 level abve that f a lwer level. This was reliable in bth experiments (Experiment I: F 2 20 = 24.95, p<.001; Experiment II: 'F^g = 7 «28» <.05). Kind f nise reliably affected this measure in Experiment II (Fi.,8 = 6.42, p<. 05). In Experiment I, kind f nise did nt significantly affect prprtin abslute errr (F^ JQ = 2.11, n.s.) althugh the directin f the verall means was the same as in Experiment II. Nthing very reliable emerged frm this set f measures with respect t the distinctin between crrelated and randm nise, but level f nise cnsistently affected the percentage measure in bth experiments. This measure als differed reliably as a functin f time f estimate (Experiment I: F 5 s = 34.52, p<.001; Experiment II: ' F 5)4 Q = 19.21, p<.001). Inspectin f the lwer panels in Figures 5 and 6 shws that this was due t the systematic decrease in prprtin abslute errr with time in the prblem. Trend analysis revealed that bth the linear and quadratic trends were significant in bth experiments (Experiment I: linear cmpnent, Fj 50= , p<.001, quadratic cmpnent, Fl, , p<. 001, the linear and quadratic cmpnents accunting fr 94% f the variance due t time; Experiment II: linear cmpnent, Fj 49= 88.24, p <.001, quadratic cmpnent, ^40 = 5.64, p<.05, the linear and quadratic cmpnents accunting fr 97% f the variance due t time). One majr reasn fr this effect, f curse, is that average actual bearing rates were quite small early in the prblems, s that small abslute deviatins wuld make fr large prprtinal deviatins at these times. Average bearing rates fr 15 the six times at which estimates were btained were:.25,.30,.34,.40,.48,. 68. The interactin f time with kind attained significance in bth Experiment I (F 5 50 = 4. 90, p<. 01) and in Experiment n (F 5 4Q = 2~. 60, p<.05). Inspectin f the data in all panels f Figures 5 and 6 reveals the fllwing picture f human perfrmance at estimating bearing rates in simple time bearing plts. Subjects appear t have n verall bias t their estimates. That is, the expected value f their distributins f estimates appears t be the actual bearing rate, and this expected value is nt altered by variatins f the independent variables in these experiments. The nly exceptin t this generalizatin was fund in Experiment I, where crrelated nise led t significantly larger estimated bearing rates than did randm nise. The quality f the estimates as measured by the abslute errrs was significantly and systematically affected by each f the independent variables. Increasing the amunt f nise r changing frm randm t crrelated nise increased the magnitude f the subjects' abslute errrs. Simr ilarly, perfrmance was prer at the beginnings and ends f prblems than in the middle. Subjects apparently used the added cntextual infrmatin fund in the center f the curves t btain better estimates f the tangent t the curve. In actual peratinal plts estimates f bearing rate are usually btained fr the last fur t six pints pltted, and the present data reveal that this is where subjects have the greatest difficulty.

20 Cmparisn f Human Perfrmance t that f Ratinal Curve-Fitting Techniques In rder t evaluate the perfrmance f human subjects n these tasks it is necessary t have sme ratinal measure f the "best" pssible perfrmance. The cnventin adpted here is t cntrast the perfrmance f an rthgnal plynmial curve-fitting rutine with that f the human subjects in bth experiments. The best fitting curves prvide a ratinal ptimum fr faired bearings, and the derivatives with respect t time (db/dt) are an ptimum estimate f the bearing rate. Experiments I and II were replicated exactly with a cmputerized rthgnal plynmial curve-fitting rutine substituted fr the human subjects. Slutins were restricted t third degree plynmials. Analyses f variance identical t thse reprted in the last sectins were perfrmed, using bth the human and cmputer data, with a between-subjects factr fr the surce f the data (cmputer r human) added t the design. The results f these expanded analyses were examined fr significant main effects due t the surce f the estimates and interactins between surce and ther independent variables. Cnsistent trends amng the interactins might reveal that there were systematic differences in the character f the slutins prvided by each f the tw data-generating surces. Bearing data. Figures 7 and 8 present the data fr the cmputer estimates f bearings, and shuld be cntrasted with the data f Figures 3 and 4. Analysis f variance cnfirmed that there Was a significant main effect f surce n abslute errrs in bth experiments (Experiment I: Fj 20 = 8.78, jk.öi; Experiment II: Fj' IQ = 24.73, p <. 001), with the perfrmance f human subjects inferir t that f the cmputer curve-fitting rutine. N similar differences were fund fr algebraic errrs. Thus, althugh there was n difference in the average signed errr in the faired bearings f the tw data surces, the average quality f the estimates prvided by the curve fitting rutine was cnsistently superir t that f the subjects. In ther wrds, subjects' perfrmance did nt measure up t the best pssible perfrmance. There were n cnsistent trends in the interactins f surce with the ther independent variables, althugh there were several significant F- ratis. In Experiment I the interactin f level and surce fr abslute errrs was reliable (F 2 40 = 4.13, p<.05), while fr Experiment II the interactin f kind and surce was significant fr abslute errr (F^ IQ = 16.91, p<,001) and the interactins f kind, level, and surce (F^ 16 = 4.97, p<.05) and time and surce (F = "^c>^5' P"^«001 ) were significant fr algebraic errrs. Since n pattern emerged frm these, little that is meaningful can be said abut the reasns fr these interactins. Figure 9 shws in summary frm the cmparisn f the tw data surces averaged ver level and kind f nise. The significant interactin f time and surce fr algebraic errrs in Experiment EL can be clearly seen in this figure. Why the curve fr the cmputer generated data shuld differ s markedly frm that fr the human data is unclear.' The cause may lie in a 16

