cats_v312.ps

最大似然估计算法

(error)-5 b(.)49 b(The)31 b(positions)e(are,)k(by)d(de-)324
3038 y(f)o(ault,)23 b(assumed)g(to)h(be)g(in)f(metres,)h(ho)n(we)n(v)o
(er)e(this)h(can)h(be)g(altered)g(with)f(the)h(-Sscale)p
3300 3038 V 36 w(f)o(actor)324 3159 y(option.)44 b(At)30
b(present)f(the)h(position)e(uncertainties)h(are)i(not)e(used)h(in)f
(the)h(program.)45 b(In)30 b(the)324 3279 y(future)i(the)f(indi)n
(vidual)f(formal)h(errors)i(may)e(be)h(used)g(to)f(de\002ne)i(a)f(v)n
(ariable)f(white)g(noise)324 3400 y(component.)72 b(Ho)n(we)n(v)o(er)37
b(this)h(slo)n(ws)g(the)h(algorithm)e(do)n(wn)h(considerably)g(when)h
(com-)324 3520 y(pared)22 b(to)g(assuming)e(the)i(white)g(noise)f(is)h
(the)g(same)g(at)g(each)g(epoch.)30 b(If,)23 b(for)f(instance,)g(there)
324 3640 y(w)o(as)h(only)g(one)g(component)f(of)i(information)d
(required)j(for)f(processing)g(\(for)h(e)o(xample)e(tide)324
3761 y(gauge)29 b(data\))i(then)f(the)g(other)g(columns)f(must)g(still)
f(be)j(present)f(b)n(ut)f(the)h(program)g(can)h(be)324
3881 y(told)g(not)h(to)g(process)g(those)f(columns)g(by)h(using)f(the)h
(--columns)g(\(-C\))h(option)e(described)324 4001 y(belo)n(w)-6
b(.)29 b(An)c(e)o(xample)f(of)h(a)g(\002le)g(follo)n(wing)e(this)h
(format)g(is)h(sho)n(wn)e(belo)n(w)-6 b(.)324 4188 y
Fe(#)39 b(Site)h(:)f(vyas)324 4267 y(#)g(X)h(:)80 b(-2483507.1216)324
4346 y(#)39 b(Y)h(:)80 b(-4672361.9853)324 4425 y(#)39
b(Z)h(:)120 b(3549320.5426)324 4504 y(#)39 b(Latitude)g(:)h(34.030915)
324 4583 y(#)f(Longitude)g(:)h(-117.992047)324 4661 y(#)f(Height)g(:)h
(7.856557)324 4740 y(#)f(offset)g(1999.79178082)f(7)324
4819 y(1998.5736)118 b(-0.02370)158 b(0.04070)h(0.00290)78
b(0.0009)h(0.0009)g(0.0037)324 4898 y(1998.5763)118 b(-0.02360)158
b(0.04190)h(0.00410)78 b(0.0009)h(0.0009)g(0.0030)324
4977 y(1998.5791)118 b(-0.02180)158 b(0.04140)h(0.00650)78
b(0.0010)h(0.0009)g(0.0038)1918 5251 y Fn(3)p eop
%%Page: 4 4
4 3 bop 324 548 a Fe(1998.5818)118 b(-0.02270)158 b(0.04100)119
b(-0.00130)78 b(0.0009)h(0.0009)g(0.0038)324 627 y(1998.5845)118
b(-0.02330)158 b(0.04070)h(0.00050)78 b(0.0009)h(0.0009)g(0.0037)324
706 y(1998.5873)118 b(-0.02300)158 b(0.04050)119 b(-0.00020)78
b(0.0009)h(0.0009)g(0.0038)324 785 y(1998.5900)118 b(-0.02320)158
b(0.04090)h(0.00560)78 b(0.0009)h(0.0009)g(0.0037)324
863 y(1998.5928)118 b(-0.02390)158 b(0.04030)119 b(-0.00180)78
b(0.0010)h(0.0009)g(0.0039)324 942 y(1998.5955)118 b(-0.02370)158
b(0.04020)h(0.00230)78 b(0.0009)h(0.0009)g(0.0037)324
1021 y(1998.5983)118 b(-0.02320)158 b(0.04150)h(0.00480)78
b(0.0010)h(0.0009)g(0.0038)324 1100 y(1998.6010)118 b(-0.02390)158
b(0.04020)119 b(-0.00620)78 b(0.0010)h(0.0009)g(0.0039)324
1179 y(1998.6036)118 b(-0.02240)158 b(0.03970)119 b(-0.00140)78
