need step by step solution not in code

1. Considet the problem of estimating the amplitude (A) and phase () of a single harmonic signal from samples of the signal that are contaminated by aero mean, 2 variance Gaussian noise: s(t)=Acos(et+)+E(t) Collected data points are the values of this signal at given points in time: s(0),s(2),,s(N 1). Use the theory of maximum likelihood to find best possible estimations for the amplitude and phase using the collected data. Can you compute our level of uncertainty for each estimation? Hint: First use the identity cos(a+b)=cos(a)cos(b)sin(a)sin(b) to flip this problem tor s(t)=Acos(0t)+Bsin(0t)+(t). At this point you can transform your problem to: s(0)s(N1)=1cos((N1)0)0sin((N1)0)[AB]+r(0)(N1) Now, find your best estimations for A and B and the variance of each one as a function of the noise variance. From there, compute the best estimations for A and . Finding the variances of the amplitude and phase from the variances of A and B is a bit more complicated. Howevec, if you are interested, you may find the following approximation useful: - If X and Y are two random variables, then: 1. Derivation of the Kalman filter with correlated process and measurement nolse: Consider the linear dynamical system formulated by: x(n+1)y(n)=Ax(n)+y(n)=Cx(n)+(n) And we know that: E[x(0)]=x0,E[(n)]=E[(n)]=0,E[(x(0)x0)(x(0)x0)7]=P0 ,E[(x(0)x0)(r(n))T]=0,E[(x(0)x0)(c(n))T]=0, vet: E{[r(i)(f)]r(j)Tc(j)T}=[WSTSV](ij) Prove that the Kaiman filer for this case can be formulated by: xn;n=Axnn=1+K(n)[y(n)Cxn1] K(n)=[AM(n)CT+S][CM(n)CT+V]1M(n+1)=AM(n)AT+W[AM(n)CT+S][CM(n)CT+V]1[CM(n)AT+S] Aal condition: M(0)=Pa