21 CORRELATED NOISE *»HIGH MEDIUM «LOW RANDOM NOISE *»HIGH MEDIUM «LOW I I I I H 1 1 I- -I NOMINAL TIME (min.) Fig. 7. Errr in cmputer bearing estimates fr Experiment I at three levels f nise. peculiar relatinship f the weaknesses f this particular curve-fitting rutine with the subset f prblems in Experiment II. Since n similar relatinship emerged in Experiment I, it cannt be attributed t any general characteristics f the curve-fitting rutine. Bearing rate data. Figures 10 and 11 cntain the data relevant t the perfrmance f the curve-fitting rutine, and Figures 5 and 6 have the cmparable data fr human subjects. The curve-fitting rutine was a better estimatr f bearing rates than were the human subjects n tw measures: abslute errr (Experiment I: Fi^O = 4.36, p<.05; Experiment II: Fj jg = 13.68, p<«01) and prprtin abslute errr (Experiment I: Fj 20 ~ 4.83, p<. 05; Experiment II: Fj ig = 4.74, p<.05). Algebraic errrs were nt reliably different fr the tw data surces. The nly systematic pattern f interactins t emerge were thse invlving surce and time. Figure 12 17

22 12 [4 2 NOMINAL TIME (min.) Fig. 8. Errr in cmputer bearing estimates fr Experiment II at tw levels f nise. summarizes the bearing rate data and shws the cntrast f cmputer - generated data and human data averaged ver kind and level f nise. The interactins reached significance n the fllwing measures: Experiment I, algebraic errr (F 5 ^QQ = 2.84, p<.05) and prprtin abslute errr (F5 100 ~ 4.97, p<.001); Experiment II, abslute errr ~(F$ t g = 4-07» < 01 )' These interactins indicate that nminal time affected the perfrmance f the tw data surces differently. Where these interactins attained significance it appears frm Figure 12 that this was due t the cmputer-generated data yielding a mre severely bwed functin than the human data. Table 2 summarizes the tests n the differences in trends that cntribute t the surce by time interactins, and shws that the curves differed in either their linear r quadratic trends. Thus, althugh the verall perfrmance f the cmputer rutine at estimating bearing rates was superir t that f humans, 18

23 40- EXPERIMENT I»»HUMAN EXPERIMENT H 4 HUMAN -I I f- -I 1 h +- -I I h S +05- ui m -.05 I 1 1 h l 1- H 1- ( I h- H h -I f NOMINAL TIME (min.) Fig. 9. Summary cmparisns f human and cmputer errr in bearing estimates. the frmer had x^elatively mre difficulty capturing the bearing rates f the end pints f the time bearing curves. Summary f cmparisn. The time bearing perfrmance f human subjects was cnsistently inferir t that f a mathematical estimatr. This was true fr bth the fairing f bearings and the estimating f bearing rates. Figures 9 and 12 make clear, hwever, that althugh many f the differences were reliable, they were relatively small in size, especially fr the estimatin f bearings. With bearing rates, the errrs f subjects were large relative t the cmputer estimates but were still small in abslute magnitude. All f the independent variables except time had the same kinds f effects n the perfrmance f bth data surces, Thus, the fact that crrelated nise yields prer estimates f bearings and bearing rates is due t the characteristics f the data, nt thse f the 19