b(0.0010)h(0.0009)g(0.0038)324 1258 y(1998.6091)118 b(-0.02190)158
b(0.03990)119 b(-0.00190)78 b(0.0010)h(0.0009)g(0.0030)470
1445 y Fn(If)43 b(there)f(an)o(y)g(kno)n(wn)f(discontinuities)f(or)i
(of)n(fsets)f(in)h(the)g(time)g(series)g(then)g(these)324
1542 y(should)23 b(be)i(speci\002ed)g(in)g(the)f(header)i(of)f(the)f
(\002le)i(in)e(the)h(follo)n(wing)e(format)324 1704 y
Fe(#)39 b(offset)g(decimal_date)f(component_code)470
1908 y Fn(The)30 b(component)e(code)i(is)g(calculated)f(in)h(a)g
(manner)f(similar)g(to)g(\002le)h(permissions)e(on)324
2028 y(a)e(unix-style)f(system.)32 b(The)26 b(component)f(code)h(is)g
(the)f(sum)g(of)h(the)g(components)f(in)g(which)324 2148
y(the)20 b(of)n(fsets)f(appears)i(with)f(the)g(v)n(alues)f(north)h
(\(4\),)h(east)f(\(2\))h(and)f(v)o(ertical)g(\(1\).)29
b(This)20 b(gi)n(v)o(es)f(an)324 2269 y(e)o(xclusi)n(v)o(e)27
b(number)i(between)h(0)g(and)f(7)h(for)g(all)f(combinations)f(of)h(af)n
(fected)h(components.)324 2389 y(F)o(or)19 b(e)o(xample)f(for)h(an)h
(of)n(fset)e(occurring)h(in)g(the)g(north)f(and)h(up)g(components)f
(the)h(component)324 2510 y(code)33 b(is)g(5.)57 b(F)o(or)33
b(all)g(components)f(the)i(v)n(alue)e(is)h(7.)57 b(The)33
b(of)n(fset)g(line)g(is)g(repeated)h(for)g(as)324 2630
y(man)o(y)24 b(of)n(fsets)h(as)h(there)g(are)g(thought)e(to)i(be)f(in)h
(the)f(time)g(series.)33 b(The)26 b(of)n(fsets)f(need)h(not)f(be)324
2750 y(in)c(chronological)f(order)h(nor)g(do)g(you)g(e)n(v)o(en)f(ha)n
(v)o(e)h(to)g(ensure)g(that)g(the)o(y)g(are)h(within)d(the)j(time)324
2871 y(span)27 b(of)h(the)f(data)h(set.)39 b(The)27 b(program)g(will)g
(sort)g(the)h(of)n(fsets)e(correctly)i(when)g(processing)324
2991 y(the)c(\002le.)324 3286 y Ff(2.2)119 b(\223psmsl\224)29
b(\002le)h(description)324 3454 y Fn(This)g(type)g(of)g(data)h(\002le)g
(is)f(again)g(v)o(ery)g(simplistic)e(and)j(is)f(described)g(on)g(the)h
(Permanent)324 3552 y(Service)37 b(for)g(Mean)f(Sea)h(Le)n(v)o(el)f
(web)g(site)g(\(http://www)-6 b(.pol.ac.uk/psmsl/datainfo\).)60
b(It)324 3650 y(basically)30 b(consists)f(of)i(one)g(tw)o(o)f(main)g
(columns.)47 b(Column)30 b(one)h(is)f(the)h(time)f(stamp)g(and)324
3748 y(column)c(tw)o(o)i(is)f(the)h(data.)39 b Fo(Cats)p
Fn(,)28 b(since)g(it)f(is)g(written)g(in)h(C,)g(is)f(not)g(so)h
(speci\002c)g(about)f(the)324 3846 y(e)o(xact)d(format,)g(it)h(just)e
(tries)i(to)f(read)h(3)f(columns)g(on)g(each)h(line.)31
b(If)25 b(there)f(are)i(tw)o(o)e(columns)324 3944 y(\(time)g(and)h
(data\))g(then)f(it)h(uses)f(that)g(epoch.)31 b(An)25
b(e)o(xample)f(of)h(a)g(data)g(\002le)g(is)f(gi)n(v)o(en)f(belo)n(w)-6
b(.)443 4106 y Fe(1964.625)79 b(7036)443 4185 y(1964.708)g(7103)443
4264 y(1964.792)g(7057)443 4342 y(1964.875)g(7139)443
4421 y(1964.958)g(7091)443 4500 y(1965.042)g(7072)443
