带噪声的叠加指数信号的EVLP估计的渐近性质(英文)

ASYMPTOTIC PROPERTIES OF THE EVLP ESTIMATION FOR SUPERIMPOSED EXPONENTIAL SIGNALS IN NOISE

本文研究了如下的带噪声中的指数信号模型 Y_j(t)=∑a(kj)λ_k^j+e_j(t) t=0,1,…,n-1,j=1,2,…,N k=1 其中λ_1,λ_2,…,λ_q是未知的模为1的复参数,λ_(q+1),…,λ_p是未知的模小于1的复参数。并假设λ_1,λ_2,…,λ_p不相同,p已知,q未知,a_(kj)(k=1,p,j=1,N)为未知的复参数。e_j(t)(t=0,n-1,j=1,N)为独立同分布的复随机噪声变量,且有其中δ~2未知, Ee_1(0)=0,E|e_1(0)|~2=δ~2 0<δ~2<∞,E|e_1(0)|~4<∞ 本文给出了 1.q的强相合估计、 2.λ_1,λ_2,…,λ_q,δ~2及|a_(kj)|(k≤q)的强相合估计; 3.上述某些估计的极限分布; 4.λ_k及a_(kj)(k>q)不存在相合估计的证明; 5.N→∞情形的讨论。

This paper studies the model of superimposed exponential sigdals in noise: whereλ1, …λq are unknown complex parameters with module 1, λq+1,…, λq. are unknown complex parameters with module 1, λq+1…, λp are unknown complex parameters with module less than 1, λ1,…λq are assumed distinct, p assumed known and g unknown. aky k=1,…p, j=1, …, N are unknown complex parameters. ey(t),t=0,l ,…, n-1,j=1,…, N, are i.i.d. complex random noise variables such that and σ2 is unknown. This paper gives: 1 . A strong consistent estimate of q; 2. Strong consistent estimates of λ1,…,λq, oooooo2 and |aky|,k<q; 3. Limiting distributions for some of these estimates; 4. A proof of non-existence of consistent estimates for λk and aky k>q. 5. Adiscussion of the case that N→∞