24 CORRELATED NOISE * «HIGH MEDIUM - LOW RANDOM NOISE * *HIGH MEDIUM "LOW S > c 0- < - I = Ö nr u).6 - S c NOMINAL TIME (min.) Fig. 10, Errr in cmputer bearing rate estimates fr Experiment I at three levels f nise. human estimatr. The lack f cnsistent interactins between either kind r level f nise and surce f data indicates that these prperties f the raw bearings have effects n the estimates that cannt be eliminated by altering the way in which the human des his task. Althugh the analyses reprted earlier in this reprt indicated that subjects had difficulties at the ends f time bearing curves in estimating bth bearings and bearing rates, the analyses just discussed indicate that, if anything, the curve-fitting rutine has even mre truble. Thus, the human peratr appears t be an especially effective integratr f infrmatin at the ends f curves like these and 20

25 Bearing Rate Prprtin Abslute Errr -t- -I- (D -r Algebraic Bearing Rate Errr (deg/mirt.) -t- Abslute Bearing Rate Errr (deg./min.) -t- -f- -f- JO JO z i 3 z 4 X 2 I 3) > Z 8 ffi i 7 ig. 11. Errr in cmputer bearing rate estimates fr Experiment II at tw levels f nise. prduces estimates f bearings and bearing rates that are less distrted by the lack f a cntext than des the mathematical estimatr. This is encuraging since in peratinal plts the estimatin usually takes place near the end f a grwing curve in real time. Perfrmance n Prblem 4. As nted earlier, Prblem 4 had t be excluded frm the main analysis because it yielded perfrmance radically different frm the ther eleven prblems. Figure 1 shws why. Prblem 4, ne 21

26 12 2 NOMINAL TIME (min.) Fig. 12. Summary cmparisns f human and cmputer errr in bearing rate estimates. f thse cmpsed f line segments, passed thrugh an inflectin pint. That is, there was a regin f very high bearing rate preceded and fllwed by regins f lw bearing rate. This wuld be typical f a time bearing curve prduced by a target r wn ship maneuver, r by passage thrugh the pint f minimum range (CPA) fr fixed target and wn ship curses. Thus, it represents a situatin which frequently arises in peratinal situatins. The character f Prblem 4 caused great difficulty fr bth the human perfrmers (recall that Prblem 4 was used nly in Experiment I) and fr the analytic curve-fitting rutine, apparently because the nise bscured the large change in bearing rate. 22

27 8 S H CD Ü 3 M K* Ö r" - 0 t l ^d CO 9 a + 00 C5> t 2.1L P 3 n 5 S a<5 «2 a p i-i (H ft CD GO <D M t 43 ö 0) <P c3 O 03 ft bx> 3 f^l Ü X- 00 i-i lo cd in t- t- fj T3 00 CO I-l cd 3 O" f-i * * «00 g 00 0 LO a I-«en " 1-1 i-l w rh fel cd cd 5 CM u f-i u H $ 3 pp U f4 M fc J2 f4 u <! fc w a w l-i cd 5 u > CD O a W h p O a <j < - ft «r-l I 1.. i i A' II hh II K ii - ydl ÜI.g,*l &*' W w w T-l O * * V V 23

28 Bth subjects and the cmputer rutine seriusly underestimated the bearingrate at nminal time six minutes, that time when the bearing rate was very high (it was 2. 00, cntrasting with.40 at time 4 and.20 at time 8). Figures 13 thrugh 17 summarize the perfrmance f the tw data surces at the varius time intervals fr bearings and bearing rates. These data have been cllapsed ver kind and level f nise, since insufficient data existed (each subject saw Prblem 4 nly nce, at ne level and ne kind f nise) fr a cmplete analysis. Only time in the prb - lern and the interactin f time with the surce f the data (human r machine estimatins) yielded cnsistently significant results and these are the data f greatest interest t us here. Figures 13 and 14 shw that the analytic curve fitting rutine had cnsiderably greater difficulty estimating bearings fr Prblem 4 than did human estimatrs. Since the rutine was set t find the best third degree slutin using rthgnal plynmials, in principle it shuld have been able t recver a functin like Prblem 4 Hwever, the rutine seriusly verestimated the bearings at time 4, 5, i..8- Human Cmputer.6 - <c.4 e S3 1+2 CE «I HI ID 0 Ü < tr S J L NOMINAL TIME (min) Fig. 13. Human and cmputer algebraic errr in bearing estimates fr Prblem 4. 24