4579 y(1965.125)g(6834)443 4658 y(1965.208)g(6935)443
4737 y(1965.292)g(6941)443 4816 y(1965.375)g(6920)443
4894 y(1965.458)g(7011)443 4973 y(1965.542)g(6974)39
b(12)1918 5251 y Fn(4)p eop
%%Page: 5 5
5 4 bop 443 548 a Fe(1965.625)79 b(7026)g(8)443 627 y(1965.708)g(7078)g
(3)443 706 y(1965.792)g(7078)g(3)443 785 y(1965.875)g(7075)443
863 y(1965.958)g(7115)443 942 y(1966.042)g(6990)443 1021
y(1966.125)g(7087)443 1100 y(1966.208)g(7005)470 1287
y Fn(As)29 b(for)g(the)g(\223cats\224)h(format,)f(this)g(\002le)g
(format)g(has)g(been)g(adapted)g(so)g(that)f(it)h(can)g(read)324
1407 y(in)24 b(of)n(fsets)g(and)h(ignore)f(lines)h(that)f(be)o(gin)g
(with)g(the)g Fh(#)i Fn(symbol.)324 1744 y Fp(3)143 b(Command)33
b(Line)i(Options)324 1952 y Fn(The)h(command)f(line)g(options)f(no)n(w)
h(come)h(in)f(tw)o(o)h(\223\003a)n(v)n(ours\224)g(depending)f(on)h
(whether)324 2050 y(your)21 b(machine)g(architecture)h(can)f(handle)g
(long)g(options)f(or)h(not.)29 b(In)22 b(the)f(follo)n(wing)e(section)
324 2148 y(the)i(long)g(options)g(will)f(be)i(described)g(with)f(the)h
(short)f(option)f(listed)h(in)g(brack)o(ets.)30 b(There)22
b(is)324 2246 y(a)j(slight)e(dif)n(ference)i(between)g(the)f(v)o
(ersion)g(that)g(can)h(accept)g(long)f(options)f(to)h(the)h(v)o(ersion)
324 2343 y(that)f(cannot.)31 b(The)24 b(long)g(option)g(v)o(ersion)g(w)
o(ould)g(look)g(something)f(lik)o(e)h(this)324 2489 y
Fe(cats)39 b(vyas.neu)g(--sinusoid)f(1y1)h(--verbose)g(--columns)f(4)i
(--output)f(vyas_all.mle)470 2634 y Fn(or)324 2779 y
Fe(cats)g(vyas.neu)g(--sinusoid=1y1)e(--verbose)i(--columns=4)f
(--output=vyas_all.mle)470 2924 y Fn(or)324 3069 y Fe(cats)h(vyas.neu)g
(-A)g(1y1)h(-V)f(-C4)h(-Ovyas_all.mle)470 3214 y Fn(It)33
b(can)g(ha)n(v)o(e)f(a)h(mixture)f(of)h(long)f(and)g(short.)54
b(If)33 b(using)f(long)g(options,)h(then)f(options)324
3312 y(with)20 b(additional)f(parameters)i(should)e(either)i(ha)n(v)o
(e)f(a)h(space)g(or)g(an)g(equal)f(sign)g(between)h(the)324
3410 y(option)j(and)i(the)f(parameter/s.)33 b(If)26 b(you)f(choose)g
(to)g(use)h(short)f(options)f(then)h(the)g(additional)324
3508 y(parameter)i(should)e(follo)n(w)g(on)h(from)g(the)g(option)f
(\(e.g.)36 b(-C4\))27 b(or)f(there)h(should)e(be)i(a)f(space)324
3606 y(between)38 b(\(e.g.)72 b(-C)39 b(4\).)71 b(F)o(or)38
b(the)g(v)o(ersion)f(that)h(only)g(accepts)g(short)g(options)f(then)h
(the)324 3703 y(options)23 b(should)h(al)o(w)o(ays)g(tak)o(e)h(the)g
(form)324 3848 y Fe(cats)39 b(vyas.neu)g(-A1y1)g(-V)g(-C4)h
(-Ovyas_all.mle)470 4035 y Fn(with)24 b(no)h(gaps)f(between)h(option)e
(and)i(the)g(additional)e(parameters.)324 4241 y Fo(--model)i(\(-M\))50
b Fn(A)30 b(description)f(of)h(the)g(stochastic)f(model.)45
