Devices, methods, and programs for monitoring electrical devices. A method for monitoring an electrical device may include obtaining data representing a sum of electrical signals of electrical devices; processing the data with a Factorial Hidden Markov Model (FHMM) to produce an estimate of an electrical signal of a first of the electrical devices; and outputting the estimate of the electrical signal of the first electrical device. The FHMM may have a factor corresponding to the first electrical device. The factor may have three or more states.
Please help me write a proper abstract based on the patent claims. CLAIM: 1-36. (canceled) 37. A method for monitoring an electrical device, comprising: obtaining data representing a sum of electrical signals of two or more electrical devices, the two or more electrical devices including a first electrical device; processing the data with a Factorial Hidden Markov Model (FHMM) to produce an estimate of an electrical signal of the first electrical device; and outputting the estimate of the electrical signal of the first electrical device, wherein the FHMM has a factor corresponding to the first electrical device, the factor having three or more states. 38. The method of claim 37, wherein: the three or more states of the factor correspond to three or more respective electrical signals of the first electrical device in three or more respective operating states of the first electrical device. 39. The method of claim 37, further comprising obtaining one or more parameters of the FHMM from a model storage unit. 40. The method of claim 37, wherein the data comprises a time series of current values and/or a time series of voltage values. 41. The method of claim 37, wherein the electrical signal is a current signal or a power signal. 42. The method of claim 37, further comprising: calculating a variance of the data representing the sum of the electrical signals; and using the calculated variance as a parameter of the FHMM. 43. The method of claim 37, wherein: the FHMM has a second factor corresponding to a second electrical device of the two or more electrical devices; and the method further comprises: processing the data with the FHMM to produce a second estimate of a second electrical signal of the second electrical device; calculating a first individual variance of the estimate of the electrical signal of the first electrical device, and using the first individual variance as a parameter of the factor corresponding to the first electrical device; and calculating a second individual variance of the second estimate of the second electrical signal of the second electrical device, and using the second individual variance as a parameter of the second factor corresponding to the second electrical device. 44. The method of claim 37, further comprising: restricting the FHMM such that a number of factors of the FHMM which undergo state transition at a same time point is less than a threshold number. 45. The method of claim 37, further comprising imposing a restriction on the estimate of the electrical signal of the first electrical device. 46. The method of claim 45, wherein: the electrical signal is a power signal; and imposing the restriction comprises restricting the estimate of the power signal of the first electrical device to have a nonnegative value. 47. The method of claim 45, wherein imposing the restriction comprises restricting the electrical signal to correspond to one or more combinations of a plurality of predetermined base electrical signals. 48. The method of claim 37, wherein processing the data with the Factorial Hidden Markov Model (FHMM) comprises using cloud computing to process at least a portion of the data. 49. The method of claim 37, wherein outputting the estimate of the electrical signal comprises displaying the estimate of the electrical signal. 50. The method of claim 37, wherein outputting the estimate of the electrical signal comprises transmitting the estimate of the electrical system to a remote computer. 51. The method of claim 37, wherein the estimate of the electrical signal is an estimate of a voltage signal. 52. The method of claim 37, wherein the method is performed by a smart meter. 53. A monitoring apparatus, comprising: a data acquisition unit for obtaining data representing a sum of electrical signals of two or more electrical devices, the two or more electrical devices including a first electrical device; a state estimation unit for processing the data with a Factorial Hidden Markov Model (FHMM) to produce an estimate of an operating state of the first electrical device, the FHMM having a factor corresponding to the first electrical device, the factor having three or more states; and a data output unit for outputting an estimate of an electrical signal of the first electrical device, the estimate of the electrical signal being based at least in part on the estimate of the operating state of the first electrical device. 54. The monitoring apparatus of claim 53, further comprising: a model storage unit for storing the factor of the FHMM, wherein the three or more states of the factor correspond to three or more respective waveforms of the first electrical device. 55. The monitoring apparatus of claim 53, further comprising a model storage unit for storing one or more parameters of the FHMM. 56. The monitoring apparatus of claim 53, wherein the data comprises a time series of current values and/or a time series of voltage values. 57. The monitoring apparatus of claim 53, wherein the estimate of the electrical signal is an estimate of a current signal or a power signal. 58. The monitoring apparatus of claim 53, further comprising a model learning unit for updating a parameter of the FHMM, wherein updating the parameter of the FHMM includes: calculating a variance of the data representing the sum of the electrical signals, and using the calculated variance as the parameter. 59. The monitoring apparatus of claim 53, further comprising a model learning unit for updating one or more parameters of the FHMM, wherein: the state estimation unit is for processing the data with the FHMM to produce a second estimate of a second electrical signal of a second of the two or more electrical devices, the FHMM having a second factor corresponding to the second electrical device; and updating the one or more parameters of the FHMM includes: calculating a first individual variance of the estimate of the electrical signal of the first electrical device, and using the first individual variance as a parameter of the factor corresponding to the first electrical device; and calculating a second individual variance of the second estimate of the second electrical signal of the second electrical device, and using the second individual variance as a parameter of the second factor corresponding to the second electrical device. 60. The monitoring apparatus of claim 53, wherein processing the data comprises restricting the FHMM such that a number of factors of the FHMM which undergo state transition at a same time point is less than a threshold number. 61. The monitoring apparatus of claim 53, wherein processing the data comprises imposing a restriction on the estimate of the electrical signal of the first electrical device. 62. The monitoring apparatus of claim 61, wherein: the electrical signal is a power signal; and imposing the restriction comprises restricting the estimate of the power signal of the first electrical device to have a nonnegative value. 63. The monitoring apparatus of claim 61, wherein imposing the restriction comprises restricting the electrical signal to correspond to one or more combinations of a plurality of predetermined base electrical signals. 64. The monitoring apparatus of claim 53, wherein processing the data with the Factorial Hidden Markov Model (FHMM) comprises using cloud computing to process at least a portion of the data. 65. The monitoring apparatus of claim 53, wherein outputting the estimate of the electrical signal comprises displaying the estimate of the electrical signal. 66. The monitoring apparatus of claim 53, further comprising a communication unit, wherein outputting the estimate of the electrical signal comprises transmitting the estimate of the electrical system to a remote computer. 67. The monitoring apparatus of claim 53, wherein the estimate of the electrical signal is an estimate of a voltage signal. 68. The monitoring apparatus of claim 53, wherein the monitoring apparatus is a smart meter. 69. A monitoring apparatus, comprising: a data acquisition unit for obtaining data representing a sum of electrical signals of two or more electrical devices, the two or more electrical devices including a first electrical device; a state estimation unit for processing the data with a Factorial Hidden Markov Model (FHMM) to produce an estimate of an operating state of the first electrical device, the FHMM having a factor corresponding to the first electrical device, the factor having three or more states; a model learning unit for updating one or more parameters of the FHMM, wherein updating the one or more parameters of the FHMM comprises performing restricted waveform separation learning; and a data output unit for outputting an estimate of an electrical signal of the first electrical device, the estimate of the electrical signal being based at least in part on the estimate of the operating state of the first electrical device. 70. The monitoring apparatus of claim 69, wherein performing restricted waveform separation learning comprises imposing a restriction distinctive to the first electrical device on a value of a corresponding parameter of the FHMM. 71. The monitoring apparatus of claim 70, wherein the restriction comprises a load restriction. 72. The monitoring apparatus of claim 70, wherein the restriction comprises a base waveform restriction.