29 1.0 - Human - Cmputer.8 CL a: UI i- 5 < l±j (D iu 4 _l </> CO -> < NOMINAL TIME (minj Fig. 14. Human and cmputer abslute errr in bearing estimates fr Prblem 4. and 6, and seriusly underestimated thse at times 7, 8, and 9. Bearings were again verestimated at times 10 thrugh 13w Human perfrmers'average algebraic errrs were cnsistently very clse t zer, althugh Figure 12 shws that they t had difficulty at the times listed abve. The data f Figures shw that althugh the frms f the varius functins are fairly similar fr human and mathematical estimatrs, the mathematical estimatr is cnsistently inferir. Statistical analysis cnfirmed that this was significant fr each f the measures f bearing rate (algebraic errr: F^ 12 = 7.30,jp<.05; abslute errr: Fj,l2 = 11*51, p<. 01; prprtin abslute errr: Fj 1 2= 20 «34» <. 001). The main effect fr time was f curse significant fr all measures (algebraic errr: F5,60 = , p<.001; abslute errr: F5 } g = 81 15, p<.001; prprtin abslute errr: F^f QQ = , p<.001), but s was the interactin f time with human vs. analytic estimatrs (algebraic errr: F t 60 ~ 25

30 6 8 NOMINAL TIME (min) 12 Fig, 15. Human and cmputer algebraic errr in bearing rate estimates fr Prblem , p<. 01; abslute errr: F 5 QQ , p<.05; prprtin abslute errr: F 5}60 ~ 15.88, p<.001). The trend f these data fr bth bearings and bearing rates is just the ppsite that f the data fr the ther eleven prblems. In the analysis reprted in the previus sectin, the perfrmance f the mathematical curve fitting rutines was cnsistently superir t that f the human estimatrs. On Prblem 4 the human subjects were cnsistently superir. With a sample f nly ne prblem f this kind we are hesitant t make cnfident generalizatins, but since the effects were s statistically reliable it leads us t believe the difference is real. Garnatz and Hunt (1971) 2 have reprted differences in the relative ease with which human estimatrs and mathematical estimatrs can find slutins in tasks smewhat different than this, but their results alng with thse reprted here suggest there are general classes f estimatin prblems fr which the human's perceptual and cgnitive 26

31 I.I i Human Cmputer 8 a. en a. tu < Ul CD UJ t- b _i in m < NOMINAL TIME Fig. 16. Human and cmputer abslute errr in bearing rate estimates fr Prblem 4. abilities give him a distinct advantage ver simple mathematical estimatrs. Cmparisn f Experienced vs. Inexperienced Subjects in Experiment II. Tw quite different ppulatins f subjects were represented in Experiment II. On the ne hand there were fur civilians recruited frm a lcal prgram fr the disadvantaged, and n the ther there were five Naval enlisted men, all with sme pre-experimental expsure t the time bearing plt and t fire cntrl peratins. An auxiliary analysis was. carried ut t see if this difference in backgrund resulted in perfrmance differences. One f the five Navy men was excluded frm the analysis since he differed in age and experience frm the ther fur {he was an E-7, while the ther fur were E-4? s). The mean perfrmance curves indicated that the civilian subjects were cnsistently inferir t the military subjects. Since analysis f 27