b(The)30 b(\002rst)h(tw)o(o)e(characters)i(in)568 4361
y(the)25 b(string)g(indicate)h(the)f(type)h(of)g(stochastic)f(model)g
(to)g(use.)34 b(These)26 b(include)f Fo(pl)h Fn(for)568
4482 y(po)n(wer)n(-la)o(w)j(noise,)i Fo(gm)g Fn(for)f(\002rst-order)h
(gauss)e(mark)o(o)o(v)-6 b(,)31 b Fo(wh)f Fn(for)h(white)f(noise,)h
Fo(bp)568 4602 y Fn(for)d(band-pass)f(noise,)h Fo(vw)f
Fn(for)h(v)n(ariable)g(white)f(noise,)h Fo(gg)f Fn(for)h(generalised)g
(gauss-)568 4723 y(mark)o(o)o(v)-6 b(,)23 b(and)i Fo(sw)f
Fn(for)h(step-v)n(ariable)f(white)h(noise.)568 4882 y(F)o(or)i(the)g
(po)n(wer)n(-la)o(w)g(noise)f(model)h(you)g(can)g(\002x)h(the)f(model)f
(to)h(a)h(speci\002c)g(spectral)568 5002 y(inde)o(x)23
b(by)i(appending)f(an)h(additional)e(parameter)i(as)g(follo)n(ws)1918
5251 y(5)p eop
%%Page: 6 6
6 5 bop 568 548 a Fd(--model)58 b(pl:k-1)568 793 y Fn(The)32
b(abo)o(v)o(e)f(e)o(xample)g(w)o(ould)g(\002x)h(the)g(spectral)g(inde)o
(x)f(to)g(-1)h(\(\003ick)o(er)h(noise\).)52 b(If)32 b(a)568
913 y(spectral)23 b(inde)o(x)g(is)h(not)f(speci\002ed)h(then)f(the)h
(program)g(will)f(also)g(try)h(to)f(solv)o(e)g(for)h(the)568
1034 y(spectral)g(inde)o(x.)568 1196 y(F)o(or)e(the)g(\002rst-order)h
(gauss)e(mark)o(o)o(v)h(model)f(you)h(can)h(\002x)g(the)f(model)g(to)g
(a)g(speci\002c)h Fk(\014)568 1316 y Fn(\(roughly)d(equi)n(v)n(alent)g
(to)g(the)i(cross-o)o(v)o(er)e(frequenc)o(y\))h(by)g(appending)g(an)g
(additional)568 1436 y(parameter)k(as)g(follo)n(ws)568
1681 y Fd(--model)58 b(gm:b23.0)568 1926 y Fn(The)28
b(abo)o(v)o(e)g(e)o(xample)g(w)o(ould)f(\002x)i Fk(\014)34
b Fn(to)29 b(23.0.)41 b(If)29 b Fk(\014)34 b Fn(is)28
b(not)g(speci\002ed)h(then)f(the)h(pro-)568 2046 y(gram)24
b(will)g(also)h(try)f(to)h(solv)o(e)e(for)i Fk(\014)6
b Fn(.)568 2208 y(F)o(or)31 b(the)h(band-pass)g(model)f(there)h(are)g
(three)g(parameters)g Fk(f)2734 2223 y Fg(centr)r(al)2995
2208 y Fn(\(c\),)i(width)d(\(w\))568 2329 y(and)23 b(the)h(number)f(of)
h(poles)f(\(p\).)30 b(Y)-11 b(ou)23 b(can)i(\002x)e(an)o(y)h(of)f
(these)h(parameters)g(as)f(follo)n(ws)568 2574 y Fd(--model)58
b(bp:c1w1p1)568 2819 y Fn(The)43 b(band-pass)g(model)f(is)h(de\002ned)h
(slightly)d(dif)n(ferently)i(to)g(that)f(in)h Fl(Langbein)568
2939 y Fn([2004].)36 b(Instead)26 b(of)h(the)f(parameters)h
Fk(f)1979 2954 y Fg(l)2032 2939 y Fn(and)f Fk(f)2250
2954 y Fg(h)2322 2939 y Fn(to)g(de\002ne)h(the)g(limits)e(of)h(the)h
(pass-)568 3059 y(band,)34 b(we)f(use)g Fk(f)1184 3074
y Fg(c)1219 3059 y Fn(,)i(the)d(central)h(frequenc)o(y)-6
b(,)34 b(and)f Fk(w)s(idth)p Fn(,)i(the)d(width)g(of)h(the)g(pass-)568
3180 y(band.)d(The)25 b(tw)o(o)f(sets)h(of)g(parameters)f(are)i
(related)f(using)f(the)g(follo)n(wing)1751 3446 y Fk(f)1799
3461 y Fg(l)1908 3446 y Fh(=)2159 3378 y Fk(f)2207 3393