32 HUMAN COMPUTER 2.8- w 2.4- St & 3 >< 2.0 [C O " NOMINAL TIME (min.) Fig, 17. Human and cmputer prprtin f abslute errr in bearing rate estimates fr Prblem 4. variance n the data fr the eight subjects wuld have been based n nly fur bservatins per cell, a nn-parametric test was perfrmed cmparing means frm civilian and military subjects fr each nminal prblem time within each nise cnditin. Tables 3 and 4 shw these means and the significance levels btained using the Sign Test (Siegel, 1956*, pp ) fr bearing estimates and bearing rate estimates, respectively. In bth cases, cmparing mean algebraic errrs, nly the high level crrelated nise shwed a significant difference. In the cases f mean abslute errrs, hwever, all differences were significant except the high level crrelated nise cnditin. Fr bearing rate estimates, all cnditins f prprtin abslute errr shwed significant differences. Apparently the military subjects were able t make use f their previus experience in perfrmance n this task. 28

33 Table 3. Cmparisn f Bearing Estimates Frm Civilian and Military Subjects in Experiment II and Sign Test Significance Levels Mean Bearing Estimate Errr Level f Civilian Military Significance Algebraic Errr Crrelated Nise High p =. 046 Medium n.s. Randm Nise High n.s. Medium n.s. Abslute Errr Crrelated Nise High n.s. Medium p =. 006 Randm Nise High p <. 001 Medium p=.001 Table 4. Cmparisn f Bearing Rate Estimates Subjects in Experiment II and Sign Test Frm Civilian and Military Significance Levels Mean Bearing Rate Estimate Errr Level f Civilian Military Significance Algebraic Errr Crrelated Nise High p=.016 Medium n.s. Randm Nise High n.s. Medium n.s. Abslute Errr Crrelated Nise High n.s. Medium p=.016 Randm Nise High p =.016 Medium p=.016 Prprtin Abslute Errr Crrelated Nise High p.=.016 Medium p=.016 Randm Nise High p=.016 Medium p=

34 Frm the variety f results btained in these experiments we can draw the fllwing cnclusins abut the questins investigated. The kind and level f nise in the raw bearings have a systematic and cnsistent effect n the quality f perfrmance in the time bearing plt, althugh they d nt differentially affect the average algebraic directin f the errrs in the subject's estimates. That is, there is n tendency fr subjects t either cnsistently verestimate r underestimate time bearing utputs as a functin f the prperties f the nise. Furthermre, since an analytic curve-fitting technique was affected in the same way by the prperties f the nise, there is n way t eliminate these effects shrt f eliminating the nise itself frm the data. The directin f the bearing rate had n effect at all n the perfrmance f subjects estimating bearings r bearing rates. An interesting pattern emerged frm the cmparisns f the human estimatr with the mathematical ne. Overall human perfrmance was cnsistently inferir t that f the curve-fitting rutine, but the magnitude f the differ- Winer, B.J. Statistical principles in experimental design. (2nd ed.) New Yrk: McGraw-Hill, Garnatz, D., & Hunt, E. Eyeball parameter estimatin with a cmputer. Technical Reprt N , Cmputer Science Grup, University f Washingtn, Nvember SUMMARY REFERENCES 30 ences was nt large. The curve-fitting rutine had relatively mre truble with the ends f the time bearing curves, and n the ne prblem that cntained a mre cmplicated curve shape, it was. inferir verall t the human estimatr. Thus, althugh the human cannt d as well as the curve-fitting rutine when the shapes f the curves are simple, when the estimatin must be dne with, relatively little cntext r with mre cmplicated curves, the human estimatr prduces mre stable results than the curve-fitting rutine. The human's ability t apply cgnitive cnstraints t his task and t explit perceptual abilities unavailable t the mathematical device is apparently f great benefit. A subsidiary analysis indicated that experience with time bearing prblems yielded better perfrmance, althugh the gains were small. Hwever, in Experiment II the change in perfrmance ver a 30-day cnfinement was negligible. The lnger-term effect was prbably due t a greater understanding f the rle f the time bearing task in fire cntrl prblems. 3. Siegel, S. Nnparametric statistics fr the behaviral sciences. New Yrk: McGraw-Hill, Feller, W. An intrductin t prbability thery and its applicatins. Vlume 1. (3rd ed.) New Yrk: Wiley, Green, B.F., Jr. Digital cmputers in research. New Yrk: McGraw-Hill, 1963.