y Fg(c)p 2077 3423 248 4 v 2077 3514 a Fk(w)s(idth)3445
3446 y Fn(\(4\))1732 3617 y Fk(f)1780 3632 y Fg(h)1908
3617 y Fh(=)83 b Fk(f)2115 3632 y Fg(c)2150 3617 y Fk(w)s(idth)568
3982 y Fn(or)25 b(alternati)n(v)o(ely)1860 4223 y Fk(f)1908
4238 y Fg(c)2026 4223 y Fh(=)2184 4118 y Fc(q)p 2268
4118 167 4 v 2268 4223 a Fk(f)2316 4238 y Fg(h)2360 4223
y Fk(f)2408 4238 y Fg(l)3445 4223 y Fn(\(5\))1695 4458
y Fk(w)s(idth)83 b Fh(=)2184 4304 y Fc(s)p 2268 4304
113 4 v 2287 4391 a Fk(f)2335 4406 y Fg(l)p 2278 4435
93 4 v 2278 4527 a Fk(f)2326 4542 y Fg(h)568 4865 y Fn(The)27
b(v)n(ariable)h(white)f(noise)g(model)g(uses)h(the)f(formal)h(errors)g
(recorded)h(in)e(the)h(data)568 4985 y(\002le)35 b(\(only)f(for)i(the)e
Fo(cats)h Fn(\002les\))h(and)f(solv)o(es)e(for)j(a)f(scale)g(parameter)
g(\(as)h(opposed)1918 5251 y(6)p eop
%%Page: 7 7
7 6 bop 568 548 a Fn(to)27 b(a)i(noise)e(amplitude)g(for)h(white)g
(noise\).)40 b(The)28 b(are)h(no)f(other)g(parameters)g(for)h(this)568
668 y(model.)568 829 y(The)19 b(generalised-gauss-mark)o(o)o(v)d(model)
i(is)h(described)f(in)h Fl(Langbein)f Fn([2004].)28 b(There)568
949 y(are)34 b(tw)o(o)g(parameters)f(for)i(this)d(model,)k(equi)n(v)n
(alent)31 b(to)j(the)g(spectral)f(inde)o(x)g(of)h(the)568
1070 y(po)n(wer)n(-la)o(w)f(noise)h(model)f(and)i Fk(\014)40
b Fn(for)34 b(the)h(FOGM)f(noise)g(model.)58 b(As)34
b(for)h(abo)o(v)o(e)568 1190 y(you)24 b(can)h(\002x)g(these)g
(parameters)g(as)g(follo)n(ws)568 1425 y Fd(--model)58
b(gg:b23.0k-1)568 1661 y Fn(The)32 b(equation)f(for)h(the)f(po)n(wer)h
(spectrum)f(in)g Fl(Langbein)h Fn([2004])f(\(equation)g(16\))h(is)568
1781 y(incorrect)25 b(and)f(tak)o(es)h(the)g(form)1522
2052 y Fk(P)41 b Fh(=)28 b Fk(P)1793 2067 y Fi(0)1849
1906 y Fc( )1915 2052 y Fh(\()1966 1985 y Fk(\014)p 1963
2029 66 4 v 1963 2121 a(S)2038 2052 y Fh(\))2076 2011
y Fi(2)2138 2052 y Fh(+)22 b(4)p Fk(\031)2344 2011 y
Fi(2)2383 2052 y Fk(f)2442 2011 y Fi(2)2481 1906 y Fc(!)2557
1902 y Fb(\024)p 2557 1914 37 4 v 2560 1955 a Fa(2)3445
2052 y Fn(\(6\))568 2318 y(T)-8 b(o)23 b(scale)g(these)g(equations)f
(so)h(that)f(the)o(y)h(match)f(the)h(po)n(wer)n(-la)o(w)f(only)h(po)n
(wer)f(spec-)568 2439 y(trum)i(and)h(the)f(First-Order)h(Gauss)g(Mark)o
(o)o(v)f(po)n(wer)g(spectrum)g(we)h(ha)n(v)o(e)1429 2730
y Fk(P)41 b Fh(=)1646 2663 y(2)p Fk(\033)1750 2678 y
Fi(2)1790 2663 y Fk(S)1866 2599 y Fb(\024)p 1866 2611
V 1869 2652 a Fa(2)p 1646 2707 270 4 v 1677 2826 a Fk(f)1745
2739 y Fb(\024)p 1745 2751 37 4 v 1748 2792 a Fa(2)1791
2766 y Fi([phone] y Fg(s)1943 2584 y Fc( )2008 2730
y Fh(\()2059 2663 y Fk(\014)p 2056 2707 66 4 v 2056 2799
a(S)2132 2730 y Fh(\))2170 2689 y Fi(2)2231 2730 y Fh(+)22
b(4)p Fk(\031)2437 2689 y Fi(2)2477 2730 y Fk(f)2536