35 APPENDIX A Generatin f the Statistical Nise The central limit therem f prbability thery states that the sum f n independent randm variables with a cmmn distributin appraches a nrmal distributin as n tends t infinity (see, e.g., Feller, 1968) 4. It can be shwn that n = 12 is a satisfactry apprximatin fr many applicatins, and that if the n randm variables are real numbers n the interval (0, 1), with n = 12 the distributin f the sums will have unit variance (Green, 1963, pp ). This principle was used t write a cmputer rutine t generate the statistical nise fr the raw bearings. T create the randm nise, 12 numbers were generated using a subrutine whse utput was a pseudrandm number frm a unifrm distributin n the interval (0, 1). These were summed, and the cnstant six was subtracted frm the sum, yielding a pseud-randm number frm a nrmal distributin with zer mean and unit variance. The result f 300 samples using the rutine fr randm nise is shwn in Figure A-l. Crrelated nise was generated in essentially the same way, except that each new sum cnsisted f 11 f the pseudrandm unifrm numbers frm the previus sum plus ne new ne. (The randm nise, f curse, used twelve new numbers fr each new sum.) The 150 SAMPLES 300 Fig. A-l. Three hundred successive samplings f randm nise. A-l

36 utput f this prcess was als adjusted t have a zer mean, and examples f 300 successive samplings are shwn in Figure A-2. Level f nise was cntrlled by multiplying the adjusted sum by a scale factr calculated in accrdance with standard snar equatins t simulate cnditins that might be fund in peratins at sea. In sum, the raw bearing was cmputed accrding t the fllwing equatin; raw bearing = actual bearing + (adjusted sum) X (scale factr) The adjusted sum is, f curse, distributed arund zer. 150 SAMPLES 300 Fig. A-2. Three hundred successive samplings f crrelated nise. A-2

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39 UNCLASSIFIED Security Classificatin DOCUMENT CONTROL DATA -R&D (Security classificatin f title, bdy f abstract und indexing anntatin must be entered when the verall reprt is classified) 1. ORIGINATING ACTIVI TY (Crprate authr) Naval Submarine Medical Research Labratry Naval Submarine Medical Center 3. REPORT Tl TL E 2a. REPORT SECURITY CLASSIFICATION UNCLASSIFIED 2b. GROUP PERFORMANCE ON THE EXPANDED TIME BEARING PLOT AS A FUNCTION OF BEARING ACCURACY 4. DESCRIPTIVE N O T E S (Type f reprt and inclusi ve dates) Interim reprt s. AUTHOR(S) (First name, middle initial, last name) GARY M. OLSON KEVIN LAXAR 6. REPORT DA TE 26 June a. CONTRACT OR GRANT NO- b. PROJECT NO. MF D 7fl. TOTAL NO. OF PAGES/O»A 7b. NO, OP REFS PPJ 30 and 1 Appendix* 9a. ORIGINATOR'S REPORT NUMBER(S) 11 NSMRL Reprt Number 716 9b, OTHER REPORT NO(S) (Any ther numbers that may Ö«assigned this reprt) ^0. DISTRIBUTION STATEMENT Apprved fr public release; distributin unlimited. il. SUPPLEMENTARY NOTES 12- SPONSORING MILITARY ACTIVITY Naval Submarine Medical Center Bx 600 Naval Submarine Base Grtn, Cnn. 063^0 3. ABSTRACT Tw experiments analyzed the effects f statistical nise in raw snar bearings n perfrmance in a labratry versin f the expanded time bearinq plt. Accuracy f faired bearings and bearing rate estimates were taken as the measures f perfrmance. Greater amunts f nise led t prer perfrmance, but these decrements were smaller when the nise was randm than when it was crrelated. Human perfrmance was cntrasted with that f an rthgnal plynmial curve fitting rutine designed t d the same task. The mathematical rutine was affected by the nise in the same way as humans were. Hwever, n simple plts the mathematical rutine prvided superir slutins while n curves f mre cmplex shapes r at the ends f curves humans were superir. Thus, in certain situatins the human's perceptual and cgnitive abilities gave him a distinct advantage ver the mathematical rutine. DD, F ru473 S/N 0 I 02-ÜI (PAGE I ) UNCLASSIFIED Security Classificatin

40 UNCLASSIFIED -Security Classificatin K6Y WORDS Time Bearing Plt Bearing Degradatin Human Infrmatin Prcessing Analytic Curve-fitting Fai red Bearings, ; Bearing Rate Estimatin Fire Cntrl DD, F Nr 1473 < BA CK, (PAGE 2) UNCLASSIFIED Security Classificatin